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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 29/11/2024 19:12:02 »

The passenger in an accelerating  rocket may read 1 g on his accelerometer because he is being pushed from behind. Having landed on Earth his instrument will read 1 g because he is being pulled from below.

No, both cases are due to being pushed from below. Were it not for this push, both cases would locally experience no proper acceleration. The two cases being locally indistinguishable is the essence of the equivalence principle, and not the below suggestion:

But acceleration does not produce gravity as [chatGTP] implies

I think it's the implication from equivalence principle.

You show signs of not having read the critique at all, since it is that assertion that was colored red every time it was made.  The equivalence principle is not in any way applicable to the mathematics of an accelerating frame, either locally or not. It makes it sound like the mathematics of special relativity was derived from general relativity and not the other way around.

Two balls are connected by a string, floating freely in outer space. They are spun until having a constant angular speed. No energy is expended afterwards, even though the balls are continuously accelerated.

Excellent counterexample.

Consider one ball moving in a straight line at constant speed. If we want to change its direction we need to exert a force perpendicular to the track, so work is done.

A force perpendicular to motion does no work, which is why the 2 balls on a string don't slow in their rotation over time.

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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 29/11/2024 00:26:06 »

. Having never used supposed "AI"(no intention of doing so-you can't teach an old dog new tricks!), I am in a weak position to criticise. I have seen some atrocious rubbish in replies to questions posed by others and a high degree of suggestibility. In response to a question that requires a blunt "NO", answers will often digress into unsubstantiated speculation with the seeming aim of perpetuating the discourse rather than delivering a straightforward answer.

This is very perceptive.  Yes, the answers always seem agreeable, and if you protest a correct answer by asserting your own sufficiently plausible rubbish, none of the LLMs seem capable of telling you that it's still rubbish. It might seem a bit skeptical, but it will encourage you to explore your line of thinking rather than point out where it contradicts evidence or contradicts itself.

I didn't want to tell copilot that its answers were rubbish. I had hoped that it would figure it out itself after I pointed out inconsistencies in its replies.

We may not need forum moderators in the future, an LLM can analyse and critque the work produced by the forum users LLM well enough.

Moderators are needed to moderate, to recognize and deal with posts not complying with the rules. Being correct is more of a job for site experts, be they moderators or not.
I'm no expert in pretty much any subject, but I know enough to take apart a lot of answers I see from AI.

(I copied and pasted the reply @Halc obtained from Gemini).....   

Actually, Hamdani provided replies from both chatGPT and gemini. I just copied his quotes so I could color them

My replies below are replies to chatGPT apparently agreeing with much of what gemini had to say..

You say that "spacetime is curved due to the acceleration" in an accelerated frame..... It would be better to mention that acceleration causes the perception of curvature, or locally mimics gravitational effects due to the equivalence principle.

But that isn't right. There is no curvature locally, so there cannot be any local perception of it. In the non-local case, most of the effects are due to the accelerated frame. it is quite hard to distinguish curved spacetime from flat since all the effects are present in both, but differently.
For instance, I am under proper acceleration of 1g and dangle a clock on a long rope. In both cases the clock on the rope will run objectively slower, so that effect is not due to curved spacetime. But the two cases differ a bit for how much slower since they differ. Nearby, it differs but a little, but for a gravitational field of a small mass, it can differ a lot over not that much distance.

The equivalence principle does not suggest any of this

In an accelerating reference frame, spacetime itself doesn?t curve in the same way...

It doesn't curve at all. Spacetime curvature is objective, not a coordinate effect, and an accelerated frame is just a coordinate choice. I would have immediately grilled gemini on this point, but I have no access to it.

students using LLM to write the essays and someone else using a LLM to mark and grade them.

They get what they deserve if they commit the same sins. Education should devolve into GIGO. Nobody should pay for any pseudo-education implemented in this manner.


I talked to my AI about black holes and got Newtonian answers in response. It had no clue.
Thought of another one: Sagnac effect is a favorite empirical disproof of anything Einstein.  Let me have a go:


Does light travel west faster than it does east?

Light travels at a constant speed in a vacuum, ... This speed remains the same regardless of the direction in which the light is traveling, be it west, east, or any other direction.

The notion that light could travel faster in one direction over another doesn't hold up according to our current understanding of physics. The speed of light is influenced by the medium through which it travels (such as air, water, or glass), but not by the direction.

So if I create a vacuum tunnel and some mirrors around the world and shine a pulse in both directions, both pulses will return to the origin spot at the same time?

Yes, exactly! In your vacuum tunnel setup, if you shine a pulse of light in both the west and east directions simultaneously, both pulses would return to the origin at the same time. The speed of light in a vacuum is constant and does not depend on the direction of travel.

This constancy of the speed of light is a cornerstone of Einstein's theory of relativity and is true regardless of the motion of the source or the observer. It?s one of the fascinating and sometimes counterintuitive aspects of the way our universe works.

So the Sagnac effect disproves relativity then? It predicts that west and east light go different speeds and measurement of this difference is used to detect absolute rotation. Sure, most Sagnac devices have a far smaller circumference than a planet, but the principle is the same

...The Sagnac effect occurs in rotating reference frames, such as a rotating disk or the surface of a spinning planet like Earth. In these scenarios, if you send two beams of light in opposite directions around a loop, they will take different amounts of time to complete the loop.

So the two pulses do take different times to come back to the emitter then?

Yes, in the context of the Sagnac effect within a rotating reference frame, the two pulses of light would indeed take different amounts of time to return to the emitter.

Not in the context of Sagnac. In the context of what actually happens

Let's break this down in the context of what actually happens with light pulses and rotation.

If you set up a vacuum tunnel with mirrors and shine a pulse of light in both the westward and eastward directions, the two pulses would indeed take different amounts of time to return to the origin if the system is rotating.

So I didn't color anything, but it didn't take much to get it to contradict itself. The LLM did not take into account the rotating frame of reference in the first reply because despite the real-Earth scenario, I didn't word the question in a way that drew attention to the fact that we're working with a rotating frame, despite the fact that west and east are not even defined on a planet that doesn't rotate.

I did word the one query as an attempt to discredit relativity like so much training material attempts to do, and it at least didn't take that bait. I partly wanted to see if I could lead it down a false path if it looked like it was my purpose to do so.

The copilot replies were edited heavily, cutting it down to actual replies, and cutting out all the educational stuff it tried to add on, and of course all the congratulatory stuff at the end about how perceptive my questions are. It tacks that on to ever single reply in some form or other.

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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 27/11/2024 19:09:27 »

Asking chatbots about relativity is almost always going to get wrong answers.
I can highlight the wrong and particularly correct and really wrong answers.

Is GR needed for accelerated frames of reference?

Yes, General Relativity (GR) is necessary when dealing with accelerated frames of reference, especially when the acceleration is significant or when gravitational effects are involved. While Special Relativity (SR) handles inertial frames (non-accelerating), GR extends the theory to include non-inertial frames, such as those that are accelerating or influenced by gravity.

In GR, gravity is not seen as a force but rather as the curvature of spacetime, and this curvature affects how objects move, including those in accelerated reference frames.  So, for understanding the full effects of acceleration, particularly in the presence of strong gravitational fields, GR is required.

ChatGPT tries to sneak in gravity since yes, GR is needed to deal with gravity. But acceleration does not produce gravity at it implies. It seems to just repeat this comment a number of times.


At least ChatGPT doesn't attempt to leverage the equivalence principle, which I cannot say for the other examples.  Gemini is definitely the worst of the bunch.

The same question for Gemini,

Yes, General Relativity (GR) is crucial for understanding accelerated frames of reference. Here's why:
 * Equivalence Principle: GR postulates that gravity and acceleration are equivalent. This means that an observer in a uniformly accelerating spaceship cannot distinguish between the force of acceleration and the force of gravity. This principle forms the foundation of GR.
 * Curvature of Spacetime: In GR, gravity is described as a curvature of spacetime. This curvature is caused by the presence of mass or energy. In an accelerated frame of reference the spacetime is curved due to the acceleration.
 * Time Dilation and Length Contraction: GR predicts that time runs slower in a gravitational field or an accelerated frame of reference. This is known as gravitational time dilation. Additionally, objects appear shorter in the direction of motion in an accelerated frame, a phenomenon called length contraction.
 * Global Positioning System (GPS): GR is essential for the accurate functioning of GPS satellites. The satellites are moving at high speeds and are at a different gravitational potential compared to Earth's surface. Without accounting for GR, the GPS system would be significantly inaccurate.
In summary, GR provides a comprehensive framework for understanding the physics of accelerated frames of reference. It is a fundamental theory that has been experimentally verified and is essential for many modern technologies.

That was horrible. I would love to have questioned Gemini after that comment and show how it directly contradicts itself.  I tried to do it with copilot, getting this conversation, not as bad as the two above. This is actually my first intentional interaction with any LLM ever.

Is GR needed for accelerated frames of reference?

In some ways, yes. Accelerated frames of reference are closely tied to the principles of General Relativity (GR). Unlike Special Relativity, which deals with constant velocities and inertial frames, General Relativity accounts for acceleration and gravity.

Einstein's theory of General Relativity generalizes the idea of relativity to include non-inertial (accelerated) frames of reference. It essentially states that the presence of mass and energy curves spacetime, which in turn affects the motion of objects. In this context, acceleration can be considered equivalent to gravitational effects?a principle known as the equivalence principle.

So, while you might not need all the complexities of GR for simple cases of acceleration, understanding the full implications of accelerated frames and gravityindeed requires the framework provided by General Relativity. If you're diving deeper into areas like gravitational waves, black holes, or cosmology, GR becomes essential.

Try as I might, I cannot get copilot to mention accelerated frames without dragging gravity into it as well, making the comments ambiguous.

But there is no curve spacetime under special relativity. Are you saying that acceleration creates spacetime curvature?

You're correct that Special Relativity (SR) doesn't involve curved spacetime. SR deals with inertial frames of reference?those moving at constant speeds relative to each other?and doesn?t account for acceleration or gravitational effects.

Note the evasion of actually answering the question.

In General Relativity (GR), however, acceleration and gravity are indeed linked to the curvature of spacetime. The equivalence principle in GR states that locally (in a small region of spacetime), the effects of acceleration are indistinguishable from the effects of gravity. This means that in an accelerated frame of reference, the spacetime can be thought of as curved. So, yes, acceleration is related to spacetime curvature in the context of GR.

Think of it this way: in an accelerating elevator, you feel a force pushing you down, similar to gravity. GR explains this by suggesting that the acceleration causes a curvature in spacetime, akin to how a massive object like Earth curves spacetime, creating what we perceive as gravity.

What do you mean by acceleration being linked to curved spacetime? Does it curve spacetime or not? The equivalence principle indeed says that locally, the effects of acceleration are indistinguishable from gravity, but locally, spacetime is not curved, gravity or otherwise. You seem to imply otherwise when saying "This means that in an accelerated frame of reference, the spacetime can be thought of as curved" when the opposite is true, that locally, even under gravity, spacetime can be thought of (and is) flat.

You bring up an excellent point. You're right?locally, spacetime is considered flat, even in the presence of gravity. Let's clear up the confusion.

The equivalence principle states that within a sufficiently small region of spacetime, the effects of acceleration are indistinguishable from the effects of gravity. In this local sense, spacetime can be approximated as flat, which aligns with your statement that locally spacetime is not curved.

To clarify: acceleration itself does not directly cause spacetime curvature. Instead, in GR, acceleration and gravity are related through the equivalence principle. When we consider larger scales or longer durations, gravity (or the presence of mass and energy) causes spacetime to curve. This curvature affects how objects move, leading to what we perceive as gravitational effects.

So, while an accelerated frame of reference might feel similar to experiencing gravity, this does not imply that acceleration curves spacetime in the same way mass and energy do. Locally, spacetime remains flat, and the equivalence principle helps us understand why the effects of acceleration can mimic gravitational effects in small regions.

There was more, but you get the idea

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Chemistry / Re: Shrink ray or growth ray, how could they work?

« on: 22/11/2024 22:05:03 »

I recently watched the Movie "Honey I Shrunk the Kids"

Fantastic Voyage was there first, or at least earlier.

explanation was essentially that atoms are 99% empty space, so all you have to do is collapse it down a little bit or expand it a little bit. Tah dah!

That gets you a bug sized thing that masses the same as the original. It would sink into the dirt like a nail being pounded in.

That said, super-dense matter is possible such as in a neutron star, but it takes pressure. The Pauli exclusion principle prevents the explanation given above. It's a classical explanation given to a quantum problem.

One way I thought it might be possible would be y changing the mass of the involved particles.

That eliminates one of the problems I mentioned above, but introduces a whole new zoo of particles with new laws, which you seem to mention in your post,.

Very small effects can be seen in examples of isotope effects--bond length contraction in molecules composed of heavier isotopes compared to equivalent molecules with lighter isotopes.

Isotopes differ in number of neutrons. Nothing is going to shrink significantly just by making isotopes, even if the mass alters a bit.

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Question of the Week / Re: QotW - 24.11.22 - Why are boat propellers at the rear?

« on: 15/11/2024 12:41:35 »

There are exceptions to both, but in general, a propeller at the front of a boat would put higher velocity water against most of the hull, increasing drag. This is also true of aircraft, but it also increases lift.
An aircraft is more stable if pulled from the front, but a boat is more maneuverable with it at the rear.
The boat relies on the high speed water for its rudder to work, so the rudder needs to be behind the propeller.
A small boat tends to lift its bow out of the water at higher speeds, not a good thing if the propulsion is there.

A reason not to:  If somebody falls overboard, there's very much a danger of being sucked into the propeller flow, not so true if it was up front.

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Physics, Astronomy & Cosmology / Re: Has anyone heard of tresino theory?

« on: 14/11/2024 21:57:16 »

A tresino is apparently quite stable, and its discovery (a 5th phase of matter, one beyond the 4th:plasma) seems to have implications on all sorts of things unexplained until now, including why the corona of a star gets so much (100's of times) hotter that the surface of the star, and why planets take so long to cool down.

I don't see how a particle can be a phase of matter at all, but apparently this 5th phase involves some proportion of tresinos, like plasma involves nuclei stripped of their electrons, thus destroying their identity as 'atoms'.

It is theorized that tresinos were a common state of matter early in the universe, but no 'very' early since it took many epochs for things like protons to form in the first place.

Apparently cold fusion, not understood well at first, may finally be explained by properties of the tresino. It isn't fusion, but it may still well be a viable energy source. Much to learn first.

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Just Chat! / Re: A query on Trump's tactics

« on: 07/11/2024 01:02:56 »

curtail the power and influence of the "wicked elite class"

I don't think he sold this message. It was more the 'you are the elite class, and the immigrants are taking your money'.

People are super easy to herd around like sheep, at least a large portion of them are. Trump is excellent at exploiting that, creating false things to fear so the sheep run away from the phantom threat. He's not the only one to do this, and history is full of those that exploit the public this way.
The liberal party is notoriously bad at leveraging such methods, instead believing that people are intelligent and can discern fact from a fiction that bolsters their feelings.  Heck, I watched the campaign sort of passively and noticed an almost complete lack of facts about either candidate, and what those facts mean to you, the voter. For a party that is supposed to be about truth, they didn't expend very much effort educating the public, none of whom were listening anyway.

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Physics, Astronomy & Cosmology / Re: Is it Just Hadrons that The Large Hadron Collider...collides ?

« on: 29/10/2024 19:27:09 »

What is so special about Hadrons ?

They're made of smaller things.

Are there other particles on the menu to be collided too ?

For the most part, no. Electrons for instance are not thus accelerated, although it seems capable of it.

How do they store the particles ?....are they kept in a test tube or something ?

Everything is made of them, so it is simply a matter of isolating them (from Hydrogen say) and then sending em down the pipe.

How many particles are fired at one time ?

Hundreds of billions (of protons, which are hadrons) per beam, and multiple beams.  I've heard a thousand times that figure, so not sure if there are thousands of beams or they can make some beams more dense.

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Physiology & Medicine / Re: What Happens To White Cells After They Have Dealt With An Infection ?

« on: 29/10/2024 18:15:28 »

Could a white blood cell come to the end of it's life whilst it is fighting bacteria ?...do they just get reabsorbed ?

Soldiers die in the fight. Some live through the battle and die of natural causes.
A dead cell leaves litter and nutrients that either get absorbed by something or more likely filtered out by the kidneys. It's part of why it's so important to drink when sick. Kidneys are working overtime, yelling "bring out your dead!" and need water to do it.

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Physics, Astronomy & Cosmology / Re: Are Atoms Perpetual Motion Machines ?

« on: 29/10/2024 18:12:28 »

Where does the energy come from ?

It was always there since the atom was made.

2: Does this make atoms (et al) Perpetual Motion Machines ?

No. A PMM is something from which indefinite work can be extracted, at however small a rate. One cannot extract indefinite energy from the motion of an atom.

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Physiology & Medicine / Re: What Happens To White Cells After They Have Dealt With An Infection ?

« on: 29/10/2024 17:15:32 »

Blood cells (of any type) are fairly short lived, so the white cell counts go down by attrition and lack of many more being produced after their need is gone.  The counts return to normal levels around 5-25 days after infection is cleared, depending on the sort of infection involved.

Red cells might live 4 months. White cells have a life expectancy of only a few days, so if you stop making them in abnormal quantities, their numbers quickly decrease to normal levels.

I have given a unit of red blood cells, and that has the longest wait time before I'm allowed to donate again. Giving whole blood, plasma, platelets, all have shorter wait times.
I've not heard of giving white cells, but I know that early in the covid days before the vaccines came out, whole blood from a person who had recently gotten over a covid infection was in serious demand to serve as a treatment for the more dire cases.

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Just Chat! / Re: What is the purpose of the conductor in an orchestra?

« on: 28/10/2024 13:31:59 »

but the principal job of a non-playing conductor is to moderate the balance between sections more subtly than the dim and cresc markings on the score, and to add interest by varying the tempo and accent.

Not during performance I hope. This moderation (interpretation of the composer's dream) is done at rehearsal and hopefully not significantly changed in performance. There is also something to be said about changing it up when something is performed night after night, as opposed to school performances that tend to occur 1-3 times at best.


And Alan, love the anecdotes.

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Just Chat! / Re: What is the purpose of the conductor in an orchestra?

« on: 28/10/2024 13:29:24 »

To be honest, if our conductor made an impromptu change in something just on the night when a piece was being performed, then a lot of us would have missed it and played the thing as we did in rehearsals anyway.

It would seem terrible if any alteration was made without rehearsal. Yes, it's during rehearsal that he's most needed, but also most ignored because until the music is more familiar, concentration is mostly on the paper and less on the peripherally visible conductor..

We had a school band piece where you play the first half, then the 2nd which starts with one of those attacks after a long pause between the halves, then the first again exactly the same. In concert (a competition), our conductor was quite nervous and got to the end of the first half and mistaken thought he had finished, putting the baton down. We're all waiting for the attack signal. Of maybe 80 of us, I think I heard two small toots. The rest of us were watching and very confused. The band leader picked up on our distress immediately and resumed, but it wasn't supposed to go that way.

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Just Chat! / Re: What is the purpose of the conductor in an orchestra?

« on: 28/10/2024 13:21:50 »

Halc, I am going to dispute, most likely out of ignorance!, something you said. You suggested that after a long pause or a sustained note it is entirely not clear when the attack of the next note is supposed to be. Surely if one has a good sense of time(something I lack) coupled with the sheet music, one has a pretty good idea?

They've practiced, so yes, but a pretty good idea doesn't get everyone on the attack simultaneously, and there's no beat to follow through say a fermata.

In a choir, our was small enough to lack a conductor, so heads turned to the organist and head nods. You get this piece with a loud long final note that needs an abrupt cutoff. All of us are looking at the organist (well to the side, hard to see from the rear, or down in a pit, invisible to the audience) for the head nod. It sounds terrible if the voices don't cut off as one.

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Just Chat! / Re: What is the purpose of the conductor in an orchestra?

« on: 27/10/2024 17:53:22 »

It's to keep everybody in sync. If you're in one corner of the band/orchestra, you might not be able to hear all the others, and one group can get devastatingly out of sync with others. We ran into this marching in Mexico city, 6 wide down a 2 lane road. A car was parked, blocking one lane, forcing 3 columns to go and the other three to follow. This spit the drums and made it so those in the rear could not see the conductor (the drum major up front with the super tall stick).  We got measures out of sync and it was a disaster. Those who heard both sides just stopped playing.

Anyway, imagine a classical piece with a dramatic pause or long held note. It is entirely not clear when the attack of the next note is supposed to be. The conductor makes this explicit, and everybody should be watching for it.

Small groups (jazz ensembles, barbershop quartet, etc) don't need one, but usually one of the players visible to all uses head/instrument motion to fill the role.

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Question of the Week / Re: QotW - 24.11.01 - If dinosaurs hadn't gone extinct, would humanity have emerged?

« on: 25/10/2024 13:38:03 »

If the extinction event which killed off the dinosaurs hadn't occurred, would mankind still have risen to become the dominant species?

Evolution is a chaotic system, so even if one leaf took a minute longer to fall from some tree back 75 million years ago, mankind would not ever have existed.  Everything we know would be different. Some other intelligent species may have evolved, perhaps related to an octopus, probably the next most viable candidate.

Mammals were long since around since before the extinction of the dinosaurs, so there would very much be mammals of some sort, just not the ones we see today.

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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 17/10/2024 17:00:23 »

I had been told years ago by a theoretical physicist(who now holds a distinguished position at an American university but who will remain nameless) that GR was needed for accelerated frames of reference.

That's actually pretty sad for somebody claiming those credentials.  I googled "is GR needed for accelerated reference frames" and got correct replies from several sources with poorer credentials, but one from a university site.

AI overview: "No, general relativity (GR) is not required for accelerated reference frames:

    Special relativity (SR) is sufficient
    SR can handle accelerated frames and objects, and is sufficient to explain the Twin Paradox. SR is valid in the presence of accelerations because it describes flat Minkowski spacetime"

That is a very poor reference (as is any LLM), but it's correct.  The twin paradox bit is barely relevant since discussion of it is rarely described via changing accelerated reference frames.  That quote seems to answer more "Is GR needed to describe acceleration" rather than to describe accelerated frames, but accelerating objects are perfectly well described in inertial, accelerating, expanding, rotating, and other kinds of frames.

The next hit is better, from University of California, Riverside
"It's a common misconception that special relativity cannot handle accelerating objects or accelerating reference frames. Sometimes it's claimed that general relativity is required for these situations, the reason being given that special relativity only applies to inertial frames. This is not true."

I got no immediate hits that said that GR was required, but I'm sure they're out there. Bottom line is, GR is needed for curved spacetime, which only comes into play with gravity and dark energy, and none of the discussion here has been about those things.  I do not know my GR well enough to say do the tensor calculus required to generate numeric answers. Tensor mathematics is not required for anything in SR, including Rindler frames.

"What is the exact cause of the time dilation of the twin?"
The same thing that causes time.
And I'm not sure we actually know what that is.

I don't think time is something that is caused.  It is exactly like asking what causes distance, which seems to be an ill-posed question.  I do agree that most of the recent discussion has digressed from the immediate topic title, but since it is mostly framed as questions about relativity and not assertions of speculations, I've not moved any of it to the lighter side.

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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 17/10/2024 14:10:29 »

Is the bold statement backed up by experimental evidence?

I don't think they've ever made a set of gears with a 1000-1 size ratio, let alone turn any reasonably rigid object at significant relativistic speeds.  The bolded statement  is backed by the very simple mathematics of γ=1/√(1-v²) which is identical on both sides since the sole variable v is identical on both sides.

If an identical measuring tape is glued to the ship, will the earth observer see two of those tick marks go by every second?

The situation is not symmetrical since the ship is accelerating and the Earth is not.  Earth can have a tape measure of indefinite length attached to it, one that the ship can read forever.  The ship (at proper acceleration of 1G) can trail not even a light year of tape behind it.  The tape cannot extend beyond the ship's event horizon without breaking.

How many ticks per second the Earth observer sees depends on when he looks.  At some point, the ticks go by infinitely fast just before the tape ends, and then they see no more.
There was that ship event where the ship guy sees 2 ticks/sec go by.  In Earth frame, the event there that is simultaneous with that ship event, the tape will already have been exhausted.

I made the mistake of trying to apply SR to a scenario where some of the frames of reference were not inertial and were thus in need of GR for solution.

GR is only needed for situations involving gravity (which I suppose my black hole mention does).  But the accelerating frame of the ship is a straight SR exercise.  You might want to look up Rindler frame or Rindler coordinates for info on how SR treats an accelerating frame like this.

SR handles accelerating frames just fine, as it does rotating frames. It handles normal expanding frames as well, but not accelerating expansion frames which involves dark energy and puts things into GR territory.

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Physics, Astronomy & Cosmology / Re: What is the optimum speed to make a point in space disappear?

« on: 16/10/2024 16:48:22 »

I read-read that and I did come across kind of snarky. Apologies for that.

In the example in the other thread where the spacecraft was travelling at 2c relative to the tape measure you said the earth would be hardly receding at all and that it would not reach 1 light year with unlimited time of travel of the craft.

Right, but it has nothing to do with speed, but rather continuous proper acceleration.  The greater the proper acceleration, the closer the event horizon is to the ship, and Earth will never fall through the event horizon, but will instead remain close (in the accelerating frame of the ship) and forever visible, just like a lantern dropped into a black hole.
Of course quantum mechanics says that at some point the last photon to reach you will leave Earth, so looking at it from a quantum viewpoint, Earth will remain visible only until that last photon reaches you, but the 'never disappear' statement presumes continuous light, not quantum.

So there must be a speed at which the earth appears to recede the fastest

No, there's no such speed, especially since ship speed reaches any arbitrary value regardless of rate of acceleration. First of all, the appearance of velocity is dependent on one's choice of frame type.  Secondly, for all constant levels of acceleration and relative to said accelerating frame, Earth will 'appear' to drop away slowly at first, pick up speed as the ship velocity relative to Earth grows, and then slow as Earth approaches the ship's event horizon.  It will never appear to cross that horizon.

For linear non-accelerating travel, that is limited to c, and in flat spacetime, Earth will always be visible.  In real spacetime, at any ship speed, the ship will eventually cross Earth's event horizon, but both Earth and ship will always be able to see each other.  There is no way to exit the visible universe.  Despite recession velocities > 3c relative to the cosmic frame, new stars become visible (enter the visible universe) every day, and none of the ones visible ever vanish from sight (unless they cease emitting light).

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Physics, Astronomy & Cosmology / Re: What is the optimum speed to make a point in space disappear?

« on: 16/10/2024 14:18:07 »

Go too fast and the earth might never disappear from view as Halc has kindly explained in the other topic.

Maybe you should quote what I said instead of making up something that I didn't.

Presumably you would have to depart at  v > c and maintain your speed

Positing impossibilities opens things up for making up any fiction you want.  No amount of power will do this, and you know that.
If you balk at unlimited power, just make yourself very small. It takes terribly little energy to make a neutrino go fast.

My solution?  It can be done in under a minute.  Say you wanted to visit this cool place where two massive galaxy clusters are colliding (about 2.4 GLY away).  You embark on a circular path that takes you there and back to where you started.  If you do that fast enough, you'll arrive back home after less than a minute of your time, and Earth will have disappeared from view, but only very near the end of your trip.

OK, there are easier ways to do it.  Take your ship to the far side of the moon.  Or for that matter, close your eyes. Both will cause Earth to disappear from view.