[hamdani yusuf]

Relative to the inertial frame in which the ship is momentarily stationary, the Earth will be receding at around 0.964c.  Nothing can exceed c relative to an inertial frame. But if there was a tape measure glued to Earth that goes all the way along your journey, with a tick mark every light second, you'd see two of those tick marks go by your ship every second. That's what it means to be moving at a proper velocity of 2c relative to Earth.

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

[paul cotter]

To all: please ignore all I have said in the last few days. 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.

[Halc]

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.

[paul cotter]

Thanks again, Halc. 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. I will however defer to your opinion on this matter. I am vaguely cognisant of Rindler coordinates, Unruh radiation etc but don't ask me to explain such ideas.

[Bored chemist]

I may have missed something at some point in this very long thread but...
"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.

[Halc]

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.

[hamdani yusuf]

Is GR needed for accelerated frames of reference?

ChatGPT:
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.

[hamdani yusuf]

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.

[Halc]

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

[paul cotter]

What did you expect?, nothing useful, I hope.

[Eternal Student]

Hi.

...This is actually my first intentional interaction with any LLM ever....

    They're actually awesome aren't they?    Just how they seem to understand what you're asking is amazing.    Getting a perfect answer is probably still a few years away but we should see the glass as half full.
    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.   


My input:     Please criticise this work:     (I copied and pasted the reply @Halc obtained from Gemini).....   

Output from Chat GPT:     ..... (loads of stuff but I'm just picking out the most relevant bit)....


        Areas for Improvement:

        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. In an accelerating reference frame, spacetime itself doesn?t curve in the same way as it would near a massive object (like Earth), but an observer would perceive certain effects similar to those in a gravitational field.....


------------
    Overall, the LLM generated critique did catch many of the errors in the original LLM generated response.
Maybe the trick is to make two passes,   get your article written by one LLM and then get it criticised by a different one.
After all,  that's probably how many online courses will go in a few years....  students using LLM to write the essays and someone else using a LLM to mark and grade them.
   So at the moment the way to stay ahead in the game is for the student to make these two-passes themselves at home and refine the essay until the critique comes out quite positively.    Then they would deliberately put in a few spelling errors here and there to dodge the AI detection software that the establishment may run on the work submitted by the students.
    I think I've mumbled stuff about this in another thread some time ago but it's really about always trying to look at the glass as being half full.   The new graduates in Physics may know nothing about Physics but they are are going to be very highly skilled and competent in using LLM and AI software.   This is going to be a valuable skill for their future jobs:    Writing to others, maybe some other company, in a way that the recipients LLM software will understand and regard as being of very high quality.    This is precisely what a future employer will be needing from their graduate employees in a few years.
     
Best Wishes.

[alancalverd]

The essence of science is scepticism. The essence of AI is faith in the published word. They don't mix well.

Teaching science, particularly physics, is about teaching people to think, not to regurgitate facts or "facts".

[paul cotter]

. 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.

[Halc]

. 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.

[hamdani yusuf]

But acceleration does not produce gravity at it implies

I think it's the implication from equivalence principle.

[hamdani yusuf]

The essence of AI is faith in the published word.

Only LLM. There are other types of AI trained using different sets of data types, such as CCTV cameras, industrial sensors and actuators, financial transactions, self playing games, etc.

[alancalverd]

"Equivalent" is not "identical".

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.

Continuous acceleration requires the expenditure of energy. No energy is expended by standing on the surface of a planet.

[paul cotter]

Thanks for your kind words, Halc, but I would not consider my observations as being "very perceptive", more very obvious. I don't wish to divert the original discussion any further and I will say no more here on "AI". 

[hamdani yusuf]

Continuous acceleration requires the expenditure of energy. No energy is expended by standing on the surface of a planet.

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.

[alancalverd]

A good point.

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.

I await your analysis of two balls on a string, with eager anticipation!