What is time anyway?

[Ken G]

Many people use phrases like "seeing into the past" when talking about looking at distant objects, without recognizing that such language implies the existence of an absolute and unique time scale that we have known for a century does not exist. A key distinction to make to understand this is the difference between time as a coordinate, and time as an actual physical thing or process. The latter is known in relativity to be the concept of proper time, which is the time registered on a clock. "Looking back in time" when seeing some distant star is not that kind of time, it is actually just coordinate time-- which has a very nonunique and arbitrary contextual convenience associated with it. In my opinion, recognizing the difference between proper time and coordinate time should come well before anyone is even exposed to more intricate details like time dilation and the relativity of simultaneity, and the fact that this rarely actually occurs is why so few people really understand those latter topics.

But before we get into all that, let me give you two examples of how commonly used coordinate times can give two rather different meanings to how "far back in the past" we are seeing distant objects:
1) The Einstein simultaneity convention in special relativity: the simplest example of this is when you observe a distant object with no relative velocity to you, and then you associate your "now" with a time at that distant object that would be reached by a time signal from the central point between you and it, at the same time that you yourself receive that same signal.
2) The cosmological principle: here we associate our "now" with distant points that have the same age as us (13.7 billion years after the Big Bang).
Questions to the reader to get you started in understanding the arbitrariness of coordinate time:
A) Do #1 and #2 associate our "now" the same way to distant events?
B) Which would be relevant to a distant star in our galaxy? To a different galaxy? Is there a smooth transition of some kind, and why?
C) If the universe did not obey the cosmological principle, which it easily could not have, then what would we use to associate our "now" with cosmologically distant events?
Give special attention to C-- for those of you who think that "seeing into the past" really means something when applied to other objects that do not share the past of your own "world line" through spacetime, what is your answer to C?

[caveman1917]

Ok i'll have a go

A) Do #1 and #2 associate our "now" the same way to distant events?

My guess would be no. In #1 from the moment we have both received this light signal we are synchronized. No relative velocity essentially means same frame of reference, so we are connected 'forever'. After one year has passed with us, one year has passed over there. So in this situation we might say we actually do 'look back in the past'. Not taking into account differential local gravity fields.

#2 associates our "now" with some other point, however both its past and future may take totally different ways relative to us. Hence no "looking in the past".

B) Which would be relevant to a distant star in our galaxy? To a different galaxy? Is there a smooth transition of some kind, and why?

If by 'relevant' you mean the one we can most accurately say 'looking back in time', that would be #1.
I don't understand what you mean by "smooth transition".

C) If the universe did not obey the cosmological principle, which it easily could not have, then what would we use to associate our "now" with cosmologically distant events?
Give special attention to C-- for those of you who think that "seeing into the past" really means something when applied to other objects that do not share the past of your own "world line" through spacetime, what is your answer to C?

I don't really understand this question either. I guess we would simply associate our "now" with this distant event by saying it happened "now" if its light just reached us "now". But this seems a bit too obvious to be an answer.

[Ken G]

My guess would be no. In #1 from the moment we have both received this light signal we are synchronized. No relative velocity essentially means same frame of reference, so we are connected 'forever'. After one year has passed with us, one year has passed over there. So in this situation we might say we actually do 'look back in the past'. Not taking into account differential local gravity fields.

Even in the absence of gravity, a universe that was expanding and exhibited a cosmological principle could still have the two given senses of "now" between different places, and they would not be the same in approach #1 and approach #2. Hence the distinction is not just about gravity (though you are right gravity changes the situation in additional ways that complicate matters further). The bottom line is, there is simply no unique way to talk about "seeing the past" unless you are talking about the past along a single world line, which is another way of saying that the scenarios I gave are not referring to proper times.

#2 associates our "now" with some other point, however both its past and future may take totally different ways relative to us. Hence no "looking in the past".

Yet the cosmological sense of looking into the past, in concert with the cosmological principle, is actually quite a bit more meaningful than looking into the past of some planet whose timeline is completely independent of our own. However, that cosmological sense of looking into the past is heavily reliant on the cosmological principle, rather than some physical law. The point I must stress is that physical law singles out only one type of looking into the past-- the past along a single world line.

If by 'relevant' you mean the one we can most accurately say 'looking back in time', that would be #1.
I don't understand what you mean by "smooth transition".

You talked about a case where gravity doesn't matter, and one where it does-- what is the line you are drawing? Is there not actually a smooth transition there-- and how do you navigate it if you cannot use either #1 or #2 to do so?

I don't really understand this question either. I guess we would simply associate our "now" with this distant event by saying it happened "now" if its light just reached us "now". But this seems a bit too obvious to be an answer.

That is yet a third way to do it-- not used generally, but no less valid than the others. That's the point-- how we associate nows is purely a matter of convention, and convenience. It is not a physical truth.

[EDG]

2) The cosmological principle: here we associate our "now" with distant points that have the same age as us (13.7 billion years after the Big Bang).

How do we know they have the same age as us?

[Ken G]

How do we know they have the same age as us?

As I said, that concept relies on the cosmological principle, which means a given region has the same as we do (13.7 billion years) when it has had the same basic sequence of events that we have, and is immersed in the same CMB that we are. The key point there is that this is highly reliant on the cosmological principle, which is not a physical law, it is just the way things happen to be in our universe. One could easily imagine all the same laws of physics, but no cosmological principle-- and then there'd be no way to attribute a coherent concept of "now" between two cosmologically separated events. Which is my point about what time means-- and what it does not mean.

[EDG]

OK, but then how do we know a given region has had "the same basic sequence of events that we have" (whatever that means) and "is immersed in the same CMB that we are"?

All we have to go on are our own observations of that region, and because of lightspeed travel time we're seeing them at a time that isn't "now" according to us. Something seems a bit circular here.

[Ken G]

OK, but then how do we know a given region has had "the same basic sequence of events that we have" (whatever that means) and "is immersed in the same CMB that we are"?

It is simply that we adopt the cosmological principle, and that's what that principle asserts. When do we know a principle is correct? Never, of course. We adopt principles as long as they serve us to do so, and often continue to adopt them in various situations even after we know they have limitations.

All we have to go on are our own observations of that region, and because of lightspeed travel time we're seeing them at a time that isn't "now" according to us. Something seems a bit circular here.

What you refer to as "circularity" is in fact "self-consistency", the core principle of scientific thinking. But these are larger issues about what science is, let's stick to what time is.

[EDG]

So the cosmological principle is just an assertion, for which there is no actual evidence? So what if it is actually incorrect?

[Jens]

Many people use phrases like "seeing into the past" when talking about looking at distant objects, without recognizing that such language implies the existence of an absolute and unique time scale that we have known for a century does not exist.

Fundamentally I think you're right, but it seems to me a fairly normal convention (no more than a convention, though) to use the term "now" to refer to the time when something is happening on a star 10 light years away that will appear to us in 10 years when the light arrives. I think you are getting at something deeper, but this issue sometimes comes up in popular literature on astronomy. People sometimes write "Betelgeuse may be about to explode," but what they really mean in that case is that it about to explode at the time when the light that is arriving at us today left, which you might call "640 years ago" but that would be a convention as well. Doing it in a way that may be more rationale, "The light reaching us from Betelgeuse may soon give us evidence of an explosion that took or will take place at some arbitrary time" is very awkward.

Defining time in a distant place either as "the time when the events took place whose light is reaching us now" or "the time when the light that was emitted will reach us in the number of years that is the same as the distance in light years from that place" (my personal preference) seem fairly reasonable.

You can get into some strange language if you don't accept some conventions. Imagine getting on the phone and asking no, "what are you doing now?" but "what will you be doing when the sound of this question reaches you?"

[Strange]

2) The cosmological principle: here we associate our "now" with distant points that have the same age as us (13.7 billion years after the Big Bang).

I share EDG's problem: how do we identify a distant point that has the same age as us? Or does this simply mean that there are other locations which have the same age as us (a purely existential [if thats the right word in this context] argument) even if we can't specifically identify them?

And with our current understanding of the universe, why wouldn't you say that everywhere is the same age as us?

[Jens]

And with our current understanding of the universe, why wouldn't you say that everywhere is the same age as us?

I don't have a good answer, but I'm perplexed by the idea. In relativity, time seems slowed in an accelerating frame. So if there is an asteroid 2 million km from us, and we launch a rocket that is accelerating, at the moment the rocket passes the asteroid the clocks will be different. So are they of different ages? Is the age of the "space time" different from the age of the matter that is passing through it?

[Ken G]

So the cosmological principle is just an assertion, for which there is no actual evidence?

It's not just an assertion, but it is underconstrained by observation. This is not unusual in science-- the law of conservation of energy is also underconstrained by observation. All we can say is that it we encounter no devastating inconsistencies by asserting either, though we know we do encounter minor problems (the cosmological principle loses its meaning on smaller scales, the conservation of energy loses its meaning on very short timescales). The connection between evidence, and principles of science, is that we have evidence the principle will serve us to invoke, and so it is with the cosmological principle.

So what if it is actually incorrect?

It is actually incorrect, that's part of what I'm saying in this thread. The concept of "seeing into the past" that we get cosmologically relies on a principle that is not formally correct, but may well be correct to a good approximation on large enough scales, and appears to serve us quite well as things have turned out in our universe.

[Ken G]

Fundamentally I think you're right, but it seems to me a fairly normal convention (no more than a convention, though) to use the term "now" to refer to the time when something is happening on a star 10 light years away that will appear to us in 10 years when the light arrives.

Right, I'm distinguishing what is true by convention (like, say, that an electron has a negative charge) from what is true by physical reality (like the charge of the electron is opposite the proton). This distinction is often not made, so people think they are in some sense really seeing the past, when they look at a distant object, when in fact they are seeing some time on that object that some coordinate system they themselves chose claims is "in the past" there. That is really something rather different, and not understanding that difference leads to ill-posed questions, a rash of which we have recently seen in Q&A.

I think you are getting at something deeper, but this issue sometimes comes up in popular literature on astronomy. People sometimes write "Betelgeuse may be about to explode," but what they really mean in that case is that it about to explode at the time when the light that is arriving at us today left, which you might call "640 years ago" but that would be a convention as well. Doing it in a way that may be more rationale, "The light reaching us from Betelgeuse may soon give us evidence of an explosion that took or will take place at some arbitrary time" is very awkward.

Then we should seek language that is neither awkward nor incorrect nor implying truths that are mere conventions. We could, for example, just say that "we may, within the next few decades, see Betelgeuse explode." (I'm not claiming this is true, by the way.) My point here is, this way of talking about time is clear that we are talking about our own time, which is also what is called proper time (from the French "propre") and has a clear meaning, rather than invoking some confused, nonunique, and somewhat arbitrary combination of our time and Betelgeuse's time.

Defining time in a distant place either as "the time when the events took place whose light is reaching us now" or "the time when the light that was emitted will reach us in the number of years that is the same as the distance in light years from that place" (my personal preference) seem fairly reasonable.

Except that isn't what we do in cosmology, so it is contextually and convenience based-- and that's all I'm saying, it's not a physical truth, it is a matter of convenient coordinatization. Our language about it should recognize that, or we instill misconceptions. Also, I'm saying it's not that hard to do this while still avoiding awkward language-- we simply use time the way it was meant to be used, it is our time we are talking about, not a combination of our time and the object's. Since it has been known for 100 years that time is not absolute but rather is "owned" by a clock, is it so hard for us to use language that recognizes this, thereby becoming part of the solution instead of part of the problem of rampant misuse of the physical meaning of time?

You can get into some strange language if you don't accept some conventions. Imagine getting on the phone and asking no, "what are you doing now?" but "what will you be doing when the sound of this question reaches you?"

That is only because the context you cite doesn't need to make the distinction. In one where the distinction is needed, you darn well better specify that difference. So when someone asks a question on Q&A, they need to specify that context of convenience, or at least recognize it exists if it is implicit, or else it sounds like they think they are talking about nature rather than the conveniences of coordinates.

The bottom line is, a time measured on a single clock is a "real" time, or a "proper" time, but times that cannot be measured on a single clock (like when "looking into the past" of some distant object) are coordinate times and are based on some implied or implicit choices of convenience, not on nature herself. The physical meaning of time is not shared by distant objects like that, that's the concept that should have gone out the window with Newton's absolute time.

[Ken G]

I share EDG's problem: how do we identify a distant point that has the same age as us?

It requires a complete cosmological model, one solving the equations of general relativity and the cosmological principle. It is simply not a model-independent concept, which is part of my whole point here.

Or does this simply mean that there are other locations which have the same age as us (a purely existential [if thats the right word in this context] argument) even if we can't specifically identify them?

There would seem to be a meaningful way to talk about the age of distant regions, we simply imagine special hypothetical clocks that have existed since the very early times and have the average movement of the matter around them (on large scales). Then the reading of that clock is a proper time, and gives the age of the universe at that location at that time in question. So the basic concept seems well posed, but how we can figure out what that age is for any given distant region we are seeing then requires a model to apply to our observations. The model cannot be established as true, but we can ask it to be consistent with our observations, so that we have a model that serves us even if it is underconstrained (it requires assumptions like the cosmological principle and the applicability of the various local laws of physics, and so on). It's not a bug of physics that its principles are underconstrained, it is a feature-- the only thing that not underconstrained is all of reality itself.

And with our current understanding of the universe, why wouldn't you say that everywhere is the same age as us?

I wouldn't say that every person on the planet is the same age as me, I would say that every person who lives to an old age was at some time the same age that I am now. The universe is just out there, and has all kinds of times and ages associated with it-- there's no particular reason to think that the age I now perceive (13.7 billion years) somehow picks out a special time for the rest of a universe that is completely ambivalent to the significance of that particular age. This is all consistent with relativity's most fundamental lesson about the physical meaning of time-- it is something that is owned by each clock, and does not have an absolute or universal meaning. Why, 100 years later, do we still not embrace this truth?

[Strange]

Right, I'm distinguishing what is true by convention (like, say, that an electron has a negative charge) from what is true by physical reality (like the charge of the electron is opposite the proton).

This is a useful analogy. But, I'm afraid, I'm still not 100% sure what the equivalent distinction is when it comes to time.

In the case of electron charge, we have two cases:

(A) We make an arbitrary choice of one value from an arbitrary pair (they could have been called anything, as in quark "color" charge).

(B) There is also an "absolute" (real) value which can only be expressed in relative terms (the opposite of the proton).

So for time, what I think you are saying is that we can create an arbitrary notion of a universal "now" based, for instance, on the time it takes light to reach us from distant objects. Other conventions are available. This is the equivalent of (A) above.

I'm not quite sure what the equivalent of (B) is, with regard to time. Is it simply that the only "absolute" (real) time we can have is our own proper[*] time? Everything else (the time at a distant galaxy, for example) can only be defined as a convention (case A).

This distinction is often not made, so people think they are in some sense really seeing the past, when they look at a distant object, when in fact they are seeing some time on that object that some coordinate system they themselves chose claims is "in the past" there.

But, presumably, the other thing we can always say is that a distant event happened before we see it (finite speed of light, an all that). However the precise meaning of "before" varies with the chosen convention. Am I getting close?

[*] I assume that "our own proper time" is a tautology with this meaning of "proper" (related to property rather than correctness).

[Ken G]

So for time, what I think you are saying is that we can create an arbitrary notion of a universal "now" based, for instance, on the time it takes light to reach us from distant objects. Other conventions are available. This is the equivalent of (A) above.

Right, and I'm also saying that the choice can be different in different contexts of convenience (like the way engineers take the sign of current to be opposite the sign of charge).

I'm not quite sure what the equivalent of (B) is, with regard to time.

I would say there really isn't any choice B within science-- choice B makes assertions that are fundamentally outside the ability of science to establish. No difference between A and B could ever be established, so there is, in effect, no such thing as choice B, with regard to time or charge or anything.

Is it simply that the only "absolute" (real) time we can have is our own proper[*] time? Everything else (the time at a distant galaxy, for example) can only be defined as a convention (case A).

Bingo, that is exactly the purpose of this thread.

But, presumably, the other thing we can always say is that a distant event happened before we see it (finite speed of light, an all that). However the precise meaning of "before" varies with the chosen convention.

Yes, you are correct that there is something else going on here, relating to the concept of "before", without specifying exactly how much before. That "other thing" has to do with the concept of causality, which is what things could ever be influences on other things. Whatever our conventions about times in different places, they must preserve which is the cause and which is the effect, or we lose something very important to the basic structure of physics.

[Strange]

Yes, you are correct that there is something else going on here, relating to the concept of "before", without specifying exactly how much before. That "other thing" has to do with the concept of causality, which is what things could ever be influences on other things. Whatever our conventions about times in different places, they must preserve which is the cause and which is the effect, or we lose something very important to the basic structure of physics.

Ah, and does this lead on to all that stuff about light cones, etc. Which I have all but forgotten about. (it was in the distant past, after all )

[uncommonsense]

While it may at first sound rather overly fundamental, we humans seem to share the intuition that the faster we move, the less time it takes to get to where we are going. But we rarely consider distance as a possible variable. In other words, if the location, say, a store, you want to go to is one mile away from your home, you know you will get there in less time by moving faster in a car than you would if you walked: BUT, we never consider that moving faster may shorten the distance between your home and the store, and maybe this is why it takes less time to get there.

It is interesting to consider the above scenario at ever increasing speeds. Since our daily life experience is limited to the speed of our cars, our imaginations stop there; but imagine speeds that are fractions of C. Then, as scientists, we can imagine that our speed of travel acually shortens the distance. So, we too can imagine that the reason the trip took less time (than walking) was because our increased velocity "shortened" the distance - and therefore the trip took less time (than walking).

So, as for the modern uses of "time", perhaps we could imagine the universe in terms of velocity dependant distance, even at a local everyday level (as in the scenario). In the above scenario, in 3 dimensionsal space - if I am sitting in my home, then the store and I have 0 relative velocity - and so my time to get to the store is infinite.

However, as I move at some velocity towards store, the distance along my axis of travel shortens, more so the higher and higher my velocity. Therefore, although I don't "see" it, my velocity has "distorted" the formerly symetrical 3 dimensional space - and - if I were to achieve velocity c, there would no longer be any distance between me and the store, and my universe would be 2 dimensional - therefore I would no longer experience or interact with the world as I did before, nor would my former 3 dimensional world be able to have the same 3 dimensional relationship with, or understanding, of me.

The above scenario is meant to help imagine some hard to imagine dichotomies in science, ex, we can experience starlight from a star that we measure as being 4 light years away, but the light from the star does not experience a 4 year trip. - perhaps because we and the starlight exist in different dimensional space - and we should take a closer look at velocity dependent distance when examining the universe.


The above is simply attempting to address to OP by encouraging a different look at "time", and what it is anyway.

[Ken G]

The above is simply attempting to address to OP by encouraging a different look at "time", and what it is anyway.

What isn't clear if you are suggesting a "velocity dependent distance" that is different from the version of that we already have in relativity-- length contraction. It doesn't really show up in everyday travel, though, only very fast speeds. Are you suggesting that velocity-dependent distances be generalized in some way beyond what happens with the Lorentz transformation? That would probably require a different definition of velocity, because the time a journey takes is measurable (that's a proper time that we can use a clock for), and we want the velocity times the proper time to be the distance reckoned by that observer. In other words, with a normal definition of velocity, the "velocity-dependent distance" is the product of the velocity and the time of the journey. But you could play with the definition of distance to get a new meaning for velocity, and perhaps come up with one where even everyday distances vary with velocity. I'm not sure what is gained though.

[uncommonsense]

What isn't clear if you are suggesting a "velocity dependent distance" that is different from the version of that we already have in relativity-- length contraction

Yes, same thing.

.......... But you could play with the definition of distance to get a new meaning for velocity, and perhaps come up with one where even everyday distances vary with velocity. I'm not sure what is gained though.

Perspective, perhaps. I am simply imagining several ideas about time I have posted in other threads. Ex., I have stated elsewhere that without motion, there can be no measurement of time - just as in my scenario in this thread, if there is no relative motion between me and the store, then there is no measurable time for me to travel the distance to the store (yes, that is overly obvious) - but it helps make it clearer that:

as time is dependent on motion (velocity), and c is the cap on velocity, and since 0 relative motion between objects will require an infinite amount of time for one of them to span the distance between them, yet at maximum known velocity of c, light requires 0 time or distance to travel between objects, then it seems distance must vary dependent on velocity at all speeds between 0 and c.

Yes, a bit of word salad, but it is simply meant to consider whether our time-centric view of the universe should be reexamined as a distance, motion, velocity centric universe, both astronomy and at the subatomic level, so that we might make better use, understanding, and application of the ratio we call "time".

We may not notice length contraction in our conventional daily lives, but, unless I am wrong, it is still there.

No new ideas here, just consideration to reexamine the obvious.

[Ken G]

as time is dependent on motion (velocity), and c is the cap on velocity, and since 0 relative motion between objects will require an infinite amount of time for one of them to span the distance between them, yet at maximum known velocity of c, light requires 0 time or distance to travel between objects, then it seems distance must vary dependent on velocity at all speeds between 0 and c.

Yes, that shows the requirement of relativity that we must have length contraction.

We may not notice length contraction in our conventional daily lives, but, unless I am wrong, it is still there.

Yes, it's there.

[caveman1917]

But then we must also say there is simply no actual time (relative to us). Even proper time is only defined relative to a specific frame. However, any physical construct which is large enough to contain something capable of creating "conventions" (ie humans,AI,...) cannot have its constituent parts be in the same reference frame, strictly speaking (P). At the very least mutual gravity will mess it up.
As such one could say there is a continuum in a variable d (as into how much a system is removed from being a frame), which could be defined as some function of summed time dilation within the system. The minimum of d cannot be 0 due to P. So we must define some "cutoff" point from which we assume convention=actual. However, once again, this cutoff point is by pure convention. Saying the two parts of a brain are not in "synchronized" time would be technically correct, but nobody would see it that way, where do you put the cutoff?

Actually, any causally consistent surjective mapping from the set of the perceived "source" events to the set of the "detector" events will do for convention.

So why not pick a useful one, such as using hypothetical clocks from the cosmological principle, using the estimated distance to the source and using the speed of light, it is both a constant and relates distance to time.

But if we go that strict, we can assume the meaning of the phrase "seeing into the past" is also set by pure convention. So why could we not be simply consistent in our conventions and say "yes, we are indeed looking into the past".

[Ken G]

But then we must also say there is simply no actual time (relative to us). Even proper time is only defined relative to a specific frame.

I would say there's no particular problem saying that there is an "actual" time, but it lives on a world line, it has meaning along a series of events experienced by a clock/observer. It is actualized by the observer, but it is still "actual" because the observer is "actual." And since the observer can also be taken to be hypothetical (a common device in physics), time can also have a hypothetical flavor. But even when it is hypothetical, it is still owned by the world line, it is owned by the series of events connected by some kind of motion.

Actually, any causally consistent surjective mapping from the set of the perceived "source" events to the set of the "detector" events will do for convention.

I would say the need for convention stems from the desire to be able to say that the time interval between any two events depends on the observer attributing that interval, rather than depending on the inertial path that connects those events (the former being "coordinate time", the latter being "proper time"). But that approach, the coordinate time approach, is a kind of "hanger on" to outdated ways of thinking about time, wherein the time interval between two events is an extension of the time measured on an observer's clock (even though the observer does not follow a path between the events in question). Once we recognize that time doesn't work that way, which is one of the lessons of relativity, we should just drop the idea altogether, and let the time interval between two events depend on the events and not the observer. Poof, goodbye to "time dilation" and "relativity of simultaneity" and all those awkward and purely coordinate-dependent notions. We struggle so hard to fit those concepts into a deeper framework of relativity, but they never do fit, because they are simply not part of that deeper framework-- because the deeper framework is coordinate-free. The main lesson is just not getting through.

So why not pick a useful one, such as using hypothetical clocks from the cosmological principle, using the estimated distance to the source and using the speed of light, it is both a constant and relates distance to time.

On cosmological scales, that time coordinate has an important physical meaning, but that's because it properly associates time with the world line that gives it meaning-- comoving world lines. But then it's not a coordinate time, it's a proper time that can be used by observers who are also (approximately) comoving.

But if we go that strict, we can assume the meaning of the phrase "seeing into the past" is also set by pure convention. So why could we not be simply consistent in our conventions and say "yes, we are indeed looking into the past".

Technically, we are always seeing into the past, we always see (and hear, and feel) something that has already happened, something that can affect us but we cannot affect what we see, hear, feel. The question is quantifying how far into the past we are seeing. When we use our own special relativistic concept of that quantity, as is generally done, we are not using cosmological coordinates, because neither we nor the object we see are comoving with the rest of the universe. The difference is small, but that's where all the relativity is-- the problem with the usual way people talk about "seeing the past" is exactly how Newton, with his concept of absolute time, would have put it.

[caveman1917]

I've had some thought about this, if you're interested to continue the discussion?

Just to make sure we have no misunderstandings, is the following what you were saying?

The main point i see you making is that time has only meaning along a single worldline. The time interval between two events is 'owned' by the clock that is present at both events.

Another point i see you making is that the cosmological principle provides us with some sort of 'universal' reference frame, from which we can also infer time intervals in a similar way as the above single worldline example. This would be any frame at rest with the CMB.

I would fully agree on both counts.

Let's take the example of some hypothetical supernova, which happened ~1 million lightyears away. We have just now seen it happen. Then the usual way of relating these two events would be to say the supernova happened 1 million years in the past. This is of course by pure convention. However i don't see how we could improve on that. There is no valid clock present at both events (since it would have to travel at c), and neither us nor the supernova are at rest with the CMB.

[Ken G]

The main point i see you making is that time has only meaning along a single worldline. The time interval between two events is 'owned' by the clock that is present at both events.

Yes. When we form the concept of time, this is the only way it can be applied that tells us something about reality. We can also apply the concept of time in other ways, but then it is pure coordinatization, which means it is purely a choice for how to talk about something. This is a bit like saying there is a concept of "love" , but many different languages have different words for it. "Love" itself is the concept that is analogous to proper time, and the various different words in different languages are like the coordinate times-- many ways to say the same thing.

Another point i see you making is that the cosmological principle provides us with some sort of 'universal' reference frame, from which we can also infer time intervals in a similar way as the above single worldline example. This would be any frame at rest with the CMB.

Right.

Let's take the example of some hypothetical supernova, which happened ~1 million lightyears away. We have just now seen it happen. Then the usual way of relating these two events would be to say the supernova happened 1 million years in the past. This is of course by pure convention. However i don't see how we could improve on that. There is no valid clock present at both events (since it would have to travel at c), and neither us nor the supernova are at rest with the CMB.

We do need some kind of language to talk about it, but the time we settle on, by convention, has no physical importance in and of itself, except that which comes from the cosmological principle (and even that is no help on only million-year timescales).

[caveman1917]

In that case we both agree. Our main difference here was misunderstanding.

If i may clarify my previous points?

I was considering it purely from the practical astrophysics point of view. While acknowledging your theoretical objections, i meant to say that, if we need to choose a convention anyway (which we need to do, since physics by itself doesn't give us the practical tools for talking about it in this way), we could as well choose the one which we are using now, since it's a convenient one. We could choose any causally consistent surjective mapping though, they're all equally valid (as a convention). I was just taking the stance that, once we acknowledge we have to work with some 'random' convention, we just pick a convenient one and get it over with.

has no physical importance in and of itself, except that which comes from the cosmological principle (and even that is no help on only million-year timescales).

I would dare to take this one step further, and say the convention arising from the cosmological principle would be no help on any scale. That is on a practical level.
It would count if we average things out over these (grand enough) scales, but in astrophysics we are dealing with specific events, so it won't be much of a practical help on the issues where 'looking back into the past' is generally used. Though it is a nice feature of our current model.

[Ken G]

I was considering it purely from the practical astrophysics point of view. While acknowledging your theoretical objections, i meant to say that, if we need to choose a convention anyway (which we need to do, since physics by itself doesn't give us the practical tools for talking about it in this way), we could as well choose the one which we are using now, since it's a convenient one.

I agree-- conventions are all about convenience. Laws of physics are never what is convenient, they try to describe what is. But we wish to find the most convenient way to do that, so that's where conventions, like coordinatizations, come into play. So a question like "what is time" can be asking a lot of things, it can be asking what is the concept that is an effort to access some physical truth, or it can be asking about what conventions we have chosen to talk about time. In the latter camp would be issues like "what time is it" in London right now, or what does "noon" mean. In the former camp would be issues like whether or not there is a universal absolute time, whether it applies at all scales, and whether it exists independently from our intelligence or is a kind of by-product of our intelligence trying to understand its reality. I've been addressing the OP strictly in that latter sense.

We could choose any causally consistent surjective mapping though, they're all equally valid (as a convention). I was just taking the stance that, once we acknowledge we have to work with some 'random' convention, we just pick a convenient one and get it over with.

Or even, we move between several conventions-- we just take pains to identify our choices, and the conveniences we expect to receive as a result.

I would dare to take this one step further, and say the convention arising from the cosmological principle would be no help on any scale. That is on a practical level.
It would count if we average things out over these (grand enough) scales, but in astrophysics we are dealing with specific events, so it won't be much of a practical help on the issues where 'looking back into the past' is generally used.

I'm not quite sure what you mean here-- the convention of time arising from the cosmological principle is what we use now on large scales, and it is very convenient because it maps into a concept of "age", and it means that we can expect similar conditions in our own environment a long time ago when we see distant regions. To me, that's the only meaningful sense of "seeing into the past" that there is-- seeing into one's own past, or at least one's own statistically expected past.

[caveman1917]

I'm not quite sure what you mean here-- the convention of time arising from the cosmological principle is what we use now on large scales, and it is very convenient because it maps into a concept of "age", and it means that we can expect similar conditions in our own environment a long time ago when we see distant regions. To me, that's the only meaningful sense of "seeing into the past" that there is-- seeing into one's own past, or at least one's own statistically expected past.

Perhaps i could explain my point with using the supernova example again. Let's now say it's 10 billion light years away, we just received its light.
Now, when we need to map the source event to the detection event (our time convention), the cosmological principle wouldn't help much. This supernova could have been inside a strong gravitational field, we could be, and the trace of the light when reaching us might have gone through some.

What i'm saying is that, although the cosmological principle will give us this 'universal' time, it is really only by averaging out over large scales. Saying this region of the universe has the same general properties (age and history) as our region. It doesn't help when we try to couple a specific event to a specific detection event (eg the supernova for example).

I'm merely looking at it from a very practical perspective. "Here you got some specific event, how long ago did it happen".

EDIT: though i agree fully that once we average out over big enough scales (talk about big enough regions) the cosmological principle provides such a universal reference.

[Ken G]

Perhaps i could explain my point with using the supernova example again. Let's now say it's 10 billion light years away, we just received its light.
Now, when we need to map the source event to the detection event (our time convention), the cosmological principle wouldn't help much. This supernova could have been inside a strong gravitational field, we could be, and the trace of the light when reaching us might have gone through some.

But that's just it-- if the supernova occurs in a region that has had a strong gravity for that whole 10 billion years, then on what basis are you going to say it happened 10 billion years ago, or that it happened 10 billion LY away? Those two statements only have meaning in the context of a larger model of some kind, a model that can account for any gravitational redshifting and dimming that is not part of the Hubble law. All you observe is a redshift and a brightness, but if the local gravity is an important variable in those, and if you don't have any model for the motion of the source (or the "expansion of space"), you'll not get a unique concept of distance no matter what you do. At least with the cosmological principle, you can hope to disentangle the Hubble redshift from the local gravitational redshift, and thereby get a sense of when and where the SN happened within that overall model and the coordinatization it supports.

What i'm saying is that, although the cosmological principle will give us this 'universal' time, it is really only by averaging out over large scales.

That is true-- but it's not a weakness, because if you take away that ability to average and at least get a statistical result for an ensemble of observations, then you can't say anything at all. If the universe were made of little pockets of material with totally different ages and different gravitational redshifts (in regions of different expansion), what could observations ever tell you? Every quasar you see, every SN, is an independent entity coming from a disconnected piece of the complex tapestry, you'd never be able to place it into a larger model if the large-scale averaging were not meaningful.

Saying this region of the universe has the same general properties (age and history) as our region. It doesn't help when we try to couple a specific event to a specific detection event (eg the supernova for example).

But it's all we've got. It's a bit like observing the physical features of a large crowd-- it's true that we cannot tell the age of each individual in any but a vague kind of way, but we could still make statements about what fraction are statistically in each age range, just from general averages about how people's physical characteristics change with age. But if every person had a different rate of development or different characteristics with age, you'd never be able to know anything about the age of the people you are observing, either individually or as a statistical ensemble. Indeed, the way the concept of "age" actually plays out in practice has to do with these general physical characteristics, as much as it does the actual time people have been alive (we speak of certain high-stress jobs as causing "more rapid aging", or we say "that person really got a lot older since I last saw them" ).

I'm merely looking at it from a very practical perspective. "Here you got some specific event, how long ago did it happen".

I get that, but that's what the cosmological principle enables you to do-- without it, you'll never know the "age" of the material you are looking at, because you have no model for connecting the march of time at the place you are observing from the march of time owned by your own corner of the universe. We only see each region at a single age-- it's like looking at people's scrapbooks where there's only one picture in each. What could we tell about the age of the people in that one picture, if we didn't have a consistent model for how all people age and how that affects what we see in the scrapbook?

[caveman1917]

But that's just it-- if the supernova occurs in a region that has had a strong gravity for that whole 10 billion years, then on what basis are you going to say it happened 10 billion years ago, or that it happened 10 billion LY away?

I'd say there is no basis for making these inferences for a single datapoint. As long as we talk about single datapoints all we have is our chosen convention, which is nothing more than a convention, albeit a very convenient one.

That is true-- but it's not a weakness, because if you take away that ability to average and at least get a statistical result for an ensemble of observations, then you can't say anything at all.

I couldn't agree more. However note that we are now talking about an ensemble of observations.
I was merely saying that that which is true for an ensemble of observations isn't necessarily true for every consituent observation itself.

But if every person had a different rate of development or different characteristics with age, you'd never be able to know anything about the age of the people you are observing, either individually or as a statistical ensemble.

I beg to differ here. It depends on the distribution of their different rates of development. Suppose we map these different rates and find that they cluster to a simple gaussian distribution centered on some mean rate. Then, even though each and every person has a different rate, we can still say things about a bunch of people as a statistical ensemble. While we can hardly say anything about the age of each individual person, though this would depend on the specifics of the distribution of development rates.

Suppose we observe some region about 10 billion LY away. We find that the rate of supernovae is significantly higher than in our region here (lower metallicity stars etc).
Using the cosmological principle, we can infer from this that in our own region of space, about 10 billion years ago, we would also have had such a higher supernovae rate. In this sense we are 'truly' looking into the past.

However we can't infer that each and every one of those supernovae happened 10 billion years "ago". For that (making inferences about single datapoints) all we have is our chosen convention.