Hypothetically, you should be very cautious when mixing relativity with quantum mechanics.
I reran this with an egg cooking instead of the observer. That allows them to continue observing, which is handy for both the experiment and recruitment. We had some difficulty getting volunteers after the last incident.
To start, we have Alica and Bob, our two observers. Alice will stay home on Earth as the non-accelerating observer and watch the contents of Bob's spaceship using the Bloody Expensive Telescope (BET). Once he's safely out of the atmosphere, Bob will accelerate rapidly enough to cook an egg using the Unruh effect. All observers and equipment will be made indestructible before beginning in order to avoid death by ageing, radiation, or the Humpty Dumpty effect.
The acceleration needed to heat an egg to boiling via the Unruh effect is truly absurd, some
10^24 m/s/s. You can produce accelerations of that magnitude and
we have, just not for very long. But, as any of you who have ever cooked an egg will know it takes about 10 minutes or so, depending on how you like your yolk. In those minutes Bob will accelerate very, very rapidly. Long before the egg timer has ticked off its first second, relativity has kicked into overdrive to keep Bob from accelerating through the speed of light. He will get within a gnat's whisker of that universal speed barrier as the egg cooks.
What Bob Sees:
Inside the spaceship, Bob sees enough acceleration to grind individual atoms to a fine subatomic paste. Good thing we built out of Indestructium. Due to the acceleration, the temperature of the quantum vacuum within the rocket rises to the boiling point and over the next few minutes the egg cooks, much as one might expect it to. Hopefully he remembered to poke a hole in it, because the egg isn't cooking via normal heat transfer, it's cooking because the temperature of the quantum vacuum in the spaceship is 100 C!
What Alice Sees:
Back on Earth, Alice watches Bob go hurtling off into the cosmos. Although initially spectacularly and devastatingly bright, especially to all life on Earth, Bob's spaceship rapidly dims and dwindles, almost as if it were time dilated and redshifted by travelling so close to the speed of light as makes no difference. The light from his spaceship becomes more and more redshifted, eventually reaching such absurd wavelengths that it can't be meaningfully contained within the observable universe. Sadly for Alice, this is a thought experiment and there are no such realistic constraints. Standing amidst the ashes of her world, she realises with growing horror that the few minutes needed to cook the egg will be stretched to near eternity by relativistic effects. Imprisoned in her observatory for all time, Alice watches as glaciers come and go, the stars burn out, and the universe itself burns down to a fine ash of subatomic particles, all the while the last human in existence recedes from her through the eternities of her torment. She watches as the egg, the very last morsel of food, damn you for concocting this thought experiment and not even providing your creations with food oh if only I weren't indestructible and could seek release in oblivion! Where were we? Right, I suppose that Alice might take a moment away from using a near-eternity and the now-abandoned resources of a once bustling and highly advanced space-faring civilization to plot the cold-blooded murder of her tormentors to check the egg now and then.
To Alice, time aboard Bob's spacecraft slows to a nearly imperceptible crawl. The temperature of the quantum vacuum never changes, but the temperature of the egg, and all of the material within the spaceship, rises ever so very slightly. Over timespans meaningful only to cosmologists and geologists the egg inexorably cooks. The energy required to heat the egg is drawn via quantum processes from the power being applied to the rocket in order to accelerate it. This all takes place at rates that make plate tectonics look downright giddy.
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