Perception and calculating when events happened

[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.

 

[pervect]

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?

Probably not. See for instance "If the Universe is only 14 billion years old, how can we see objects that are now 47 billion light years away?" in Ned Wright's cosmology FAQ at http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2 for a counterexample. There are events further away than the age of the universe, so this prescription obviously can't work, and the FAQ provides one way of explaining this.

While it's not mentioned in the above FAQ, I think It's also worth noting that the distances cosmologists report are "cosmological distances" computed in cosmological coordinates, rather than Fermi-Normal distances computed in Fermi-Normal coordinates.

Both distances can be thought of as the distance measured by a "chain of observers" each measuring the distance to the next observer via radar "at the same time". What differs is the notion of simultaneity used to create the chain. For cosmological distances all observers are at rest with respect to the Hubble flow - but are thus all moving away from one another, the notion of distance is not equivalent to that of a ruler where all parts are bound together and not moving with respect to each other.