Relativity of Simultaneity question (use Einstein synchronization)

[ESponge2000]

TL;DR

Goal is to calculate the v/c and distance from
Earth for a ship traveling away from earth such that from ship passenger perspective they perceive in the ship rest frame … a moment eating pretzels to occur during World War 2 year 1942 on earth ,

But a year 2025 earth in earth rest frame perceives the ship passenger eating the pretzels to be happening now

So what we need is basically an 83-year discrepancy between the ship’s resting frame relativity of simultaneity ; and the one from the earth

Such that in a fiction hypothetical where FTL
Instant communication were possible to be transmitted , a 2025 passenger could communicate with a world war 2 aircraft through bouncing the signals off the ship. What must the velocity be of this ship and its distance from earth?

 

[phinds]

Instant communication were possible to be transmitted , a 2025 passenger could communicate with a world war 2 aircraft through bouncing the signals off the ship.

Huh? What ARE you going on about? WWII is over and done with. No amount of "instantaneous communication" is going to change that.

Also, nothing with mass can travel as fast as c, so a ship that has left Earth will NEVER catch up with a signal that was emitted from Earth 83 years ago. Or yesterday, for that matter.

If you posit an alien ship that was already in place to catch the 83 year old signal from Earth, instant communication from Earth to that ship and back would just end up with the person on Earth talking to themselves in real time.

I don't wish to be rude, but your whole scenario is just nuts.

 

[jbriggs444]

Earth for a ship traveling away from earth such that from ship passenger perspective they perceive in the ship rest frame … a moment eating pretzels to occur during World War 2 year 1942 on earth ,

But a year 2025 earth in earth rest frame perceives the ship passenger eating the pretzels to be happening now

So what we need is basically an 83-year discrepancy between the ship’s resting frame relativity of simultaneity ; and the one from the earth

Such that in a fiction hypothetical where FTL
Instant communication were possible to be transmitted , a 2025 passenger could communicate with a world war 2 aircraft through bouncing the signals off the ship. What must the velocity be of this ship and its distance from earth?

This is the tachyonic antitelephone.

 

[Nugatory]

Such that in a fiction hypothetical where FTL Instant communication were possible to be transmitted , a 2025 passenger could communicate with a world war 2 aircraft through bouncing the signals off the ship.

Better to describe what you’re looking for as “When we use coordinates in which the ship is at rest at the origin, the event ‘pretzels eaten on earth’ is assigned the time coordinate ‘2025’”. That captures the notion of “at the same time” without assuming impossible instant communication and all the contradictions and inconsistencies that come with that assumption. (A serious problem with your formulation is that if 2025 on the ship and pretzel eating on earth are simultaneous using the ship frame they won’t be simultaneous using the earth frame - so the “instantaneous communication” cannot be defined consistently).
And with that said….

What must the velocity be of this ship and its distance from earth?

The time coordinate using a frame in which the earth is at rest is related to the time coordinate in which the ship is at rest by the Lorentz transformation: $t’=\gamma (t-vx)$ where $t$ is the time coordinate using the ship frame, $t’$ is the time using the earth frame. So set $t’=1942$, $t=2025$, and do some algebra to find $x$ and $v$ values that work. (And in setting it up this way I have chosen a common origin for both coordinates - the ship moving at speed $v$ passed the earth in the year 0).

 

[Orodruin]

The time coordinate using a frame in which the earth is at rest is related to the time coordinate in which the ship is at rest by the Lorentz transformation: $t’=\gamma (t-vx)$ where $t$ is the time coordinate using the ship frame, $t’$ is the time using the earth frame. So set $t’=1942$, $t=2025$, and do some algebra to find $x$ and $v$ values that work. (And in setting it up this way I have chosen a common origin for both coordinates - the ship moving at speed $v$ passed the earth in the year 0).

This is not what the OP requires. This describes a situation where the ship’s clock shows 1942 when (in the Earth frame) time is 2025. This is not what the OP requires, which is a setup where, in the Earth frame, 2025 on Earth is simultaneous with event P(retzl) but P is simultaneous with WWII on Earth in the ship’s frame. These two situations are not equivalent.

Huh? What ARE you going on about? WWII is over and done with. No amount of "instantaneous communication" is going to change that.

Also, nothing with mass can travel as fast as c, so a ship that has left Earth will NEVER catch up with a signal that was emitted from Earth 83 years ago. Or yesterday, for that matter.

If you posit an alien ship that was already in place to catch the 83 year old signal from Earth, instant communication from Earth to that ship and back would just end up with the person on Earth talking to themselves in real time.

I don't wish to be rude, but your whole scenario is just nuts.

You focus on entirely the wrong part of the OP. They are - admittedly clumsily - trying to describe what ”the same coordinate time” would mean. That doesn’t mean the actual question itself is nonsensical.

 

[Ibix]

TL;DR Summary: Goal is to calculate the v/c and distance from
Earth for a ship traveling away from earth such that from ship passenger perspective they perceive in the ship rest frame … a moment eating pretzels to occur during World War 2 year 1942 on earth ,

But a year 2025 earth in earth rest frame perceives the ship passenger eating the pretzels to be happening now

So what we need is basically an 83-year discrepancy between the ship’s resting frame relativity of simultaneity ; and the one from the earth

Such that in a fiction hypothetical where FTL
Instant communication were possible to be transmitted , a 2025 passenger could communicate with a world war 2 aircraft through bouncing the signals off the ship. What must the velocity be of this ship and its distance from earth?

As others have noted, the inclusion of FTL communication is unphysical and makes arbitrary interpretation of your question possible. If you mean you want to find an event $E$ on the ship's worldline that is simultaneous by the ship's rest frame with event W (WW2, 1942) and simultaneous by the Earth's rest frame with event P (pretzel eaten, 2025), then state it like that.

@Nugatory has laid out the algebra. I'd draw a spacetime diagram using the Earth's rest frame.

1. Draw Earth's worldline on this diagram.

2. Draw events W and P.

3. Draw Earth's simultaneity plane through P.

4. Mark out the region that cannot be simultaneous with W.

5. Where are you left with that E can possibly be?

6. When could the ship have left Earth to reach points in the region you worked out in 5?

7. You'll find you have a lot of choices. You may either pick a distance in Earth's 2025, a departure year in Earth time, a departure velocity, or the equivalent values in the ship frame (athough those are harder to work with in this diagram). How does this constrain the location of E? (Hint: worldlines and their rest frame's simultaneity planes are orthogonal in the Minkowski sense.)