Because simultaneity itself is relative, in our frame it actually does happen in 2022. It doesn't make sense to say the stars already collided if it's not in our past light cone.
But in a classic Minkowski diagram like this one (https://en.wikipedia.org/wiki/File:Minkowski_lightcone_loren...), don't you define the horizontal line (or at least a single line) as simultaneous in a given frame, instead of the entire white region? In all frames, the blue region are past or future, but in our particular frame, we can say more than that, like when the event happened.
As far as I can remember, the star blowing up and the light reaching us are only simultaneous in the light's frame.
That is a diagram of empty space, figuring out what that horizontal line represents in places with strong gravity is a bit tricky. In fact I'm not 100% sure there's a way to define it uniquely.
You could define the global time for a position to be the time at which light it sends reaches the earth, minus the time it took for the light to travel, but with things like gravitational lensing this can have some weird results, and may in fact not be well defined.
I get that it might be hard/impossible to uniquely define a single correct 3D subspace of the full 4D spacetime we're in as simultaneous to a given point in a given frame, but surely simultaneity is a 3D notion, right? This 3D spacelike subset of spacetime is simultaneous in some frame (or set of frames)?
I imagine that if you define everything on the boundary of your past light cone as simultaneous to you, it requires that everything on your future light cone to be simultaneous too, which would mean that everything between them is also simultaneous. That kind of definition defines a 4D subset of spacetime as simultaneous. In that set are points in each others future and past light cones, which we can unambiguously say are not simultaneous to each other. I think that's the heart of the argument everyone's having. I never took GR, so maybe you can shed some light on it (heh) from that perspective?
I'm not a physicist, but pretty sure you are conflating two different physical phenomena... One is the delayed observation due to the limited speed of light, the other is reference frame distortions due to special relativity.
I'm a physicist. OP is correct. OP is not conflating 2 different phenomena. The light cone is defined by the speed of light and hence they are one and the same phenomenon.
You're right that they're not conflating the phenomena, but to say that two events are only simultaneous if they're on the light cone is still incorrect - that's the boundary of the region of simultaneity, whereas the OP was suggesting that it's the entirety of it.
Since the light hasn't reached us yet, it's perfectly valid to state that in some frame of reference, the event is happening right now. 2022 is the last possible time at which we could make that claim because the events become causally separated, which is I think what OP was getting at, though the wording was a bit off.
I'm a physicist, too. And I don't understand what you and OP are talking about. In out frame, the collision happened ~2000 years ago. The light will arrive to Earth in a couple more years. That's it.
By the way, what's the need of talking about frames? Which other frame do you have in mind apart from ours?
Reference frames are local constructs, they cannot be used to (uniquely) define simultaneity over large distances. The time of any single event is just a "tag" in relativity. In fact there are infinitely many surfaces of simultaneity that contain the merger of those two stars and meet the Earth at a particular time "t" in the range ~[-2000, +5] from now, so that it is equally valid to state that the merger happened ~2000 years ago or ~20 years ago, or that it has not happened yet.
For this reason, to avoid confusion, it is much better and customary to "tag" astronomical events by the time we observe them. That is to say that they happen when we observe them.
IANAP, but doesn't speed of light actually define "at the same time"? I.e. for all intents and purposes, it's happening "now" for us, because there's no meaningful way of getting there faster than light.
In a way what I'm imagining is speed of light being a kind of "clock signal" of digital electronics, except continuous, not discrete.
If you wanted to say that when a light signal goes from A to B its emission and reception should be considered simultaneous, then you'd have to say the same about a signal sent back from B to A when the first one is received. ... And then, if you also wanted to believe that "x is simultaneous with y and y is simultaneous with z ==> x is simultaneous with z", you'd get the absurd conclusion that two events in the same place but separated in time are simultaneous.
So here's the actual situation (at least in special relativity):
Once you define a frame of reference, which is basically the same thing as a velocity of motion, you then have a notion of simultaneity in that frame. If you fix your frame of reference, simultaneity has the nice properties you might want it to have (like transitivity, which I appealed to above). But you can have "x simultaneous with y in frame F" and "y simultaneous with z in frame G" without x and z being simultaneous in any frame.
If a signal can get from x to y (here x and y are locations in spacetime, not just in space) then there is no frame in which x and y are simultaneous. If it's possible only for a signal propagating at the speed of light, then it is (just barely) impossible to find a frame in which they are simultaneous. If it's not possible even at the speed of light, then there is a frame in which they are simultaneous.
So, in particular, consider the collision between these stars and the arrival of the light from the collision here on earth. In an (impossible) reference frame moving at the speed of light in the direction from there to here, the events would be simultaneous. Actually, they can't quite be -- but by considering a frame that moves fast enough, you can make the time difference as short as you like.
In an (equally impossible) frame moving at the speed of light the other way, they would be 3600 years apart. With actually-admissible reference frames, the time can be anywhere strictly between zero and 3600 years.
So far as I know, we and these stars are not moving very rapidly (in comparison with the speed of light) relative to one another. It seems reasonable to use a frame corresponding roughly to their motion and ours. That gives you a time difference of about 1800 years, and any plausible adjustment for our actual relative motion will make no difference to speak of because we're moving so much slower than light relative to one another.
But: There is another related notion that you may have in mind. You can compute a numerical measure of separation between any two points in spacetime, called the "interval", which is positive when the separation is "space-like" and negative when it's "time-like". If light could go from one to the other, this separation is zero.
(How does this escape the scenario I described in the first paragraph above? Because knowing the interval, as it's called, between x and y, and the interval between y and z, isn't enough to determine the interval between x and z any more than knowing the distances x-y and y-z is enough to determine the distance x-z. In fact the situation is worse for intervals than for distances because there isn't anything corresponding to the triangle inequality. And the "interval=0" relation isn't transitive. So knowing that the intervals x-y and y-z are zero tells you nothing at all about the interval x-z.)
Alright, so J'Kaziof [1] actually lives on a nearby planet in Cygnus. This was/is a tragic event that whiped out J'Kaziof's home planet. Luckily, they had super duper advanced technology with spaceships that could reach c * .99999...
J'Kaziof witnessed this event when s/he was n seconds [old] per their atomic clocks, and immediately set out in our direction.
What is the age of J'Kaziof in seconds when s/he arrives on Earth?
[p.s. assume their ships can instantanously accelerate to c and slow down to 0 from c.]
[p.s.s. In the year of our lord 222 here on Terra, Bardesanes of Edessa [2] went to meet his maker. Let's just say he passed away at the exact moment of J'Kaziof uttering 'make it so' to his 1st officer.]
No, it happened 1795 years ago. There is only one frame of reference involved here, one we can attach to the Milky Way neglecting the relatively small movements of earth and KIC 9832227 within it. And two events are simultaneous in a given frame of reference if light emitted from both events reaches a point midway between the locations of the two events at the same time.
So you position your space ship in the middle between were earth and KIC 9832227 were 1795 years ago, about 900 light years away from each and sometime about the year 1122 you will see the stars colliding and at the same time, with a good enough telescope, what was happing on earth in the year 222 which establishes that the the collision of KIC 9832227 and the year 222 on earth were simultaneous in the frame of reference attached to the Milky Way.
Please see my other reply below. Reference frames are local constructs. There is no such a thing as a (unique) reference frame of the entire galaxy that can be used to define simultaneity. In fact there are infinitely many of them.
I have seen that your profiles says theoretical astrophysicist so you certainly know a lot more than me about the topic. Nonetheless I can not see why we can not have a reference frame extending over 100,000 light years or at least over 1,800 light years. That seem relatively small distance, the relative velocities are relatively small, space is relatively flat, expansion of space is, I guess, not really relevant within galaxies.
So naively I would expect that you can attach a reference frame to almost all objects in the Milky Way and they would agree on simultaneity to within hours or maybe days. There are certainly some notable exceptions like the central black hole or particles traveling at an appreciable fraction of the speed of light and you can certainly just invent a reference frame with huge relative velocity changing simultaneity a lot.
But are there really places within the Milky Way so that simultaneity would be off by hundreds and thousands of years over a distance of just 1,800 light years? If yes, what is the cause of that, as far as I can tell it would have to be an effect of general relativity because, again as far as I can tell, there is no problem of defining simultaneity across extended distances in special relativity and the involved velocities are not large enough to have an appreciable effect to begin with.
EDIT: Just calculated an example Lorentz transformation, 500 km/s relative velocity and 1,800 light years distance, and the time difference comes out at almost exactly 3 years. That is certainly more than I expected and adds up to 166 years across the entire Milky Way, on the other hand 500 km/s is probably quite a bit above common relative velocities within the Milky Way.
So I am still not convinced that picking a reference frame for the entire Milky Way, say with the origin at the center of mass, one axis coinciding with the axis of rotation and rotating with the Milky Way so that the angular momentum vanishes, could not provide a good enough reference frame for the entire Milky Way for back of the napkin calculations.
I agree that you can make such a construction in theory. However, in practice there is no way we can synchronize our clocks with an observer at the location of that binary star system. There is also no reason to do it: the precise time of the star merger does not have any physical meaning, it is just a label. Saying that some astronomical event took place on the date we observe it, is equally valid and free from ambiguities.
That's just nonsense. We know the distance between us and the star, we know that light travels at c, and therefore we know that, in our reference frame, the event being observed happened 1795 years ago.
Simultaneity is only defined when you talk about two (or more) events. The discussion was about an event: the collision of two stars. What is the other event?
The generous interpretation of what he means is that considering that this event is outside of our past light cone, there exists an inertial reference frame such that the collision happens “after” our “present”.
Of course, relative to our own inertial reference frames as we experience them, i.e. where we are mostly not moving, the collision would be thousands of years in the “past”.
When he says “in our frame” he is clearly at least slightly confused.
But we do say we see the Sun as it were 8 minutes ago because of distance/c. Are you suggesting that this notion be removed as well, because I agree with you regarding the light cone, but the Sun being 8 minutes away makes too much sense for me to abolish the concept.
Is there any philosophical speak about this topic or is it basically resolved?
There exists a reference frame in which the distance between the Sun and earth is so compressed by Lorentz contraction that the light leaves the Sun and arrives at the earth in 1 second. In relativistic terms, the photon leaving the Sun and arriving at the earth can be considered to be simultaneous.
> In relativistic terms, the photon leaving the Sun and arriving at the earth can be considered to be simultaneous.
No they cannot, unless you boost to a reference frame that's moving at the speed of light, which is a useless frame. In all other frames, including the ones we are in, the photon left the Sun before arriving to Earth.
> In relativistic terms, the photon leaving the Sun and arriving at the earth can be considered to be simultaneous.
You just constructed an argument that can be readily used to argue that all events are simultaneous. That should flip your internal bozo bit and help you see that the argument is not sound.
> You just constructed an argument that can be readily used to argue that all events are simultaneous
No, I haven't. I have studied relativity in University, have you? Lol @bozobit
I will make the statement more rigorous.
"Let event A represent the emission of a photon. Let event B represent the arrival of a photon elsewhere. Event here refers to a unique location in space-time i.e (x,y,z,t). As per special relativity, you can always find a reference frame such that the time separation between A and B can be arbitrarily small. It can't be made exactly zero, but it can be made as close to zero as you wish to."
Use this formula to figure out the reference frame of interest.
If you feel like getting mystical about it, for a hypothetical Photonic Being all events are in fact simultaneous: It is always 'now' and per various mystic schools, that 'timelessness' is the actual meaning of 'Eternal'.
Well, maybe so, theoretically. But in fact, there may be multiple light paths between us and remote stuff. And the length of those light paths is in constant flux. Indeed, having data from multiple light paths has proved very useful. So it seems sensible to talk about stuff happening in its own frame, and distinctly about observation delays.
That's true in our reference frame, with some error bar, but astronomers rarely make the distinction when talking about observing events, so I always find it odd when laymen insist on making it.
I guess the distinction is rarely made by professionals because
- It requires defining a reference frame.
- It makes no difference to the causality.
- Time is a function of distance, which usually has large error bars on it, so it's better to discuss the distance instead.
- Time as a function of distance gets more complex on cosmological scales.
On the last point, you can get the exciting realisation that, due to the expansion of space, objects actually start getting larger the further away they get beyond a certain distance.
