# Perception and calculating when events happened

1. Jun 8, 2014

### 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?

2. Jun 8, 2014

### ghwellsjr

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.

3. Jun 8, 2014

### Staff: Mentor

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.

4. Jun 8, 2014

### Staff: Mentor

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".

5. Jun 8, 2014

### johnny_bohnny

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

6. Jun 8, 2014

### Staff: Mentor

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

7. Jun 8, 2014

### 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.

8. Jun 8, 2014

### Staff: Mentor

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.

9. Jun 8, 2014

### pervect

Staff Emeritus
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

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.

10. Jun 8, 2014

### johnny_bohnny

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?

11. Jun 8, 2014

### pervect

Staff Emeritus
Newtonian mechanics wont 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.

12. Jun 8, 2014

### WannabeNewton

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.

13. Jun 8, 2014

### 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?

14. Jun 8, 2014

### Staff: Mentor

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.

15. Jun 8, 2014

### D H

Staff Emeritus
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.

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.

16. Jun 8, 2014

### Staff: Mentor

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.

17. Jun 8, 2014

### Staff: Mentor

Thanks for the correction!

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.

18. Jun 8, 2014

### Staff: Mentor

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.?

19. Jun 8, 2014

### D H

Staff Emeritus
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.

20. Jun 8, 2014

### 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?

21. Jun 8, 2014

### D H

Staff Emeritus
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.

22. Jun 8, 2014

### Staff: Mentor

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.

23. Jun 9, 2014

### ghwellsjr

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.

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?

24. Jun 9, 2014

### ghwellsjr

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 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?

Last edited: Jun 9, 2014
25. Jun 9, 2014

### Staff: Mentor

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.

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".

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 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.

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".