Betelgeuse captured by ALMA

https://en.wikipedia.org/wiki/Angular_resolution explains the relevant formula for being able to take pictures like this.

Space telescopes like the James Webb are not actually as good as the ground-based arrays that were used here, which put together multiple receivers over a distance to create a much wider "eye".

I'm hoping that some day we'll have space-based arrays for this. Imagine if the virtual "eye" on the array was as wide as the orbit of the Moon!

That's a pretty good Fermi calculation!

The article [1] linked on ESO page mentions that "observations lasted for 75 min with 61 min spent on source". It also mentions only 47 antennas.

[1] https://arxiv.org/pdf/1706.06021.pdf

I gently disagree that this is a skewed definition. By convention, a "resolved" image of an object implies an extremely high quality measurement. On the other hand, we can resolve the separation of the star and planet in the Gemini image, but it would be misleading to claim that this is a resolved image of the planet. It may seem like a petty distinction, but I think it is better - for clarity's sake - to reserve the term "resolved" for its most natural contextual definition. Perhaps I am oversensitive to this as many non-astronomers are often led to believe that artistic renditions of exoplanets are actual images, not conceptions.

This type of direct detection was one of the first of its kind, so I wouldn't characterize this as an old capability - 2008 is relatively recent. Telescope turnover time is very long; Gemini remains a prominent telescope for science-class observations. Additionally, most new telescope generations don't achieve an order-of-magnitude improvement in resolution, or at least, not anymore. There are a lot of serious, decadal-scale barriers to improving resolution that must be overcome.

In terms of angular resolution, the order-of-magnitude estimates are the minimum improvements, assuming that such a close and large exoplanet exists. (AFAIK, there is no such system.) In practice it is likely that we need even better angular resolution, as there are not many systems within 10 ly away, and extremely large exoplanets are not very common (relatively speaking.)

No, this is not a good way to think about relativity and its implications.

When we talk about time in the sense of things happening "now" or "in the past" or "after", we have to think about reference frame, _not_ location. Reference frames are inherently global, as opposed to an "event", which encodes both location and time relative to all possible inertial reference frames.

The typical metaphor is imagine that you infiltrate space with a three-dimensional grid of clocks that are kept a fixed distance from each other (say by a rigid rod). Those clocks are not moving relative to each other, and it is trivial to synchronize them, because the distance between them is fixed -- fire a light pulse to your neighbor with the current time, and you neighbor will know when you sent the symbol by subtracting off the time it takes light to travel the distance. This grid, that covers all of space, represents a single reference frame.

So if Betelgeuse had in fact exploded six hundred years ago, then the clock grid in Earth's inertial frame would have recorded the event of the Battle of Orewin Bridge on Earth at the same time as the event of the beginning of the Betelgeusian supernova in the Betelgeuse system.

The complexity of this comes in the fact that the inertial frame travelling towards Betelgeuse from Earth at some significant fraction of the speed of light would, with its clock grid, measured Orewin Bridge well before the supernova's start. That's independent of the amount of time it would take for those two clocks to communicate with each other -- we can almost imagine a scientist who finally downloads the logs for all the clocks in a given reference frame collating the data.

What we _can_ say, though, is that once the event of someone on Earth seeing the supernova occurs, then that event is strictly _after_ the supernova -- no inertial reference frame will ever see that event, "observation of supernova", occur before the "initiation of supernova".