Shown solutions to physics problems in lucid dream

It's accelerating away as the ground observer measures, even as v decreases. The v is a locally measured velocity. If the projectile were rising alongside a tower, v would be the velocity someone in the tower would measure as the projectile passes by.
Velocity with respect to what? The tower? Well the ground observer knows he's at rest with respect to that observer. Radar timings would provide the required velocity measurements. The issue of making things local is some which you've assumed by construction and now you're arguing the opposite.

If you're taking an SR construction to be sufficiently valid that you can ignore GR then you're saying you're able to pick a global set of coordinates. In fact I've already explained to you this problem; in GR SR is only a valid approximation for a small region about a given point (and even then your choice of SR construction is not uniquely defined simply by your choice of point), if you intend to start comparing things further away then you need to use the full GR theory as the variation in what the tower and the ground see in such vectors as velocity is determined by the Riemann curvature tensor, through its use in parallel transportation.

Clearly you're tripping over yourself because you're unable to quantify the full GR construction. If you can't give a formal and rigorous justification for your use of SR over the space-time regions you're considering you'll run precisely into these problems, how much disagreement there is between observers in different points in space.

Out of interest, do you think you could do the full GR theory if you could be bothered? Or is your knowledge (and I use that in a very loose manner) confined to SR?

I've amply shown that Alpha is wrong/QUOTE]And yet no one who knows any relativity agrees with you. Of course if you're so sure why aren't you submitting your work to a journal? Why can't you provide the full GR calculation so there's no doubt your approximations are valid? All I see if you tap dancing around the issue of you justifying your claims.

, which predictably resulted in a dump of red herrings
Its a red herring to ask you demonstrate the validity of your claims? And 'predictable' suggests this isn't your first account here, as you have some expectations about how I treat cranks.

and even a CV to look superior no matter what.
You're the one who queried if I really am a postgrad in some area of science. But I imagine you already knew I wasn't lying, if you're a new account for an old poster. You accused me of being unable to see the woods from the trees and suggested I read a book on logic. The fact I have a science orientated CV suggests the people who research physics think I'm pretty capable too. Its hardly irrational for me to trust actual physicists to evaluate my abilities and knowledge than someone who gets his physics from dreams. Besides you accusing me of trying to look superior is laughably hypocritical. Particularly when you follow it with :

I'm the one being scientific here, besides the dream itself. .... It's natural human reaction to accuse those with new ideas of arrogance.
You claimed to have solved major problems in physics by having a dream and you're accusing me of trying to come across as superior!? When someone says "I had a dream about physics and now I've got the solution to several problems in physics which have withstood decades of research by professional physics" then calling that person 'arrogant' is not a matter of fear that you might be right, its an entirely justified conclusion, along with the view you're delusional and irrational.

People like Alpha are satisfied only when you kowtow to them.
No, I just expect people to justify their claims. I have no problem disagreeing with people, I disagree with people I work with on a number of things, ranging from whether a scalar Higgs could exist through to the physical validity of generalised geometry. I enjoy talking to informed intelligent people on subjects I don't know or on which I hold different views. That's part of the reason peer review exists, for people to scrutinise your methods and to help you improve.

As I said to Jack in regards to SR, if you have something which could kill SR tomorrow or which actually solves various problems in physics I'd want to help in any way I could. But it seems to me you haven't and when I point out the things which I think you've failed to justify you start making excuses. If you can't justify your claims then why do you make them? Why ignore what people say about your work? If you're honest and believe your claims then you plan to submit it to a journal, where you'll get given similar comments. If I see areas you've failed to justify then reviewers will too.

I've read & responded to the objections
Response is not retort. Your entire claim rests heavily on your assumption that the equivalence principle can be applied for regions rather than point by point in your set up. A retort would be to do the full GR calculation and show you're right. Pretty much anything short of that is a failure to retort.

I'm the one being scientific here,
Other than the fact you fail to justify properly critical assumptions you make, you ignore all comments by people who have experience with relativity, you fail to answer direct questions and you're here on a forum and not already undergoing review from a reputable journal. Your failure to respond to my comment that everyone here who is in academia doesn't post their work on forums in order to get it to the attention of others, they (or rather we) use journals.

Here's a few direct questions so we can actually move forward :

1. Can you do the full GR calculation? If no then how do you know your approximations are sufficiently valid to make your claim valid? If yes why do you not include it in your posts, why use SR instead when it is less accurate and requires numerous assumptions?

2. Do you plan to submit your work to a journal? If yes then which journal and why haven't you done it already? If no then why post it at all as without being seen by academia it'll likely never be known in the relativity community.

3. In a related question, what level of detail and explanation would you, hypothetically, need to be presented with in order for you to say "Fair enough, I am wrong". Obviously comments and criticisms from half a dozen people with degrees or higher in relevant areas isn't enough.

4. Closely relating to Q1 and Q3, what is the upper threshold for your mathematics knowledge, so that should any of us wish to go down the route of discussing the specifics we know at what level to pitch any responses. An answer of 'yes' to Q1 implies at or above degree level, is this the case? If not from formal education where did you pick up said knowledge, assuming your claim to have any.

And remember, you claimed you're being scientific so your answers shouldn't contradict following the scientific method. You've done quite enough of that already.
 
Make an analytical analysis, then.
Not sure what you mean, maybe you can elaborate. I may try to find a work around in Excel or do it by hand for three values, the minimum required.

How do you know that SR returns correct results for your region?
Because SR is correct to a certain precision for a sufficiently small region, physics texts say, and I declared that my experiment is within such a region. (I said "I’m assuming a planet for which g is sufficiently constant over the whole experiment, so that SR gives high-enough precision results.")
 
Then I think you're using a faulty measure of acceleration, because that sentence is clearly inconsistent.
Did you read my next sentence there, where confusion would be cleared up? The v is locally measured. The ground observer cannot measure v accurately except initially, when the projectile is launched. You seem to be assuming otherwise. The acceleration g (or a, used at the site) is not measured in the ground observer's frame; see the site for details on how it must be measured. "Acceleration away" means that the change in distance per unit time is increasing, as measured by the ground observer, and not that v is increasing.

Let the projectile rise alongside a tower. Let someone in tower measure the speed of the projectile as it passes by. That would be a good measure of its speed, right? That observer calculates a small change in distance divided by a small change in time. However, that observer is using a ruler and clock that are incompatible with the ground observer's ruler and clock. For example the ground observer's clock runs slower than the tower observer's clock.
 
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Its a red herring to ask you demonstrate the validity of your claims?
This may be all I respond to from your post, although I'll read it, as long-winded as it is, just in case there's anything new there. Yes your requests for me to "demonstrate the validity" are red herrings. Then you repeat a dump of the red herrings you dumped before. You've been proven wrong that a fuller GR treatment is needed. SR gives correct results in the way I'm using it and to the given precision, thus no reason to use GR because GR would return the same result. Physics texts agree with me, and you've shown nothing to the contrary other than your opinion. Anything about my ability or inability to do unnecessary GR calculations or about a journal is irrelevant here. Etc. etc. I'd just be repeating ad naseum what you've been told before. All you offered in this thread is baseless accusations and irrelevant junk. If you want your ego massaged isn't there a better place to do it?
 
I've just flicked through Wald as a bit of bedtime reading and in Section 4.4 - Linearised Gravity he goes through how to obtain the Newtonian gravity limit of a full GR theory and then constructs the motion of objects in a weak gravitational field, precisely the issue in this thread.

First he constructs the relationship between matter and gravity through the Einstein Field Equations. If you write $$g_{ab} = \eta_{ab} + \gamma_{ab}$$, expand out the field equations in linear $$\gamma$$ and set the stress-energy tensor to be of the form which describes slow moving mass which is causing the gravitational field you end up with the only non-trivial expression of $$\nabla^{2}\phi \propto \rho$$ where $$\phi$$ is what we'd normally consider the Newtonian gravity potential. A second approach is to solve the geodesic equations (something I've asked Bert to do as well as Jack) in such a limit and you get $$\frac{d^{2}x^{\mu}}{d\tau^{2}} = -\Gamma^{\mu}_{\phantom{\mu}00}$$ and $$\Gamma^{\mu}_{\phantom{\mu}00} = \frac{\partial \phi}{\partial x^{\mu}}$$ and thus $$\underline{a} = -\nabla \phi$$, the usual Newtonian expression for acceleration under a gravitational potential.

But this is not the end of his discussion. He notes that the stress-energy tensor conservation equation $$\nabla_{a}T^{ab} = 0$$ simplifies to $$\partial_{a}T^{ab}=0$$ for this limit and so the limit taken leads to the result that observers move along geodesics of the flat metric. But this is not the case if $$\underline{a} = -\nabla \phi \neq 0$$ and thus though it was examined from the point of view of linearations about a flat metric $$\underline{a} = -\nabla \phi$$ is not an approximation to leading order. Wald's comments are as follows :

Wald said:
... it illustrates the difficulties which occur when one tries to derive the equations of motion of bodies from Einstein's equations via a perturbation expansion in the departure of flatness. In order to get a good approximation to a solution for a given order, one must use some aspects of the higher order equations.

Wald is pretty much the defacto textbook on relativity and if he says you need to be careful then you need to be careful. Given you're dabbling with precisely the same kind of concept, using a flat metric and having small enough variations in it that you simply your considerations to special relativity then it would seem I was entirely justified in requesting you do everything in the full theory and then simplify the answers at the end. The fact is that if you have a non-zero $$\rho$$ (ie matter density) then you'll have non-zero $$T_{ab}$$ and thus contributions to your metric. Yes, they are small perturbations away from flat but they are precisely the things whose effect you're interested in.

/edit

I see you've replied to my previous post. As expected, nothing retorted. You also ignored several direct questions, one of which was to ask you what it would take to convince you you're wrong. You've claimed I was mistaken when asking for the full GR treatment and now I've been vindicated by a professor whose work is on the shelf in pretty much every GR academic's office in the world. You claim "Physics texts agree with me". Why ones? Provide title and page numbers. I've provided them for my justification, you should be able to do the same because if you can't then you aren't being scientific, you're just being a dishonest fraud. But then your unwillingness to answer direct questions, even when repeatedly asked, is testament to that.

Of course its no skin off my nose if you ignore my posts. I'll just keep demolishing your claims and pointing out your mistakes without you replying. I generally post in reply to hacks not to convince them they are incorrect (they, you, are too far gone), I do it so a casual reader wouldn't be suckered into believing your nonsense. It's like shooting fish in a barrel.
 
Yes, they are small perturbations away from flat but they are precisely the things whose effect you're interested in.
In that quote, Wald is saying to take care "when one tries to derive the equations of motion of bodies". I'm not doing that. I'm using equations of motion that have already been correctly derived, in the authoritative book Gravitation.

You really should read Thinking Physics. The author encourages figuring out each problem presented without the use of math. When you can do that, likely you could come back to this issue and easily see that a fuller GR treatment is not required. You say:

Yes, they are small perturbations away from flat but they are precisely the things whose effect you're interested in.
If the "perturbations away from flat" can be made smaller by making the region of interest smaller, then obviously they can be made negligible; i.e. too small for SR to return a different result at a given precision than a fuller GR treatment does. That is why "For sufficiently small regions, the special theory of relativity is correct!!" (not my quote, google it).

What if g ranges from x to x + 1x10^-4000. Is full GR treatment going to return a different result than SR (equations for a constant g) at 10 significant digits? Of course not. All the variation of g will drop out when rounding for significant digits. Using thinking like that, one need not break out Wald.

The result I showed, namely acceleration away as measured by a ground observer, has nothing to do with the negligible variation of g in the sufficiently small region used.

I generally post in reply to hacks not to convince them they are incorrect (they, you, are too far gone), I do it so a casual reader wouldn't be suckered into believing your nonsense.
Uh huh, sure you do. Yeah I bet there's plenty who'd treat the pseudoscience section as gospel if not for your fine work here.
 
Bert, you're working with uniform acceleration in flat space. Stick with that to begin with.

Don't attempt to move on to gravitation until you've confirmed your understanding of the flat space case.

You're talking at cross-purposes with AlphaNumeric, getting way over your head into matters that you don't even need to be discussing yet, when you could be engaging in productive discussion regarding the flat space scenario.

BertBonsai said:
Did you read my next sentence there, where confusion would be cleared up? The v is locally measured. The ground observer cannot measure v accurately except initially, when the projectile is launched.
Yes, I did read the rest of that post, and the point remains.
You acknowledge that the inertial object's velocity can't be reliably measured except at the object's location.
It seems obvious that the same applies to acceleration.

BertBonsai said:
You really should read Thinking Physics. The author encourages figuring out each problem presented without the use of math. When you can do that, likely you could come back to this issue and easily see that a fuller GR treatment is not required.
Such arrogance will get you nowhere, Bert.
Really, if you want to discuss uniform acceleration in flat space, then just say so. Say "OK, forget gravity for the moment. Consider a uniformly accelerating observer in flat space, launching a projectile in the direction of acceleration..."
When you have that sorted, then you could consider moving on to gravity an cosmic solutions.
 
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Not sure what you mean, maybe you can elaborate. I may try to find a work around in Excel or do it by hand for three values, the minimum required.
Don't use a numerical analysis: it is error-prone if you are unused to scientific computing. Rather, make a symbolic expression for the acceleration, and analyse it.
Because SR is correct to a certain precision for a sufficiently small region, physics texts say, and I declared that my experiment is within such a region. (I said "I’m assuming a planet for which g is sufficiently constant over the whole experiment, so that SR gives high-enough precision results.")
You've "declared" it? Does it seem reasonable to you that you should be able to decide that your region is sufficiently small simply by decree?
 
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Make the analysis qualitative, rather than quantitative.
Whoa, numerical and analytical analyses are both quantitative. Qualitative is for airy fairy fluffy stuff descriptions.

You've "declared" it? Does it seem reasonable to you that you should be able to decide that your region is sufficiently small simply by decree?
It's a thought expeiment, so why not?
Really, Bert has jumped the gun by introducing planets at all. In his equations he's really working with a uniform accelerating reference frame in flat space.
 
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Whoa, numerical and analytical analyses are both quantitative. Qualitative is for airy fairy fluffy stuff descriptions.
Don't know what I was thinking, there. Embarrassing, really.
It's a thought expeiment, so why not?
Well, an approximation is reasonable only if the error introduced by the approximation is much smaller than the effect one is demonstrating. I haven't seen any analysis to support that, and plenty against.
Really, Bert has jumped the gun by introducing planets at all. In his equations he's really working with a uniform accelerating reference frame in flat space.
I know you've been trying to get him to see that, but I don't think you'll succeed.
 
In that quote, Wald is saying to take care "when one tries to derive the equations of motion of bodies". I'm not doing that. I'm using equations of motion that have already been correctly derived, in the authoritative book Gravitation.
Provide page numbers.

'Gravitation' is a pretty big book. I know GR researchers in a number of universities and none of them own that book, they just get it from the library for the rare occasions it is needed. If you own that book then your initial attempts to present yourself as an interested layperson was dishonest. Do you own that book? Or are you just throwing out a title in the hopes I'll back off?

You really should read Thinking Physics. The author encourages figuring out each problem presented without the use of math. When you can do that, likely you could come back to this issue and easily see that a fuller GR treatment is not required.
You're making the common crank mistake of thinking that because I know some mathematics and am comfortable talking mathematically then its the only mode in which I can converse and think. Besides, I do not require a book to tell me experiences I have had first hand. I've got hands on experience doing GR and other areas of physics, being taught it, researching it and teaching it. I have developed ways of thinking about science by actually doing science.


If the "perturbations away from flat" can be made smaller by making the region of interest smaller, then obviously they can be made negligible; i.e. too small for SR to return a different result at a given precision than a fuller GR treatment does. That is why "For sufficiently small regions, the special theory of relativity is correct!!" (not my quote, google it).
*sigh*. I'm not arguing with that, I'm arguing with your application of it where you don't justify that your assumptions are valid. I have said this before, please try to keep up.

Yes, for a sufficiently small region about a given point in a given space-time with given metric then you can use SR. How large this region is about a specific point is a point which should be addressed whenever someone does such a calculation. The person doing the calculation should compute such things as curvature, as it arises in a Taylor expansion of the metric about the point.

What if g ranges from x to x + 1x10^-4000. Is full GR treatment going to return a different result than SR (equations for a constant g) at 10 significant digits? Of course not. All the variation of g will drop out when rounding for significant digits. Using thinking like that, one need not break out Wald.
I have yet to see you demonstrate this kind of result comes up in your physical setup. You're consider regions light years in size.

Why are you struggling to grasp this? Yes, its well known that GR simplifies to SR for given limits but if you're going to do that you need to show the physical system you're considering satisfy such limits. Have you? No.

Uh huh, sure you do. Yeah I bet there's plenty who'd treat the pseudoscience section as gospel if not for your fine work here.
I didn't say that's a lot of such people. Generally its easy to see who the nuts are, they have no problem making stupid claims. But every now and again there's people who come here who present themselves as informed and able and then proceed to misrepresent the mainstream or put forth claims whose mistakes are perhaps subtle to the casual reader. Jack for instance makes a great many claims about SR and wants people to believe he understands it. He makes claims about what SR is and its methodology but almost invariably he's wrong and I (and others) point it out.

And its a little silly you try and call me arrogant, given you're here claiming you have solved huge problems in physics and when asked you have to tap dance around the issue. Can't you answer my direct questions? Or were they a little too subtle for you to spot? You are here to swindle people, that much is clear. If you weren't you'd be submitting to a journal, not coming to a forum where you know most people don't have the knowledge to evaluate your claims. Having a pet theory and coming to a forum, rather than a journal, is a sign you want to avoid the scrutiny of those who understand the area of physics you make claims about. The fact you haven't retorted this comment of mine shows you know what I'm saying is true and you, like all the other cranks here (particularly the likes of Jack), aren't honest enough to admit it.
 
Bert, you're working with uniform acceleration in flat space. Stick with that to begin with.

Don't attempt to move on to gravitation until you've confirmed your understanding of the flat space case.
It's impossible to do one without doing the other, in a sufficiently small region. The principle of equivalence implies (and many physics texts agree) that within a sufficiently small region, no experiment can distinguish between being at rest in a gravitational field and uniform acceleration in flat space. Google for "Locally being at rest on the Earth's surface is equivalent to being in a uniformly accelerated spaceship."

You're talking at cross-purposes with AlphaNumeric, getting way over your head into matters that you don't even need to be discussing yet, when you could be engaging in productive discussion regarding the flat space scenario.
Productive discussion is impossible with that type. Scientifically speaking, you shouldn't mention Alpha unless you can support his/her claims, which no reasonable person could do. You're encouraging bad behavior.

Yes, I did read the rest of that post, and the point remains.
You acknowledge that the inertial object's velocity can't be reliably measured except at the object's location.
It seems obvious that the same applies to acceleration.
That's true, as the rocket site says as well. But so what? Where's the inconsistency? When astronomers found that supernovae are accelerating away from us, they effectively measured an increasing change in distance per unit time, from Earth. They didn't measure that acceleration at the locations of the supernovae.

Really, if you want to discuss uniform acceleration in flat space, then just say so. Say "OK, forget gravity for the moment. Consider a uniformly accelerating observer in flat space, launching a projectile in the direction of acceleration..."
When you have that sorted, then you could consider moving on to gravity an cosmic solutions.
Those situations are equivalent. In flat space for uniform acceleration, acceleration away is also the finding, as I've proven to you by example. You're just suggesting a problem without showing one; guilty by suspicion. Show a problem, then you'd have a point.
 
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Don't use a numerical analysis: it is error-prone if you are unused to scientific computing. Rather, make a symbolic expression for the acceleration, and analyse it.
How would that change the fact that the equations predict acceleration away as described, and that I'm using those equations correctly?

You've "declared" it? Does it seem reasonable to you that you should be able to decide that your region is sufficiently small simply by decree?
Yes, it's perfectly fine to do that in a thought experiment.

Well, an approximation is reasonable only if the error introduced by the approximation is much smaller than the effect one is demonstrating.
Following the rules of significant digits, any variation of g beyond the final precision + 1 significant digit drops out before the equations are even employed. For example, if the final answer has 5 significant digits and g ranges from 1.00000000 to 1.00000007, the only g that need be input into the equations is 1.00000. That's true for any mathematical application. Therefore in a sufficiently small region, GR can disagree with SR only if GR is invalid. Which explains (google for it) "For sufficiently small regions, the special theory of relativity is correct!!"
 
Productive discussion is impossible with that type.
That chip on your shoulder must be pretty heavy. 'That type' is people who know some physics because they've put in time and effort to understand and then apply that knowledge to develop new work which passes scrutiny by their peers.

There are people on these forums which find I can provide productive discussion. Those who think I can't are generally those people who don't like being told they're incorrect. Jack thinks he teaches me vector calculus and SR results despite the repeated times I've provided lengthy discussions well above the level of discourse he's capable of. Looks like you and he are kindred spirits.

Tell you what, why don't you go through the full GR calculation, or at least get the ball rolling, and we can discuss how to explicitly demonstrate the result that GR approximates to SR for small regions. I'm entirely willing, and indeed actively want, to discuss the application of perturbation theory to relativity, its quite interesting.

I tried to raise the level of discourse with Jack from his laughably simply algebra to the application of bundle morphisms but he failed to rise to the challenge. Perhaps you'll do better?

Scientifically speaking, you shouldn't mention Alpha unless you can support his/her claims, which no reasonable person could do. You're encouraging bad behavior.
Scientifically speaking you should be able to justify your claims and explicitly demonstrate that your approximation is indeed the correct approximation. I've given a specific example of how such approximations aren't straight forward, taken from a well known textbook on GR, so scientifically the onus is on you to justify you're correct. And if you're wanting to be scientific then you'd reply to direct questions you're asked. Dodging criticisms and questions would prevent your work being published if you were following the scientific method and submitting your work to a journal for review. You can't trot out "Be scientific" when you're not. Its called hypocrisy.

I'll ask again, do you plan to submit your work to a journal? If so, which one? If not, why not, what about being scientific and submitting to academic review?
 
Provide page numbers.
You should say please. Already done, in the link I gave where I showed acceleration away.

*sigh*. I'm not arguing with that, I'm arguing with your application of it where you don't justify that your assumptions are valid. I have said this before, please try to keep up.

Yes, for a sufficiently small region about a given point in a given space-time with given metric then you can use SR. How large this region is about a specific point is a point which should be addressed whenever someone does such a calculation. The person doing the calculation should compute such things as curvature, as it arises in a Taylor expansion of the metric about the point.
*bigger sigh* (Yes I know you *sigh* to try to show superiority). I am using a sufficiently small region, by declaration. Then you need not carry on as if I didn't.

You're consider regions light years in size.
So what? Like g can't vary only at the 1000th digit in such a region in principle?

Why are you struggling to grasp this? Yes, its well known that GR simplifies to SR for given limits but if you're going to do that you need to show the physical system you're considering satisfy such limits. Have you? No.
Yes I have, by declaration.

Can't you answer my direct questions?
Not your irrelevant ones. I showed irrelevancy.

Having a pet theory and coming to a forum, rather than a journal, is a sign you want to avoid the scrutiny of those who understand the area of physics you make claims about.
Not a pet theory. I showed acceleration away, using existing equations of SR, not my theory. Your whole journal mention is irrelevant and not scientific reasoning. I proved that real physics is done right here, in forums. I didn't avoid your scrutiny, I refuted it.
 
'That type' is people who know some physics because they've put in time and effort to understand and then apply that knowledge to develop new work which passes scrutiny by their peers.
Why not use some of that knowledge to see that you're wrong here?

Tell you what, why don't you go through the full GR calculation, or at least get the ball rolling, and we can discuss how to explicitly demonstrate the result that GR approximates to SR for small regions.
That's been proven to be unnecessary.

I'm entirely willing, and indeed actively want, to discuss the application of perturbation theory to relativity, its quite interesting.
But I'm not willing to do more than what's needed to prove my points.

Scientifically speaking you should be able to justify your claims and explicitly demonstrate that your approximation is indeed the correct approximation.
What's really happening is that you can't admit you're wrong, so you're asking for more proof on top of the proof given. That's a common tactic of the unscrupulous.

I've given a specific example of how such approximations aren't straight forward, taken from a well known textbook on GR, so scientifically the onus is on you to justify you're correct.
Your example was shown to be off topic. The onus is not on me to provide additional proof. One proof is enough.

And if you're wanting to be scientific then you'd reply to direct questions you're asked.
Nope, not irrelevant ones.

I'll ask again, do you plan to submit your work to a journal? If so, which one? If not, why not, what about being scientific and submitting to academic review?
And I'll tell you again, I don't care about journals. Irrelevant. Can you show that journals are necessary to do good physics? Of course not, and you'll ignore the question too.
 
/edit

I see you've replied to my previous post. As expected, nothing retorted. You also ignored several direct questions, one of which was to ask you what it would take to convince you you're wrong. You've claimed I was mistaken when asking for the full GR treatment and now I've been vindicated by a professor whose work is on the shelf in pretty much every GR academic's office in the world. You claim "Physics texts agree with me". Why ones? Provide title and page numbers. I've provided them for my justification, you should be able to do the same because if you can't then you aren't being scientific, you're just being a dishonest fraud. But then your unwillingness to answer direct questions, even when repeatedly asked, is testament to that.
You write whole books here, then edit them and expect me to see it all? How many times did I give you the quote "For sufficiently small regions, the special theory of relativity is correct!!"? 5 times now probably. Look it up for once! You don't even disagree with it, you just use the dishonest tactic of insisting that more proof is required. Any good text on the principle of equivalence agrees with that quote. What you provided, Wald, was shown to be off-topic. It doesn't matter what you provide when it's irrelevant.
 
It's impossible to do one without doing the other, in a sufficiently small region.
Bert, you're biting of more than you can chew, and it's pissing people off.
Seriously, forget gravity for the moment, and make sure that you have agreement on the flat spacetime case. There's no point in mentioning gravity until you have that foundation properly set.

Yes, the principle of equivalence says that uniform acceleration is the same as a uniform gravity field. No, that doesn't mean you understand General relativity.
Productive discussion is impossible with that type. Scientifically speaking, you shouldn't mention Alpha unless you can support his/her claims, which no reasonable person could do. You're encouraging bad behavior.
Honestly Bert, you have no idea what you're talking about. I don't think you're trying to understand what AN is saying, all you're doing is seeing disagreement. I think that there is a misunderstanding between you and Alpha, and I think you're both behaving badly to some degree by not taking a step back and sorting out your underlying misunderstanding. A good step would be to step away from gravity for the moment, and simply focusing on uniform acceleration.

That's true, as the rocket site says as well. But so what? Where's the inconsistency?
That's the question you should explore with AN. He's much smarter at that than I am.
When astronomers found that supernovae are accelerating away from us, they effectively measured an increasing change in distance per unit time, from Earth. They didn't measure that acceleration at the locations of the supernovae.
I don't pretend to understand the details of those measurements, Bert. Do you? Remember, this is not flat spacetime. That is something we could move on to once we have our heads properly wrapped around the meaningfulness of different measures of acceleration in the flat spacetime case.

Those situations are equivalent. In flat space for uniform acceleration, acceleration away is also the finding, as I've proven to you by example. You're just suggesting a problem without showing one; guilty by suspicion. Show a problem, then you'd have a point.
If the situations are equivalent, then why bother mentioning gravity? Why not just analyse uniform acceleration in flat spacetime?

The problem is clear - you've asserted that there's an issue with gravity, but you're demonstrating it only for the special case of uniform gravity in flat spacetime. People are pointing out that this is a special case, and it's clogging up the discussion.

Do you want a productive discussion, Bert? Or do you want to continue this unproductive bickering? I think there is a good discussion to be had, but you'll have to take it one step at a time. Uniform acceleration first. Gravity and cosmic expansion later.
 
Bert, you're biting of more than you can chew, and it's pissing people off.
Seriously, forget gravity for the moment, and make sure that you have agreement on the flat spacetime case. There's no point in mentioning gravity until you have that foundation properly set.

Yes, the principle of equivalence says that uniform acceleration is the same as a uniform gravity field. No, that doesn't mean you understand General relativity.
Yet you haven't shown any problem with my understanding. Just guilty by suspicion. I used existing SR equations to show that one can match a gravity prediction of Newton's right down to the last pixel on a chart. That should give a reasonable person an indication that I might know what I'm doing. The traditional flat spacetime case is already covered on the site I linked to. In a uniform gravitational field, spacetime is flat and the ground is accelerating. That's how the situations can be equivalent.

Honestly Bert, you have no idea what you're talking about. I don't think you're trying to understand what AN is saying, all you're doing is seeing disagreement. I think that there is a misunderstanding between you and Alpha, and I think you're both behaving badly to some degree by not taking a step back and sorting out your underlying misunderstanding. A good step would be to step away from gravity for the moment, and simply focusing on uniform acceleration.
More guilt by suspicion. No evidence at all that I don't know what I'm talking about.

That's the question you should explore with AN. He's much smarter at that than I am.
Have you even read Alpha's stuff? If you had, you'd see that it amounts to this, paraphrased: "Yes SR is correct in a sufficiently small region, but you must prove your point in such a region using a full GR treatment". That's wanting it both ways. If I did a full GR treatment and it showed the same result, Alpha would want still more; that's the way such people are. Alpha has not shown one problem with my stuff here. That's not to say that Alpha isn't real smart about GR. It's just a pathological need of him/her to be "right" in the face of proof to the contrary.

If the situations are equivalent, then why bother mentioning gravity? Why not just analyse uniform acceleration in flat spacetime?
That's like saying, if you see a gold bar in the street why pick it up? Why not just walk by? ... There's no good reason not to analyze it from the equivalent gravity perspective, esp. when it results in one of the best findings in physics of the last 50 years at least, and leads to the solution of the dark energy problem. Besides, it's what I was shown in the dream, which I'm relating here. Why should I leave out the best parts?

The problem is clear - you've asserted that there's an issue with gravity, but you're demonstrating it only for the special case of uniform gravity in flat spacetime. People are pointing out that this is a special case, and it's clogging up the discussion.
So what if it's a special case? I've not said otherwise. Nor does it being a special case indicate a problem. It still means that a projectile launched upward at a speed close to c initially accelerates away as measured by a ground observer. What's clogging up the discussion is that a legitimate finding has so repelled the audience that they're grasping at straws to avoid accepting it.

Do you want a productive discussion, Bert? Or do you want to continue this unproductive bickering? I think there is a good discussion to be had, but you'll have to take it one step at a time. Uniform acceleration first. Gravity and cosmic expansion later.
Whether the discussion is productive depends on other participants. The discussion could be productive if "guilt by suspicion" wasn't being done (you started out fine), and if Alpha wouldn't use unscrupulous tactics to try to look superior. I've made my case about initial acceleration away; it's proven. I haven't tied it to cosmic expansion yet, and may not if others continue to be unscientific. (In fact it seems unlikely.) If the natives are hostile for no good reason that's the way the cookie crumbles but it's not my problem. Besides the dream itself, I've followed the scientific method here.
 
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