Default 'now' when discussing astronomical things

[Grinkle]

I would like to get some perspective on what people usually mean when they don't specify any reference and discuss things like the size of the observable universe or the distance between Andromeda and the Milky Way. The thread I would have posted this on is now defunct, so starting a new one.

There is no universal baseline 'now' in SR / GR.

It seems to me that the intuitive human 'now' is the instant that we are receiving information and from here we need to reason out how and why our intuitive 'now' may not be universal.

I claim there is a very basic frame shift that almost anyone talking about astronomical observations does often without thinking about it, and I offer the below example in an attempt to illustrate it. I don't think I am talking about SR / GR in the below, except that I am talking about c, but I am talking about c in what is to me a classical context more than a relativistic context.

If I am going to launch a satellite with the intent that it end up in orbit around Proxima Centauri, everyone with a basic knowledge of what 'light year' means can understand why I cannot "aim" the satellite to where I see PC "right now", I must account for the 4 light years it took for the signal to reach me, and I must model where I believe PC to be "right now" to calculate the engine accelerations I need my satellite to execute, or I will send the satellite to where the image I receive of PC is going to be by the time the satellite gets to its destination, and PC will be 4 years along its path relative to earth, ahead of the satellite.

SO - if I ask someone to do the exercise of plotting the course, they will AUTOMATICALLY make this frame shift as they get started and not even think about it. They will ask themselves "Where is PC right now" and the the "now" they mean is relative to photons PC is emitting, not relative the photons they receiving. Not all observers in the universe will agree that PC is 4 LY from earth, I suppose, but that is not my question.

Finally, my question ... when discussing the locations of distant bodies, is it normal to state those distances as directly measured, or is it normal to state those distances with the above conversion applied? I think the former, and usually it won't make much difference in the numbers discussed. When we discuss the size of the observable universe, does the above thinking matter in what numbers are tossed out?

 

[PeterDonis]

hey will ask themselves "Where is PC right now" and the the "now" they mean is relative to photons PC is emitting, not relative the photons they receiving.

Not quite. The "now" can't be relative to the photons PC is emitting, because we can't observe PC emitting those photons--we can only observe them when they reach us.

The "now" in your example is relative to a coordinate system in which the Earth (or more probably the solar system in this calculation) is at rest, and PC is moving at some known (to some reasonable approximation) velocity. We then plot PC's motion and the satellite's motion in this coordinate system, so that the satellite's trajectory is the right one to put it into orbit about PC.

when discussing the locations of distant bodies, is it normal to state those distances as directly measured, or is it normal to state those distances with the above conversion applied?

We don't directly measure distances to other stars, galaxies, etc. (We don't even directly measure distances to other bodies in the solar system.) We don't have a ruler 4.3 light-years long that stretches from us to Proxima Centauri. We infer its distance from other observations--the main one for PC is its parallax, since it's close enough to us for that to be measurable. In converting this parallax to a distance, we must adopt a coordinate system, just like in the satellite example above. So the distance we give is the distance in that coordinate system.

When we discuss the size of the observable universe, does the above thinking matter in what numbers are tossed out?

On this scale, the coordinate system that is almost always adopted is standard FRW coordinates. The size of the observable universe "now" is quoted in those coordinates--"now" is the spacelike hypersurface of constant FRW coordinate time that passes through the Earth now.

 

[Grinkle]

On this scale, the coordinate system that is almost always adopted is standard FRW coordinates.

Thanks, ok. And for smaller scales, eg the distance between Andromeda and the Milky Way, does it matter? I understand that question is very context sensitive, I suppose I mean whether professional astronomers who discuss that distance bother to be precise about what relativistic co-ordinate system they are using.

 

[PeterDonis]

for smaller scales, eg the distance between Andromeda and the Milky Way, does it matter?

On this scale, there's no significant difference between standard FRW coordinates and coordinates in a local "quasi-inertial" frame in which the Milky Way is at rest. (I say "quasi-inertial" because such a frame still has to take into account the gravity of the Milky Way, so it isn't quite a local inertial frame in the usual sense. But it's pretty close for many purposes.)

I suppose I mean whether professional astronomers who discuss that distance bother to be precise about what relativistic co-ordinate system they are using.

Generally, if no explicit coordinates are mentioned in astronomy or cosmology, you can assume FRW coordinates when distances to objects outside our galaxy are being quoted.

 

[Bandersnatch]

Thanks, ok. And for smaller scales, eg the distance between Andromeda and the Milky Way, does it matter? I understand that question is very context sensitive, I suppose I mean whether professional astronomers who discuss that distance bother to be precise about what relativistic co-ordinate system they are using.

For most purposes that don't involve cosmological expansion, it generally doesn't matter. Error bars on distances are often much larger than the displacement you get in the time from emission to reception. For example, Andromeda is measured to be 2.54 Mly, +/- 0.11 Mly. The distance it will have traveled between emission and reception of a signal we observe is approx. 0.00254 Mly (travelling at ~0.1% of c), so it's swamped by uncertainty in the measurement anyway.

Pretty much the only application where it'd matter that I can think of, is sending a probe/spaceship to other stars, but that's long ways away in the future.

 

[mfb]

We don't directly measure distances to other stars, galaxies, etc. (We don't even directly measure distances to other bodies in the solar system.)

Active radio astronomy (send an signal and measure time until we get the echo) makes direct distance measurements of objects in the inner solar system. As direct as it gets without physically putting rulers in space.

The reference frame matters a lot for very distant objects, but there distances are typically given as redshift (as that is measured, and the inferred distance depends on the model), and of course the objects are described as we see them today. It does not really matter how those objects look "today" as in "when the universe is 13.8 billion years old for observers there" - for very distant objects we'll never be able to observe that.

It does matter on much smaller scales as well: Mars has an orbital velocity of 24 km/s, with ~10 minutes light travel time we see it ~14,000 km behind of its current position. If you want to send a probe to Mars, that matters - it is twice its diameter!

 

[PeterDonis]

As direct as it gets without physically putting rulers in space.

As direct as it gets, yes. But the distances derived from these measurements are still indirect, because computing them, at least with the accuracy we are achieving now, requires taking into account GR effects that are model-dependent, i.e., they depend on us having an accurate overall model of the solar system, where all the objects are, what their masses are, etc. It's not the same as just reading off distance from round-trip light travel time in an idealized flat spacetime scenario.

Yes, the effects involved within the solar system are much smaller than those in cosmology, so the error involved in just converting light travel time to distance without taking GR effects into account is much smaller. But the effects are still there.