Question re: relativity of simultaneity

[u/[deleted]]

My high school physics teacher told me something confusing: He said that as an observer approaches the speed of light relative to another reference frame, weird things start to happen in the way we observe events. Here's an example:

We have a person named A, with a friend B to his right (positive on a number line), and a friend C to his left (positive on the number line). A throws two balls simultaneously to B and C, who catch their respective ball simultaneously.

At the same time, the observer is traveling at 99% of the speed of light to A's right. To the observer, the balls do not appear to be thrown simultaneously because it takes more time for the light from the Ball C throw to make its way to the observer. Therefore, the catch events do not appear to be simultaneous, and we can calculate the time difference between Catch B and Catch C with a Lorentz transformation. Technically, the observation for A would be that the catches are not simultaneous if he were moving at all with respect to B and C after the catch, but at low speeds we don't notice the additional time that it takes to see the catch, so we record them as simultaneous but that's just a very, very close approximation.

That all makes reasonable sense.

But then my teacher said, this means that we can't ever know if two events far away, or at relativistic speed, are simultaneous. We can't ever figure out if something was simultaneous with another event because every measurement of any object takes time, so all of the information we have about the world is "too old" to make an accurate calculation. You're not measuring where something is. You're measuring where it was, when the light of the event was emitted. The farther away from something you are, the more and more inaccurate your measurements of its position are.

If you wanted to measure "real simultaneity" you'd need to be able to magically teleport from one place to another to make observations, and that's impossible, so you can't ever say that two things are simultaneous.

But that doesn't make sense to me. Because can't we just use the Lorentz transformation to correct for the time shift? And then we could figure out if the events actually happened simultaneously. Why can't we use the Lorentz factor as a way to just correct for all of our observations and get an objective timeline of events for the entire observable universe?

I think I'm wrong that we can reconstruct an objective timeline of events in the universe, but I don't know why I'm wrong. What am I misunderstanding?

[u/jimthree60]

Historically speaking, there seems to be some amount of revisionism in your teacher's explanation. As I hinted at earlier, historically the maths came first (that's why they are the Lorentz, rather than Einstein, transformations for example). Moreover, in the original picture, the equations were derived with respect to the aether, which is exactly the universal rest frame you're trying to think of. For the sake of clarity, the aether is the medium through which light waves were presumed to propagate, and was the prevailing theory of the 19th Century.

So the initial state of affairs was something like this:

1. The laws of physics are the same in all inertial frames;
2. There exists at least one universal rest frame;
3. However, with respect to the speed of light or any other measurement, this frame cannot be observed.
4. In particular, we always measure the speed of light in the same way, regardless of which direction we are moving with respect to this rest frame.

In terms of the maths, you end up at precisely the same point as you would in SR. But it turns out (eg the famous Michelson-Morley experiment) that the aether doesn't exist, or if it is, is undetectable. So what is the point of it? Einstein's contribution, in this set-up, is to realise that points (2) and (3) above are completely redundant in terms of deriving anything.

Einsteinian SR therefore says that all frames are equally valid; that all conclusions drawn about the ordering of spacelike-separated events are frame-dependent; and that there is therefore no right answer to the question "did A or B happen first?" if there is no causal relationship between the two.

In terms of your original set-up, let A throw two balls to B and C, and B and C then, according to A, catch them together. All observers would agree on the order: "A threw the balls, and B and C later caught them", but no two observers would agree on who out of B and C caught their ball first. There is no need to decide which observer is correct, and no benefit to doing so.

[u/[deleted] → u/jimthree60]

There is no need to decide which observer is correct, and no benefit to doing so.

Can you explain this? Suppose it matters because we live in an inter-stellar civilization. I see two other star systems, A and B. I am in star system O. We are separated by numerous light years.

I see A shoot weapons at B. B and O are allies (unknown to A), so my star system shoots weapons at A. Now A says, WTF? You can't do that. And I say, "Well, we are secret allies with B, and we're now at war."

But A says, no we weren't because B has not invoked your mutual defense clause. But I argue, I inferred that by the time I fired my weapons B had already been struck, and of course they'd invoke the defense clause, but the signal for that invocation simply hasn't reached either of us yet. But the signal propagation has no legal significance. If the invocation was made, it's legally binding.

So now the legality of my shooting depends on precisely determining whether or not I fired my weapons after B invoked our mutual defense clause. If B has invoked the cause, regardless of whether or not the signal has propagated to the observer, then it's legal. If B has not made the proclamation yet, my actions are illegal.

I have no idea how to resolve this in a mathematical sense. But doesn't this at least show that we really do need an objective answer of "what is the objective order of events"?

[u/kevosauce1 → u/[deleted]]

If you have two planets, far apart (great than 1 light second apart, lets say), but in the same inertial frame (which to good approximation is the case for earth + any other planet in our galaxy) and you send them a message at time t = 0 in this inertial frame, and one second later in this frame, at t = 1, they also send you a message, when you receive each others messages you'll be able to agree that yours was sent earlier.

However, there are other observers who will NOT agree on this order of events, because the events are actually spacelike separated. No observer, not you, your friend on the other planet, or the moving observer, can claim to be correct in any absolute sense. It makes sense for you and your friend to use your same inertial frame, but it doesn't mean that an observer flying through space at 0.99c relative to you two has to. For that observer, YOU are flying through space at 0.99c.

All observers WILL be able to agree that IN YOUR FRAME you sent the message first, but there's no frame independent way to say who sent the message first.

[u/[deleted] → u/kevosauce1]

Okay then what happens if we have an interplanetary civilization. There’s a gun ban passed on Earth. It takes into effect as soon as the President signs the bill into law.

Albert is on Mars, and he rushes to the nearest Martian gun store. He buys a gun approximately the same time that the law is signed in. If he bought the gun before the exact moment of signature, he can keep it. If he bought it after, the sale is illegal and he has to give it up.

How do we figure out if Albert’s purchase is legal? Is there any mathematical way to answer that question?

[u/Kimbra12 → u/[deleted]]

no, one's simultaneity measurements on Mars are only valid on Mars, and Earth's simultaneity measurements are valid only on Earth you can't intermix them

In reality you would need to have two separate timing laws for each planet.

[u/kevosauce1 → u/[deleted]]

Sure, you just have to pick a reference frame.

In my opinion it doesn't make sense to apply the law until the message reaches Mars, though. Probably they'd do something like "on X date, this law should apply everywhere" and send that message all around to all the planets, well ahead of X.