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> More specifically, the event happened 26,000 years ago in our reference frame.

Isn't this wrong? Surely we would say that, in our reference frame, the event happened precisely when we observed it happening. That's what "frame of reference" means: it's whose clock we use to say when an event occurred.

No, your interpretation is not quite correct. You do indeed use your own clock to determine the time of events in your own frame of reference. But you still need to account for the light travel time of the event. This is why you need both the position and the time of the event in order to do a Lorentz transformation.

To see this another way, suppose you saw two events at the same time, one two light-years away, and the other one light-year away. In your interpretation you would call those events simultaneous. Simultaneous events cannot affect each other in any reference frame. But if the two events were in a line, the light from the first event could have triggered the second.

> To see this another way, suppose you saw two events at the same time, one two light-years away, and the other one light-year away. In your interpretation you would call those events simultaneous.

Yes, I would say that those events occurred at the same time in my reference point, while also recognizing that we can't say in an absolute sense that they were simultaneous. Isn't that the point of relativity of simultaneity?

You're confusing the local observation time of a phenomena with the time the phenomena occurred as observed from our frame of reference and relative distance from its origin.

Special Relativity states that the time (component of spacetime distance) to an event depends on the relative velocity (angle) of the observing reference frame. It does not state that an event occurs at the moment it is observed; that would imply light has an infinite velocity.

The whole point of relativity is that events do not occur at the exact moment they are observed, because light has a finite velocity. The fact that light's finite velocity is the same in all reference frames is what causes reference frames to tilt their spacetime angle according to their velocity.

It's the same as saying the Y component (height) of a line segment changes if you rotate it. The length of the line is the spacetime distance, the height (Y component) of the line is time, the x component is spatial distance, and the angle of the line depends on the relative velocity of the observer.

No, in our reference frame it took 26,000 years for the light to travel to us so that we could see it. We measure that the event occurred 26,000 light years away so we calculate that it occurred 26,000 years ago. There are other reference frames where it also happened 26,000 years ago but that are much closer and saw it occur earlier. There are also reference frames where it happened 26,000 years ago but they haven't observed it yet because they are much further away. And as OP mentioned, there are reference frames where it occurred 5 million years ago yet it still hasn't even been observed.

I clearly don't have a grasp of reference frames. Can someone elucidate?

The event occurred is 26,000 light years away, we date it as having occurred 26,000 years ago.

How is it that a location that's closer, say 10,000 light years, would have dated the event to 26,000 ago rather than 10,000 light years?

The only interval that is constant in Special Relativity is the spacetime interval. It's a distance measure. In 3D space, we normally say that distance is given by

ds^2 = dx^2 + dy^2 + dz^2.

In Special Relativity, you define a quantity called the spacetime interval:

ds^2 = -(c*dt)^2 + dx^2 + dy^2 + dz^2.

You treat time as a 4th dimension, and take it into account when calculating distances. Notice that this interval can be negative (the metric is "semi-Riemannian"). "Events" (locations in 4D spacetime) can only be causally connected (one can influence the other) if the spacetime interval separating them is negative (this is equivalent to saying that no information can ever propagate faster than light).

The key is that all non-accelerating observers agree on the spacetime interval between any two events. The spacetime interval between two events is the only solid distance you can give. The time interval by itself depends on the observer's reference frame (you've probably heard of time dilation). So too does the spatial distance (length contraction). But time dilation and length contraction behave in such a way that the spacetime interval remains constant.

The long and the short of it is that time intervals are observer-dependent.

The closer location would have received the signal 16,000 years earlier than us here on Earth. They would still say that it happened 10,000 years before they observed it, but they would still say it happened in year 24,000 BC.

> ... but they would still say it happened in year 24,000 BC.

I can't imagine that they would say that!

I'm sure that you mean the equivalent of 24,000 BC in our reference frame, after Lorentz transformation. Not that they would likely even know about us, or manage the transformation.

This is bloody confusing.

Assuming these people 10000 lightyears away from the black hole are also on a planet, their reference frame is almost the same as ours - the relative speed of different planets is very small compared to the speed of light. So they'll agree on when 24000BC is.

Why would they have a Christ?

Or know when ours was supposedly born?

The key in that case is that the other reference frame that from our reference frame will measure a different distance to the black hole. It might be 25000 light years away from them, but we would not be 25000 light years away (but longer I believe) in their reference frame.

This can happen for instance with extreme differences in relative velocities. Someone else can probably show an example with the math, but a key concept here is the that distances also change when you move real fast or are in a deep gravity well.

It isn't just about location. Someone moving between both sources near the speed of light would have the event occurring a much shorter time ago.

Are you saying that the only reference frame where the event happened "now" is the reference frame of the black hole itself? I'm quite familiar with relativity of simultaneity, and that would lead me to conclude that from my reference point, two things happened simultaneously: the black hole flared, and the clock read 11am on May 13th, 2019. Given this, I would think we would describe that in English as "the black hole flared at 11am on May 13th, 2019."

What do you mean by "now"? Which clock are you talking about? A clock here on Earth?

Clocks here on Earth currently read May 13th, 2019. And you can conclude that we observed the event on May 13th, 2019. We believe the black hole is approx. 26,000 light years away. Thus we know the light took 26,000 years to reach us. So we say the event took place around 23,981 BC.

We have 3 events here:

A. A clock on Earth reading May 13th, 2019

B. Light from the black hole flare reaching Earth

C. The black hole flaring

We can say that A and B occurred simultaneously in all reference frames (they occurred at the same location and at the same time). C did not occur simultaneously with A or B in any reference frame (except perhaps, debatably, that of something moving at the speed of light).

> Clocks here on Earth currently read May 13th, 2019.

Are you sure that we are in the same reference frame? I’m willing to accept that you started a fairly short journey at some appreciable fraction of C, turned around and gave just recently arrived back home, but I’m going to need some proof.

Hahah, oops. I assumed the date given by parent was today's date and didn't think about it much. I guess I should have said August 13, 2019. My bad.

I guess I’m just struggling to see how there is any useful sense in which the event happened in 20,000 B.C. from our perspective when it would be impossible for it to have had any causal effect on us until May. I don’t think this is a disagreement in the basic understanding of relativity, but rather a disagreement in semantics.

If a baby fall in another room and you only hear them crying half an hour later, it doesn't mean the baby just got hurt. Both you and the baby still agree when it happened, you just learned about it later.

The same is true regarding the black hole flare. Except that we are not only learning about it now due to negligence, but because we, with all current knowledge in physics we have and also our technology, we don't have a way to see what's happening right now. But say an astronomer finds a wormhole and points their telescope to it. They could know about things that will only be visible by everyone else in 26,000. Time to invest in those black hole futures.

Yes, except our clock says it happened 26 ky ago. OP mentioned how it would look in other frames.

This is a Lorenz geometry definition of reference frame, not an everyday sense of “frame of reference”

If someone is murdered now (evening of August 13th) and their body is discovered tomorrow at 7am, does that mean they were murdered at 7am?

If I call my friend at 7:30am and tell him, does that mean the person was murdered at 7:30am?

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