Perception and calculating when events happened

[johnny_bohnny]

It is often said that we basically live in the past, since it takes time for light to travel from objects to our eyes and we perceive the world as it was. If we measure the distance and speed of light we can discover by how much are we 'living in the past', or when did some event happen according to our frame.

Now the problem here is that this is clearly valid for an inertial frame, but what happens in real life on Earth, since we aren't in an inertial frame. Our eyes are also undergoing non-inertial motion. So how do we use the same method in real life to discover when did some event happen by subtracting the time that light took from an object to our eyes, since each space point of our eyes may have a different meaning of simultaneity? What is the criteria?

 

[ghwellsjr]

It is often said that we basically live in the past, since it takes time for light to travel from objects to our eyes and we perceive the world as it was. If we measure the distance and speed of light we can discover by how much are we 'living in the past', or when did some event happen according to our frame.

Now the problem here is that this is clearly valid for an inertial frame, but what happens in real life on Earth, since we aren't in an inertial frame. Our eyes are also undergoing non-inertial motion. So how do we use the same method in real life to discover when did some event happen by subtracting the time that light took from an object to our eyes, since each space point of our eyes may have a different meaning of simultaneity? What is the criteria?

In "real life" here on Earth, it hardly matters because our speeds are so slow, our distances are so short, and our clocks are so unstable. When we look at heavenily bodies outside our solar system, we can't measure their distances with a ruler or with radar techniques, so we pretty much rely on the authority of experts who base their measurements on other techniques.

 

[PeterDonis]

What is the criteria?

There is no unique criterion in general; the question "when did event E happen?" has no unique answer for you if event E is not on your worldline. The only invariant is your past light cone; at any event on your worldline, the set of events in spacetime that are within your past light cone (i.e., events that could have sent a light signal that would reach you) is invariant, and doesn't depend on how you choose coordinates or a simultaneity convention. But the "time" you assign to any particular event *does* depend on how you choose coordinates and a simultaneity convention.

If your question is about how, in practice, we choose coordinates and a simultaneity convention, there are a number of different choices, depending on what you are trying to do.

 

[PeterDonis]

When we look at heavenily bodies outside our solar system, we can't measure their distances with a ruler or with radar techniques, so we pretty much rely on the authority of experts who base their measurements on other techniques.

But in general, *none* of these distances can be used to calculate "when did some event happen by subtracting the time that light took from an object to our eyes".

 

[johnny_bohnny]

If your question is about how, in practice, we choose coordinates and a simultaneity convention, there are a number of different choices, depending on what you are trying to do.

Yes, some details would be great. Because it seems very complicated.

 

[PeterDonis]

some details would be great.

For ordinary timekeeping and distances on Earth, the usual convention is to use a frame that rotates with the Earth, and whose rate of time flow is that of clocks at rest on the "geoid", which is basically an idealized "sea level" surface:

http://en.wikipedia.org/wiki/Geoid

This is more or less the frame you probably use intuitively in your everyday life.

For keeping track of objects in space near the Earth, like satellites, it's more convenient to use what's called an "Earth-Centered Inertial" frame, which is basically an inertial frame with its spatial origin at the center of the Earth (and its "time axis" is the worldline of the center of the Earth):

http://en.wikipedia.org/wiki/Earth-centered_inertial

This means the ECI frame is *not* rotating with the Earth, so it's easier to use for computing things like spacecraft orbits. (I believe this is also the frame used for the calculations that underlie the GPS system.)

For measurements within the solar system, there is something called the "International Celestial Reference Frame", which is basically an inertial frame centered on the Sun (actually on the barycenter of the solar system, the "center" around which all solar system bodies, including the Sun, orbit):

http://en.wikipedia.org/wiki/International_Celestial_Reference_Frame

It's worth noting that neither the ECI frame nor the ICRF are true "inertial" frames, for two reasons. One is that the body on which the frame is centered may still be orbiting some other body; the Earth orbits the Sun, for instance. This means the frame is "rotating" due to the orbital motion, which leads to non-inertial effects. The ICRF has no such effects to the precision we can measure, but that's just because the solar system takes a lot longer to orbit the center of the galaxy than the Earth takes to orbit the Sun.

The other reason the ECI and ICRF aren't true inertial frames is that effects of spacetime curvature due to the Earth, the Sun, and other bodies are still measurable within them. But for many purposes these effects are too small to matter.

For a good overview of the different distance measures used in cosmology (basically, for anything outside the solar system), see Ned Wright's Cosmology Tutorial here:

http://www.astro.ucla.edu/~wright/cosmo_02.htm

 

[bahamagreen]

Just to be sure there is no misapprehension about this, the biggest local contribution is the closest - your perception runs quite a bit behind the local events because of neural transmission and processing stage delays. Even if c was infinity, your perception remains of the considerable past.

Since neurons can depolarize up to about 1K/s, and you have about 10^11 neurons and about 10^14 synapses, a tremendous amount of processing is happening during the approximate 150ms latency between light entering the eye and corresponding visual perception.

Within that latency period there is initiation and control of what will become movements, reactions, thoughts, and perceptions... you are not just perceiving the outer world in the past; your own immediate perception of your self is actually of your own past.

That is to say, your unperceiving self is living and acting within the complex world a little bit ahead of your perceiving self... you have a "leading edge" acting in the objective world with which you have an ineluctable separation; even for immediate and local events you only get after the fact perceptual constructions.

 

[PeterDonis]

Just to be sure there is no misapprehension about this, the biggest local contribution is the closest - your perception runs quite a bit behind the local events because of neural transmission and processing stage delays. Even if c was infinity, your perception remains of the considerable past.

<rest of post snipped>

None of this at all relevant to relativity; it's a matter of physiology and neuroscience, not physics. So I don't see how we're going to have a useful discussion about it on this forum.

 

[pervect]

The ICRF has no such effects to the precision we can measure, but that's just because the solar system takes a lot longer to orbit the center of the galaxy than the Earth takes to orbit the Sun.

I agree with almost all of what Peter says, but I do have a minor quibble with this point.
The ICRF uses extra galactic radio sources, so I don't think the galactic rotation is relevant. See for instance

http://aa.usno.navy.mil/faq/docs/ICRS_doc.php

The International Celestial Reference Frame (ICRF or ICRF1) is a catalog of adopted positions of 608 extragalactic radio sources observed with VLBI

Note: ICRF2 is out now, so the number of sources has changed slightly, as has as the selections of which ones are the most stable.

 

[johnny_bohnny]

For ordinary timekeeping and distances on Earth, the usual convention is to use a frame that rotates with the Earth, and whose rate of time flow is that of clocks at rest on the "geoid", which is basically an idealized "sea level" surface:

http://en.wikipedia.org/wiki/Geoid

This is more or less the frame you probably use intuitively in your everyday life.

For keeping track of objects in space near the Earth, like satellites, it's more convenient to use what's called an "Earth-Centered Inertial" frame, which is basically an inertial frame with its spatial origin at the center of the Earth (and its "time axis" is the worldline of the center of the Earth):

http://en.wikipedia.org/wiki/Earth-centered_inertial

This means the ECI frame is *not* rotating with the Earth, so it's easier to use for computing things like spacecraft orbits. (I believe this is also the frame used for the calculations that underlie the GPS system.)

For measurements within the solar system, there is something called the "International Celestial Reference Frame", which is basically an inertial frame centered on the Sun (actually on the barycenter of the solar system, the "center" around which all solar system bodies, including the Sun, orbit):

http://en.wikipedia.org/wiki/International_Celestial_Reference_Frame

It's worth noting that neither the ECI frame nor the ICRF are true "inertial" frames, for two reasons. One is that the body on which the frame is centered may still be orbiting some other body; the Earth orbits the Sun, for instance. This means the frame is "rotating" due to the orbital motion, which leads to non-inertial effects. The ICRF has no such effects to the precision we can measure, but that's just because the solar system takes a lot longer to orbit the center of the galaxy than the Earth takes to orbit the Sun.

The other reason the ECI and ICRF aren't true inertial frames is that effects of spacetime curvature due to the Earth, the Sun, and other bodies are still measurable within them. But for many purposes these effects are too small to matter.

For a good overview of the different distance measures used in cosmology (basically, for anything outside the solar system), see Ned Wright's Cosmology Tutorial here:

http://www.astro.ucla.edu/~wright/cosmo_02.htm

Great post, so what conventions do we use for substracting the light that enters our eyes and defining a sort of 'now' for Earth and everyday life, since we are in a non-inertial frame and things don't seem so simple?

 

[pervect]

It is often said that we basically live in the past, since it takes time for light to travel from objects to our eyes and we perceive the world as it was. If we measure the distance and speed of light we can discover by how much are we 'living in the past', or when did some event happen according to our frame.

Now the problem here is that this is clearly valid for an inertial frame, but what happens in real life on Earth, since we aren't in an inertial frame. Our eyes are also undergoing non-inertial motion. So how do we use the same method in real life to discover when did some event happen by subtracting the time that light took from an object to our eyes, since each space point of our eyes may have a different meaning of simultaneity? What is the criteria?

Newtonian mechanics won't work unless one chooses the correct definition of simultaneity. In GR the problem isn't crucial, because unlike Newtonian mechanics, GR doesn't require any particular "correct" choice of simultaneity. Technically, this is due to the invariance of the theory under diffeomorphisms, under which a change of coordinates (including a change of simultaneity) doesn't affect measured results.

Thus the choice of simultaneity doesn't affect physical predictions at all. This point can't be stressed enough - presumably you wouldn't be asking the question you just asked if you realized and acacepted that the choice of simultaneity didn't actually affect anything observable.

Thus in GR, the choice of simultaneity is a convention. The way the convention is typically communicated is by communicating the GR metric coefficients.

While there isn't any required choice of simultaneity, in may instances the underlying structure of space-time isn't changing , or at least isn't changing very fast. In these cases, it's often useful to use Einstein clock synchronization over a two-way path to determine an approximate notion of one-way simultaneity, if the change is "slow enough" that inconsistencies don't arise from this assumption.

 

[WannabeNewton]

Great post, so what conventions do we use for substracting the light that enters our eyes and defining a sort of 'now' for Earth and everyday life, since we are in a non-inertial frame and things don't seem so simple?

While on the relativistic calculations and considerations necessary for GPS systems as opposed to more mundane Earthly tasks, the following paper by Ashby is about as pedagogical a treatment as you can find on the various factors you seek concrete elucidation of: http://www.aapt.org/doorway/tgru/articles/ashbyarticle.pdf

It would be much more instructive for you to work through the paper on your own and then come back with explicit questions as you'll learn much more that way than if someone just spoon feeds you every iota of detail.

 

[ghwellsjr]

When we look at heavenily bodies outside our solar system, we can't measure their distances with a ruler or with radar techniques, so we pretty much rely on the authority of experts who base their measurements on other techniques.

But in general, *none* of these distances can be used to calculate "when did some event happen by subtracting the time that light took from an object to our eyes".

Really? I thought when a distant event such as a supernova explosion is observed, the distance (x number of light years) determined how long in the past (x number of years) the explosion occurred, "according to our frame". Is it more complicated than that?

 

[PeterDonis]

what conventions do we use for substracting the light that enters our eyes and defining a sort of 'now' for Earth and everyday life

We don't. We define "now" on Earth by what local clocks read; to get the time of a distant event we ask people who were there what their local clocks read when it happened.

If we really want accuracy, we set local clocks from atomic clocks that synchronize with each other by various means (nowadays they mostly do it over the Internet, but I think GPS is used as well). Those synchronization methods try to take account of signal travel time, but the signal won't always be traveling at the speed of light. The end result of this convention is *not* any kind of consistent assignment of "now" based on light travel time; it's just a practical convention that works well enough for practical purposes.

 

[D H]

This means the frame is "rotating" due to the orbital motion, which leads to non-inertial effects. The ICRF has no such effects to the precision we can measure, but that's just because the solar system takes a lot longer to orbit the center of the galaxy than the Earth takes to orbit the Sun.

ECI and ICRF are not rotating frames, at least to within observational error. They are accelerating frames. There are a number of so-called Earth centered inertial frames because observational error has decreased markedly over the decades. The most recent, the geocentric celestial reference frame (GCRF), uses the same axes as the ICRF, but translated from the solar system barycenter to the center of the Earth. The ICRF is the astronomers current best guess as to what constitutes a local non-rotating reference frame, and hence so is the GCRF.

For a good overview of the different distance measures used in cosmology (basically, for anything outside the solar system), see Ned Wright's Cosmology Tutorial here

No. For anything many tens of millions of light years or more outside the solar system, yes. But within our galaxy, and even within the local group, what you wrote just isn't true.

 

[PeterDonis]

Really? I thought when a distant event such as a supernova explosion is observed, the distance (x number of light years) determined how long in the past (x number of years) the explosion occurred, "according to our frame". Is it more complicated than that?

Yes. Read Ned Wright's cosmology tutorial (I linked to a section of it in an earlier post). There are multiple different "distances" that don't match up, and none of the ones we can actually observe exactly correspond to "distance in our frame". In popular accounts you often see people glossing over all the complexities and saying things like "the light we see from a galaxy that's a billion light years away left that galaxy a billion years ago", but that is just what I said, a glossing over of a lot of complexities.

 

[PeterDonis]

The most recent, the geocentric celestial reference frame (GCRF), uses the same axes as the ICRF, but translated from the solar system barycenter to the center of the Earth. The ICRF is the astronomers current best guess as to what constitutes a local non-rotating reference frame, and hence so is the GCRF.

Thanks for the correction!

For anything many tens of millions of light years or more outside the solar system, yes. But within our galaxy, and even within the local group, what you wrote just isn't true.

Hm, yes, it's been a while since I actually read through Ned Wright's tutorial; I thought he talked about distance measures like parallax that are used for closer objects. You're right, all the distance measurements he talks about in that article are only used in the distance range you give. (Luminosity distance, which he mentions, is also used, IIRC, to obtain distances to objects like Cepheid variables that have a known absolute luminosity, but I see he doesn't talk about that either.) Sorry for the mixup on my part.

 

[PeterDonis]

ECI and ICRF are not rotating frames, at least to within observational error. They are accelerating frames.

I'm asking about this separately because I'm not sure what you mean here. Do you just mean the frames aren't exactly inertial because of the spacetime curvature due to the gravity of the Earth, Sun, etc.?

 

[D H]

I'm asking about this separately because I'm not sure what you mean here. Do you just mean the frames aren't exactly inertial because of the spacetime curvature due to the gravity of the Earth, Sun, etc.?

Sorry, I meant from a Newtonian perspective. From a Newtonian perspective, gravity is a real force and the Earth is accelerating toward the Sun and other bodies. That makes ECI a Newtonian accelerating frame. That the frame origin itself is accelerating needs to accounted for in the equations of motion. Solar system astronomers and aerospace engineers denote the acceleration toward other heavenly bodies as "third body effects". You would probably call them tidal effects. That name is already used, at least for bodies in low Earth orbit. The Moon perturbs the oceans and the shape of the Earth itself. That very subtly changes the orbits of satellites about the Earth.

Third body effects are fairly small, tidal effects are very small, and relativistic effects are smaller yet (at least insofar as equations of motion are concerned). Solar system astronomers and aerospace engineers pretend that the universe is mostly Newtonian. Relativistic effects are but a minor perturbation calculated via a linearized post Newtonian approximation.


From a general relativistic perspective, ECI locally is an inertial frame. If we could encapsulate an accelerometer and rate gyro in unobtanium, somehow send that package to the center of the Earth, make it non-rotating with respect to the ICRF, that package would register zero acceleration and zero rotation.

 

[ghwellsjr]

Really? I thought when a distant event such as a supernova explosion is observed, the distance (x number of light years) determined how long in the past (x number of years) the explosion occurred, "according to our frame". Is it more complicated than that?

Yes. Read Ned Wright's cosmology tutorial (I linked to a section of it in an earlier post). There are multiple different "distances" that don't match up, and none of the ones we can actually observe exactly correspond to "distance in our frame". In popular accounts you often see people glossing over all the complexities and saying things like "the light we see from a galaxy that's a billion light years away left that galaxy a billion years ago", but that is just what I said, a glossing over of a lot of complexities.

I know long distances are difficult to determine, that was my point in my first post. But if we determine that an event that we see was a billion light years away "according to our frame", do we then determine that it happened something other than a billion years ago?

 

[D H]

I know long distances are difficult to determine, that was my point in my first post. But if we determine that an event that we see was a billion light years away "according to our frame", do we then determine that it happened something other than a billion years ago?

When you are using terms such as "a billion light years away," you are definitely in the regime where those cosmological concerns raised by PeterDonis and others become paramount.

As a starter, what do you even mean by "a billion light years away"?

The Milky Way and the object that emitted that light we are just now seeing were much less than a billion light years apart when the object emitted that light a billion years ago. The distance between the two objects is now much greater than a billion light years. Once those cosmological concerns kick in, it's easier (at least to me) just to look at things from the perspective of how long it took the light to get here. That's easy: It took a billion years. How long the light traveled over the course of those billion years, and what that means are different questions.

 

[PeterDonis]

if we determine that an event that we see was a billion light years away "according to our frame", do we then determine that it happened something other than a billion years ago?

First of all, what exactly does "according to our frame" mean? I have been taking it to mean "according to the FRW coordinate chart", which is the chart we use to describe the universe on large distance scales, but perhaps you mean something different? (Which would raise the question of whether "our frame" is even well-defined at such large distances; many ways of constructing coordinate charts that work OK on the scale of, say, our solar system, will run into problems on much larger scales.)

Second, assuming we have chosen the FRW coordinate chart as "our frame", how do we determine that an event we see was a billion light years away according to "our frame"? None of the distance measures give that number directly. We have to adopt some sort of model to estimate the distance according to "our frame". And any such model will have to be constructed by using the very distance measures we are depending on.

Third, assuming we know that an event was a billion light years away in the FRW coordinate chart, at what FRW coordinate time are we quoting that distance? If we mean a billion light years away "now", then the event did not happen a billion years ago, because the universe is expanding. And the rate of expansion is not constant, so we can't just use the expansion rate we directly measure from the redshift of the light we get from the event to correct our time estimate. Again, we have to have some sort of model of how the universe has expanded, and the model will depend on the distance measures.

 

[ghwellsjr]

I know long distances are difficult to determine, that was my point in my first post. But if we determine that an event that we see was a billion light years away "according to our frame", do we then determine that it happened something other than a billion years ago?

When you are using terms such as "a billion light years away," you are definitely in the regime where those cosmological concerns raised by PeterDonis and others become paramount.

As a starter, what do you even mean by "a billion light years away"?

I have a book of Hubble images and most of them state a distance in light years. They are the experts I referred to in post #2. I have no idea how they determined those distances but I didn't think their statements were meaningless.

The Milky Way and the object that emitted that light we are just now seeing were much less than a billion light years apart when the object emitted that light a billion years ago. The distance between the two objects is now much greater than a billion light years. Once those cosmological concerns kick in, it's easier (at least to me) just to look at things from the perspective of how long it took the light to get here. That's easy: It took a billion years. How long the light traveled over the course of those billion years, and what that means are different questions.

Could it be that when NASA states that an object is a billion light years away, they just mean the light from that object left it a billion years ago? Is that what you're saying?

 

[ghwellsjr]

if we determine that an event that we see was a billion light years away "according to our frame", do we then determine that it happened something other than a billion years ago?

First of all, what exactly does "according to our frame" mean?

I'm quoting the OP and I presume he meant "according to the frame in which we are at rest", as opposed to a frame in which we are traveling at a significant fraction of the speed of light.

I have been taking it to mean "according to the FRW coordinate chart", which is the chart we use to describe the universe on large distance scales, but perhaps you mean something different? (Which would raise the question of whether "our frame" is even well-defined at such large distances; many ways of constructing coordinate charts that work OK on the scale of, say, our solar system, will run into problems on much larger scales.)

Second, assuming we have chosen the FRW coordinate chart as "our frame", how do we determine that an event we see was a billion light years away according to "our frame"? None of the distance measures give that number directly. We have to adopt some sort of model to estimate the distance according to "our frame". And any such model will have to be constructed by using the very distance measures we are depending on.

Third, assuming we know that an event was a billion light years away in the FRW coordinate chart, at what FRW coordinate time are we quoting that distance? If we mean a billion light years away "now", then the event did not happen a billion years ago, because the universe is expanding. And the rate of expansion is not constant, so we can't just use the expansion rate we directly measure from the redshift of the light we get from the event to correct our time estimate. Again, we have to have some sort of model of how the universe has expanded, and the model will depend on the distance measures.

I was recommending to the OP that we let the experts decide about the very long distances. I'm not sure what they mean but they don't seem concerned that it might be ambiguous. What do you think they mean? And is their stated distance to the object in any way related to how long ago the light left the object?

 

[PeterDonis]

I have a book of Hubble images and most of them state a distance in light years.

Is it a scientific treatise? Or just a popular book for lay people? If it's the former, there should be an explanation somewhere of how they determined the distances; I would expect to see terms similar to those in Ned Wright's cosmology tutorial (things like "angular size distance" or "luminosity distance").

If, OTOH, it's the latter (which is what I'm guessing), then the people who published it probably either didn't ask the experts about all the complications, or decided the answers were too, well, complicated, and just quoted a number without worrying about what it actually meant.

Could it be that when NASA states that an object is a billion light years away, they just mean the light from that object left it a billion years ago? Is that what you're saying?

I would have to see the context, but ordinarily I would expect that, assuming it's actually someone with scientific expertise talking, when they say some object is a billion light years away, they mean something like "taking the actual observations and doing a best-fit estimate with our current cosmological models, we think this object's coordinate distance from us in FRW coordinates at the current instant of FRW coordinate time is a billion light-years".

I'm quoting the OP and I presume he meant "according to the frame in which we are at rest"

And one of the points I'm making is that, if that's what the OP meant by "our frame", it's not the frame we usually use for cosmological distances. The Earth, and indeed the solar system, are not at rest in standard FRW coordinates; we see a significant dipole anisotropy in the CMBR. As I understand it, cosmologists routinely correct for that before quoting distances and times, i.e., they convert to a standard FRW coordinate chart.

I was recommending to the OP that we let the experts decide about the very long distances. I'm not sure what they mean but they don't seem concerned that it might be ambiguous. What do you think they mean?

I think, in general, they simply don't bother to talk about all the complications and ambiguities; it's not that they aren't there, it's that the lay people they are talking to either don't understand or don't care about them. For an example of what I think they mean, see above where I responded to your question about NASA.

And is their stated distance to the object in any way related to how long ago the light left the object?

Only if you have a cosmological model of how the universe expands; the model gives you the relationship. As I noted above, cosmologists have a current "best-fit" model that, as far as I know, is the one they use when making estimates. Given a model, there is a relationship, but it's not a simple one, and it's certainly not "if the object is a billion light-years away, then the light we're seeing left that object a billion years ago".

 

[PeterDonis]

Once those cosmological concerns kick in, it's easier (at least to me) just to look at things from the perspective of how long it took the light to get here. That's easy: It took a billion years.

Wouldn't this depend on which particular distance measure is being used? (Also, at least as I understand it, it's harder to estimate the light's travel time than it is to estimate the object's FRW coordinate distance.)

 

[bahamagreen]

None of this at all relevant to relativity; it's a matter of physiology and neuroscience, not physics. So I don't see how we're going to have a useful discussion about it on this forum.

I didn't mention it to invoke a discussion about it. I mentioned it hoping to ensure a useful and on-track discussion of the OP's question.

The OP's "...since it takes time for light to travel from objects to our eyes and we perceive the world as it was." might be assuming that the light's travel time was the only part of the latency of "and we perceive the world as it was".

Because of the approximate 150ms of visual system neurophysiology latency, its contribution to total latency magnitude would be about 50% when light is coming from a source about 45,000Km from the observer... subtracting out "...the time that light took from an object to our eyes..." definitely does need to be understood as doing only that, and not accounting for the total degree to which we perceive the past.

I only wanted to remind that all perceptual results of light finally reaching the eye are still about 150ms later, so you also must include perceiving the results of light's entry to the eye as also in the past... and its portion of the total latency depending on the source distance.

If the OP had written "instrument" or "device" or something suggesting negligible latency I would not have posted, but all his questions and scenarios were about the eye, mentioned four times, so I did.

 

[johnny_bohnny]

I still don't understand, the speed of light is c, so if we substract it over distance here on Earth we will find out when the event happened. In inertial frames this seems easy. So what conventions are possible to define 'now-ness' from Earth's perspective, or to substract the time that is necessary for the light to travel to our eyes?

 

[D H]

What do you mean by "distance"? There are a number of different distance metrics in cosmology.

And why this focus on the eyes?

 

[PeterDonis]

the speed of light is c

The speed of light *in an inertial frame* is c. But a frame at rest with respect to the rotating Earth is not an inertial frame; and in the presence of gravity there are no inertial frames that cover an extended region anyway, there are only local inertial frames.

In many practical situations, the error involved in assuming that the speed of light is c, even in a rotating frame and in the presence of gravity, is small. But it's still there.

if we substract it over distance here on Earth we will find out when the event happened.

If all you want is an approximate answer, sure, you can do this. For example, to a good approximation, the Moon is 1 1/4 light-seconds away, so you are seeing the Moon as it was 1 1/4 seconds ago. But this is still just an approximation; the exact answer is going to vary according to where the Moon is in the sky (which affects your motion, standing on Earth, relative to the Moon) and what altitude on Earth you are at (which affects gravitational time dilation); and the exact answer will be different for different people at different points on the Earth.

We can define a convention, such as using clocks at rest on the geoid for "rate of time flow" and the worldline of the center of the Earth to define simultaneity, that allows us to assign a unique "time" to every event in the Earth's vicinity that everyone on Earth can use as a reference (this is more or less how Coordinated Universal Time, UTC, works); but the time this convention assigns to events is *not* the same as the time you, or anyone else at rest on the rotating Earth, would get for an event by assuming light travels at c and subtracting light travel time based on the event's distance from you. It will be a very good approximation to that time for most cases, but it won't be identical.

In inertial frames this seems easy.

That's because in inertial frames, it is. But unfortunately, as I noted above, inertial frames are limited in what they can cover.

what conventions are possible to define 'now-ness' from Earth's perspective

I described one above.

or to substract the time that is necessary for the light to travel to our eyes?

Nobody uses this method to assign times to events on Earth. As I said before, people assign times to events by having clocks co-located with those events, and keeping those clocks synchronized with a common time and simultaneity convention like UTC.

 

[johnny_bohnny]

What do you mean by "distance"? There are a number of different distance metrics in cosmology.

And why this focus on the eyes?

The focus on the eyes is because I'm trying to connect our mental representation of the world with the world itself.

The basic problem lays here. If our eyes were a sort of inertial frame, we could easily substract the time that light takes to travel to our eyes with the velocity of c and find out when an event happened relative to 'here-now' or our frame.

But in non-inertial frames, it seems that each point of our eyes has its own different simultaneity definition, so I'm not sure how to really deduce when some event happened from our limited perspective and our perceptions, since we're traveling non-inertially and things get complicated.

 

[PeterDonis]

I'm trying to connect our mental representation of the world with the world itself.

As I said before, this is a matter of physiology and neuroscience, not physics.

If our eyes were a sort of inertial frame, we could easily substract the time that light takes to travel to our eyes with the velocity of c and find out when an event happened relative to 'here-now' or our frame.

No, we couldn't, because we don't directly perceive how far away events are that we see. If we have some independent knowledge of the distance, we can *calculate* the time; but your perceptual system doesn't do that, because it doesn't have independent knowledge of the distance.

in non-inertial frames, it seems that each point of our eyes has its own different simultaneity definition

Simultaneity is a convention; it's an abstraction that we impose when we make mathematical models of the world. Your eyes don't have *any* "simultaneity definition"; nor does the rest of your perceptual system or your brain. Nothing in reality "has" a simultaneity definition. It's a feature of mathematical models, not reality. And it's an unnecessary feature even of mathematical models; you can compute all observables without ever having to talk or think about simultaneity.

(Your perceptual system does create (or helps your brain to create) a model of the world, but it isn't a mathematical one. It doesn't assign coordinates to events, nor does it know or care about simultaneity. At least, as far as we can tell, it doesn't, but as I said, this is a matter of physiology and neuroscience, not physics.)

 

[D H]

My suggestion: Drop the eyes business. It is a red herring. If you want to talk about physiology, this question needs to be moved to the biology, medical sciences, or social sciences of PhysicsForums (and then you should drop relativity). If you want to talk about relativity, forget about our eyes.

 

[bahamagreen]

My suggestion: Think harder to understand the OP's question.

Perhaps the OP's focus on the eye (and simultaneity) is because he recognizes that the retina is not an event, it is a spatially extended surface of events. Op seems to be wondering to what degree the Andromeda paradox is applicable to the retina... a fine and insightful relativity question.

Or are you going to say that the Andromeda paradox is about two people walking past each other, so that should be asked in the Exercise forum?

 

[PeterDonis]

the retina is not an event, it is a spatially extended surface of events.

This is true, but I don't think it means what you (and possibly the OP) think it means. See below.

Op seems to be wondering to what degree the Andromeda paradox is applicable to the retina... a fine and insightful relativity question.

If that was indeed the question, it wasn't very clear. However, the answer is, "not enough to matter", because the retina's cells are at rest relative to each other to a very good approximation, and the retinas of your two eyes are at rest relative to each other to almost as good an approximation. "Very good approximation" means here that any "time uncertainty" due to relative motion is much, much smaller than the latency times in the nervous system, which you have already mentioned.

There's another point here, though, which I was trying to get at with my previous post. Getting wrapped up in whether there is a single "simultaneity" for the retina, or for your two eyes, is pointless, because "simultaneity" is an abstraction in our mathematical models; it doesn't exist anywhere in the retina cells or the signals or the brain, and it doesn't have any physical effects in the retina cells or the signals or the brain. (Relative motion of the retina cells or the eyes might have physical effects, but those effects would have nothing to do with "simultaneity" being shared or not shared.)

And, as I've said before, "simultaneity" is not even a *necessary* feature of our mathematical models. You can compute all relativistic effects and physical observables without ever even using it; in fact computations often are simpler that way. These incessant questions about simultaneity are driven by our pre-relativistic intuitions, not by the physics. The proper cure, IMO, is to retrain one's intuitions.