Shown solutions to physics problems in lucid dream

I'll get back to you later Alpha

What relevence is it that the dream was lucid?

A fictonal character in your mind that you interacted with was already dead? I hope you see the dissonance in your statement.

Why is the opinion of a fictional character in your mind relevant?

Why is the opinion of a fictional character in your mind relevant?

What relevance does a dream character's opinion have with actual science?
Fictional or not, relevant or not, I'm just reporting what happened, and got some good info there that sounded highly plausible. The info is all that matters here, in pseudoscience where it belongs.

For example, he told me that space itself is not expanding, as cosmologists think. (Think of the rising raisin loaf example.) That was a false assumption based on Hubble's result, he said. He gave me a thought experiment to show that space need not expand to explain Hubble's result:

In an infinitely large universe whose space neither expands nor contracts, sprinkle an infinity of galaxies. Within some section of this universe let all of the galaxies approach one another. This is possible in principle. The size of the section is arbitrary; make it the size of the universe. Now all of the galaxies in the universe approach one another, yet there is no cosmic center or edge. Now play the film backwards, so to speak, to find that all of the galaxies in the universe can recede from one another, with no cosmic center or edge.

Removing the notion of expanding space solves the flatness problem, he said, for then space can be flat by default. An infinitely large universe can become sparser or denser without need for space itself to expand or contract. Galaxies and other matter need only move relative to each other. He said there are other implications of this too, for example the observable universe becomes the entire universe.
 
You claimed that approximating to constant gravitational fields is okay, the difference between the actual result and your approximation are in some sig fig down the line. This isn't correct.
That's closer to what I said, and it is correct, for a sufficiently small region like the one I mentioned. The principle of equivalence demands that it's correct. The proof is in the pudding: I can do the calculation using SR and get the same result as a physical experiment involving gravity, like those done in high school. That trumps any purported invalidity you can come up with.

Nowhere did I say that SR alone can be used for vast distances involving gravity.

I've pointed out that we've done experiments involving gravity on the Earth's surface, in orbit, in deep space over distances ranging from millimetres to billions of light years, we know a great deal about how it behaves.
We don't know everything about it. Namely, we don't know (and haven't tested) that an object launched upward at a speed close to the speed of light accelerates away as we measure.

You talk about sig figs but by your own admission you have no knowledge in these things so what are you basing your claims about sig figs on if you can't do or understand the relevant calculations?
My "admission" wasn't that. An example of your giant assumptions.

Describe clearly and precisely an experiment which could be done which is relevant to the effect you're making claims about.
I'll do this, but not for you, which clearly that would be a waste of my time. I'll do it for any other polite poster who asks for it here. The experiment is obvious. What I'll do is show that SR predicts acceleration away.
 
I'll get back to you later Alpha


Fictional or not, relevant or not, I'm just reporting what happened, and got some good info there that sounded highly plausible. The info is all that matters here, in pseudoscience where it belongs.

The info was a product of dream character. There's no reason to think its plausable.

For example, he told me that space itself is not expanding, as cosmologists think. (Think of the rising raisin loaf example.) That was a false assumption based on Hubble's result, he said. He gave me a thought experiment to show that space need not expand to explain Hubble's result:

In an infinitely large universe whose space neither expands nor contracts, sprinkle an infinity of galaxies. Within some section of this universe let all of the galaxies approach one another. This is possible in principle. The size of the section is arbitrary; make it the size of the universe. Now all of the galaxies in the universe approach one another, yet there is no cosmic center or edge. Now play the film backwards, so to speak, to find that all of the galaxies in the universe can recede from one another, with no cosmic center or edge.

Removing the notion of expanding space solves the flatness problem, he said, for then space can be flat by default. An infinitely large universe can become sparser or denser without need for space itself to expand or contract. Galaxies and other matter need only move relative to each other. He said there are other implications of this too, for example the observable universe becomes the entire universe.

And this confirms you being simply wrong. We can observe some galaxies moving away from each other at 2x the speed of light (or more). It's impossible for mass to move at those speeds, however, it's perfectly fine if more points of space are being added in between the galaxies (i.e. expansion).

Knowledge gained from a dream is going to be limited to the knowledge you already posess. You already outlined your knowledge limits at the beginining of the thread; hence, there was never any reason to think those limits were magically exceeded.
 
Wait... so you've "read some books on the basic ideas, enough to mostly follow what [dream guy] said," and that gives you sufficient assurance that you understand this science better than AlphaNumeric? Some might consider this a little arrogant. Have you considered the possibility that perhaps your understanding of the basic concepts isn't perfect?
BertBonsai said:
Nowhere did I say that SR alone can be used for vast distances involving gravity.
But dream guy did, according to your account:
BertBonsai said:
He said that an object launched upward from a planet at close to the speed of light will measurably accelerate away and not decelerate like you'd think. He said that's predicted by special relativity (I'm still working out some calcs he showed me), and the idea can be extrapolated to distant receding objects.

But, perhaps you're right. Perhaps we're just not understanding what you mean. Please explain how SR predicts acceleration. Be careful - if you use time and distance measurements, you'll need to be precise about the reference frames of those measurements.

It would also be useful if you describe clearly and precisely an experiment which could be done which is relevant to the effect you're making claims about. Again, this needs to be very precise. For example, it's not enough to say "measure the time elapsed between x and y", you need to be explicit about how that time is to be measured.

BertBonsai said:
We don't know everything about it. Namely, we don't know (and haven't tested) that an object launched upward at a speed close to the speed of light accelerates away as we measure.
Are you sure? A thorough literature search is not easy, and sometimes impossible to be really sure it was thorough, even with access to a good tertiary library and extensive research databases. Did you look at any research involving supernovae, pulsars, quasars, neutrinos, etc?
 
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We can observe some galaxies moving away from each other at 2x the speed of light (or more). It's impossible for mass to move at those speeds, however, it's perfectly fine if more points of space are being added in between the galaxies (i.e. expansion).
It can also be fine when the speed is determined from afar, like those observations do. The speed of light limit applies only to locally measured speeds.

Space does expand, in the explanation the physicist gave me that resolves the dark energy problem. That can lead to measurements of speed greater than the speed of light, when measured from afar, but this expansion is relative (depends on frame) rather than absolute.
 
But dream guy did, according to your account:
No, look closely, I said the idea can be extrapolated to distant receding objects. I haven't explained that extrapolation yet. If it involves plugging values for vastly distant objects into SR, then you can scold me.

Please explain how SR predicts acceleration. Be careful - if you use time and distance measurements, you'll need to be precise about the reference frames of those measurements.
OK, but tomorrow or the weekend. I'm out of time now.

It would also be useful if you describe clearly and precisely an experiment which could be done which is relevant to the effect you're making claims about.
I'm only going to show that SR predicts that an object thrown upward at close to the speed of light accelerates away as measured from the ground. (To be clear, by "accelerate away" I mean that its change in distance per unit time increases.) The experiment is obvious from that.
 
It can also be fine when the speed is determined from afar, like those observations do. The speed of light limit applies only to locally measured speeds.

This statement is gibberish.

Space does expand, in the explanation the physicist gave me that resolves the dark energy problem.

Your dream character isn't a real physicist. It shouldn't be referenced as such.

That can lead to measurements of speed greater than the speed of light, when measured from afar, but this expansion is relative (depends on frame) rather than absolute.

Again, this is gibberish.
 
I'm just reporting what happened, and got some good info there that sounded highly plausible
Sounds highly plausible to whom? To you. Doesn't sound in the slightest bit plausible to me and I'd wager the same about anyone else who has studied physics to any great depth.

In an infinitely large universe whose space neither expands nor contracts, sprinkle an infinity of galaxies. Within some section of this universe let all of the galaxies approach one another. This is possible in principle. The size of the section is arbitrary; make it the size of the universe. Now all of the galaxies in the universe approach one another, yet there is no cosmic center or edge. Now play the film backwards, so to speak, to find that all of the galaxies in the universe can recede from one another, with no cosmic center or edge.
You only believe this plausible because you have no clue of the data you're supposed to be explaining. Galaxy dynamics cannot be explained by simply running gravitational collapse backwards. The data contradicts your claim.

Removing the notion of expanding space solves the flatness problem, he said, for then space can be flat by default.
It could but we reason people say its expanding faster is that the evidence disproves flatness in the manner you're talking about.

That's closer to what I said, and it is correct, for a sufficiently small region like the one I mentioned.
Doesn't mean your claim is correct, things don't accelerate when projected upwards, be it over a millimetre or a mile.

I can do the calculation using SR
I asked you to show it. You haven't. I'll give you another chance to provide it before I simply conclude you're a liar.

and get the same result as a physical experiment involving gravity, like those done in high school.
I'm not arguing with you invoking the equivalence principle, I specifically said I know its applications to GR.

That trumps any purported invalidity you can come up with.
My disagreement is with your claim things accelerate upwards, not downwards, when projected upwards. You have yet to say anything to justify that. Please pay attention to what I'm actually saying, I know its difficult given you don't actually know any physics, particularly relativity, but at least try.

Nowhere did I say that SR alone can be used for vast distances involving gravity.
Then why are you talking about it? All you've done is say the equivalence principle, which you already knew before your dream because you've read books on relativity. I'm asking you to justify things which you disagree with the mainstream on, like the claim I just mentioned.

We don't know everything about it. Namely, we don't know (and haven't tested) that an object launched upward at a speed close to the speed of light accelerates away as we measure.
Why would close to light speed make any difference? Are you saying the direction gravity works in is dependent on the motion of the object its acting upon? You need to justify that if so. All projectile experiments disagree and while none have been done involving objects moving close to the speed of light there are experiments done involving light and it behaves in the way expected, not as your claim would imply. You can't change the speed of a photon but gravity will red or blue shift its frequency. Red shifting is the photon equivalent of slowing down for a massive object. The Pound Rebka experiment saw photons redshift when fired upwards over a distance of a few dozen metres.

You claim you have the equations but you can't provide it. You don't have any experimental evidence either, you're having to ignore things you don't get right and as a result you're just changing your story. Every experiment disagrees with the notion of things speeding up when fired upwards and so you're having to make your claims only about things we haven't done experiments on. If you can show the derivation of this result in relativity then I'd love to see it, it would validate your claim. If you can't provide them then you're just making stuff up about something you know you can't be checked on.

My "admission" wasn't that. An example of your giant assumptions.
You sad "I don't have a formal background in physics but I have read some books on the basic ideas, enough to mostly follow what he said.". I took that to mean you've read pop science books. If I'm wrong about this please explain precisely what you have read and know about relativity so as I know what level to pitch my explanations. I assumed low because anyone who gets his physics knowledge from dreams is not putting themselves in a position which makes them seem rational and informed.

I'll do this, but not for you, which clearly that would be a waste of my time. I'll do it for any other polite poster who asks for it here. The experiment is obvious. What I'll do is show that SR predicts acceleration away.
Are you a sock puppet for Jack_ or is it just a coincident he goes and now a new nut who makes claims he can't back up in relation to relativity turns up?

You came here and started this thread and it would be logical you want to get your claims/ideas to the attention of people who can evaluate it in an informed manner. Now you've had an informed person give you his opinion which isn't just a pat on the back you don't want to play any more.

People post their 'work' on line for generally one of two reasons. Either they don't believe their work, having just made it up, and just want to be thought of as clever and get attention or they honestly believe they have something which could contribute to physics. If you're the former then you're a troll. If you're the latter then it would mean you want your work to come to the attention of academics and physics researchers and so you surely would expect at some point to be evaluated by such people. If you can't justify your claims to a single postgrad on a forum what makes you think you'll have an easier time with journal reviews by professors? You have to be prepared to justify claims and retort criticism, as that's what peer review is about. Everyone in academia has had to correct their work at some point due to peer review, why should you be different? I ask you to justify your claims in a manner expected of anyone who knows relativity or hopes to get his work to the attention of the mainstream community and now you're disgruntled? You should have expected you'd be asked further questions!

And if you think I'm rude then you've never been to as conference. I've seen people giving talks to hundreds of researchers be told "You're wrong, this is terrible and stupid because of X, Y and Z", people storm out in disgust or to be ripped to shreds in front of all their fellow researchers by one person who isn't going to take any shit from someone making unjustified claims.

A good physics result (or any in science) stands up on its own merit. If you think I'm rude then post retorts to every one of my criticisms, prove I'm wrong about you. Ignoring me doesn't retort them. Ignoring a journal reviewer's comments will mean you won't get published. People didn't like Einstein's work but it stood for itself. Einstein didn't like quantum mechanics but it stood up for itself. I'm being rude to you because if you're honest and have the results you claim you'd be able to meet the basic standards expected in science but you aren't so it seems your attitude/behaviour is dishonest. You justify your claims then I'll admit I'm wrong. You being rude to me wouldn't bother me in the slightest as I am not making claims about my work.

Nah, it comes right from the physics books. So does relative expansion. I can give examples if you ask nicely.
I've asked several times and if you are honest you'd provide justification for your claims. The fact you're dancing around justifying your claims demonstrates you're not honest, you came here simply to preach your pet theory. If you had actual results you'd have provided them immediately. And it doesn't come 'right from the physics books'. If I'm wrong provide a reference to such a book (including the page or chapter number).

I'm only going to show that SR predicts that an object thrown upward at close to the speed of light accelerates away as measured from the ground. (To be clear, by "accelerate away" I mean that its change in distance per unit time increases.) The experiment is obvious from that.
Now I'm thinking you're MacM or whoever it was because I now realise what you're actually going to do, that you've been playing silly word games and I'll say it out loud for anyone else.

From the point of view of the ground the projectile decelerates as expected. Its less simple for the point of view of the projectile. Initially it sees the Earth as a squashed sphere due to length contraction but since slowing down means less length contraction, it sees the Earth get fatter and the corresponding distance between it and the Earth increase, on top of the distance increase due to its relative motion. Hence it might seem that from the projectile's point of view its accelerating. This is an argument MacM used in previous threads.

Your point of view is wrong, you have failed to calculate worldlines, you're instead relying on your physical intuition which is false. You've taken a result about how GR reduces to SR instantaneously at a given space-time point and then tried to extend it, using your intuition, to more complicated cases and thus you've gotten it wrong. If you do the calculation properly using the Schwarzchild metric to calculate the times and distances measured by objects moving along geodesics (as any projectile will) you'll find there's no contradiction. This is the difference between t and $$\tau$$. Instantaneously at a point you can pick coordinates such that $$t=\tau$$ but irrespective of how small a region you consider motion for a non-zero amount of time. Under the gravitational influence the object's velocity changes and length contraction is changed BUT so is time. This is seen in the Schwarzchild metric where $$g_{tt} = \frac{1}{g_{rr}} = 1-\frac{GM}{r}$$. When you calculate how much distance the object believes itself to have moved over what time you'll find there's no contradiction of the sort you're claiming.

When you do the full GR calculation you get a consistent result. You are obviously unaware of this and I'd wager you can't actually do any GR and that's why you're making such a fuss about simplifying to SR so you can use the good old $$\gamma$$ factor. Cranks can just about handle $$t' = \frac{t}{\gamma}$$ and $$L' = \frac{L}{\gamma}$$ equations and I suspect you're the same. As a result you have to convince yourself you're able to reduce the system to SR else you're unable to justify your claim.

If I'm wrong about this show you can do the full GR case. That way we can all be sure you do know what you're talking about and any approximation introduced by using SR isn't an issue. Solve the geodesic equations for the Schwarzchild metric and consider a projectile with initial velocity $$v = \partial_{r}$$.

And given I'm certain you're unaware of it, the examination of radial motion for projectile motions in GR via geodesics is standard homework on any GR course and has real world applications in GPS systems as they aren't in perfectly circular orbits and their ability to very very accurately measure distances via light timings is essential for the system to work. You are, once again, contradicted by experiment.

Also you need not have considered GR since the manner in which the projectile has a force applied to it is immaterial, you're only considering its position and motion relative to some given observer located in space. Then you can use SR but you get the same result, no contradiction. Two objects moving apart, becoming relatively stationary and then doing distance and time measurements are bog standard homeworks. Look at the threads started by Jack_ (if you aren't him that is), he tries to invalid SR using such systems (but a different particular effect/result in those systems) and its explained to him many times these are all common homework problems, they aren't new or unknown. They have been worked through and known to be consistent and experimentally accurate. And you, like him, are trying to make an argument from ignorance.
 
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Books and page numbers please.
No, interweb only.

Google for: "Does the notion that space inside the horizon of a black hole falls faster than the speed of light violate Einstein's law that nothing can move faster than light? No. Einstein's law applies to the velocity of objects moving in spacetime as measured with respect to locally inertial frames."

And this:
Code:
Here are some of the times you will age when journeying to a few well known space marks, arriving at low speed:

4.3 ly        nearest star            3.6 years
27 ly         Vega                    6.6 years
30,000 ly     Center of our galaxy     20 years
2,000,000 ly  Andromeda galaxy         28 years

For example, when traveling from Earth to Vega, arriving at low speed, after 6.6 years on your clock the Earth will have moved 27 light years away, an average speed of 4 light years per year. That's perfectly fine in relativity because it isn't a locally measured speed. What makes this trip possible without exceeding the speed of light limit, as locally measured, is relative contraction and expansion of space (a.k.a. length contraction and uncontraction).
 
Sounds highly plausible to whom? To you. Doesn't sound in the slightest bit plausible to me and I'd wager the same about anyone else who has studied physics to any great depth.
A request: Please don’t write such long posts. I only have a so much time for this stuff. Just point out a couple things you think are wrong. Leave other things for subsequent posts. Please? I really have no choice but to make some drive-by comments here.

Galaxy dynamics cannot be explained by simply running gravitational collapse backwards. The data contradicts your claim.
Like what? I’m sure nature provided a superfluous expanding space, to satisfy our original incorrect thought about what was needed to prevent a cosmic center or edge. Data other than from Hubble came after the notion of expanding space was formed.

It could but we reason people say its expanding faster is that the evidence disproves flatness in the manner you're talking about.
The explanation for dark energy that I’ll give here will explain accelerating cosmic expansion without space itself expanding. Dark energy and the energy of inflation theory will be removed from cosmology, and nothing ad hoc will be added back.

Doesn't mean your claim is correct, things don't accelerate when projected upwards, be it over a millimetre or a mile.
They do in fact, and I have just completed the calculations to see it. It will take me through the weekend to format it for here.

I asked you to show it. You haven't. I'll give you another chance to provide it before I simply conclude you're a liar.
I told you I wouldn’t do them for you. I’m doing them for Pete. He asked nicely. And I told him it could take me through the weekend.

Why would close to light speed make any difference?
You’ll see why. All will be explained in due time.

The Pound Rebka experiment saw photons redshift when fired upwards over a distance of a few dozen metres.
That doesn’t change the fact that SR can provide the correct answer for a gravity experiment, to a certain precision. Pound Rebka just shows that SR would provide the wrong answer at a higher precision.

You don't have any experimental evidence either, you're having to ignore things you don't get right and as a result you're just changing your story.
I don’t need experimental evidence for acceleration away. It’s a prediction. Using existing well-tested theory, no less.

You sad "I don't have a formal background in physics but I have read some books on the basic ideas, enough to mostly follow what he said.". I took that to mean you've read pop science books. If I'm wrong about this please explain precisely what you have read and know about relativity so as I know what level to pitch my explanations. I assumed low because anyone who gets his physics knowledge from dreams is not putting themselves in a position which makes them seem rational and informed.
A layman can understand anything given the right teacher. If you throw something at me and I can’t tell whether it’s relevant, I’ll ask you to clarify.

If you can't justify your claims to a single postgrad on a forum what makes you think you'll have an easier time with journal reviews by professors?
Peer review, give me a break. Who knows how much further along we’d be without it. Real physics is done right here. Watch.

You should have expected you'd be asked further questions!
Just don’t ask so many or bring up so many issues, and don’t repeat them. I’ll get to them all if you do that.

And if you think I'm rude then you've never been to as conference. I've seen people giving talks to hundreds of researchers be told "You're wrong, this is terrible and stupid because of X, Y and Z", people storm out in disgust or to be ripped to shreds in front of all their fellow researchers by one person who isn't going to take any shit from someone making unjustified claims.
I don’t care if rudeness is rampant in your industry. I can take it, I just don’t tolerate it. Do you see the difference? If you want to know solutions to some of physics’ biggest problems, don’t be rude to me.

You justify your claims then I'll admit I'm wrong.
Doubtful! But we’ll see.

You being rude to me wouldn't bother me in the slightest as I am not making claims about my work.
True scientists are polite.

…OK, I see I’ve got another page of your stuff left. Not gonna happen, sorry. I’ve got calculations to format, after all.
 
A request: Please don’t write such long posts.
You back up your claims and I'll post less. How's that?

The explanation for dark energy that I’ll give here will explain accelerating cosmic expansion without space itself expanding. Dark energy and the energy of inflation theory will be removed from cosmology, and nothing ad hoc will be added back.
And I bet it can't actually produce quantitatively accurate results.

I don’t need experimental evidence for acceleration away. It’s a prediction. Using existing well-tested theory, no less.
Its not. I explained in my previous post what it is you're doing, you're talking about from the point of view of the projectile which is not in inertial motion.

You're not doing anything new or unknown, you're just coming up with a more convoluted way of saying "When something slows down relative to a given observer length contraction reduces". You didn't need to come up with the gravity case and then talk about the equivalence principle, the limiting case is basic special relativity. As I'll explain :

A is stationary in Frame 1 at x=0 for all t.
B is moving, in Frame 1, at speed v and at x=vt for t>0.
B is stationary in Frame 2 etc
B undergoes instantaneous deceleration at t' = T and sees the distance to A go from vT to $$\gamma$$vT by length contraction disappearing.

This is what you're referring to, that B decelerates yet gets further away. This is not a contradiction, other members (if you aren't them) have brought it up before. Such basic mechanics are covered in any SR course and there's no contradiction. All frames agree on all physical predictions and causality. Nothing else is needed, anything else is a hang up people have due to believing their intuition, which is Newtonian.

A layman can understand anything given the right teacher.
Yes, the amount of time required might be considerable though due to the sheer volume of information required.

Peer review, give me a break. Who knows how much further along we’d be without it. Real physics is done right here. Watch.
You're obviously not someone who just 'had a dream', you're a crank who wanted some excuse to post his nonsense. Your comment about peer review demonstrates you don't like it and probably have had experience in being rejected. You're saying "Basic standards?! Give me a break!". If your work can't stand up to scrutiny then why should it be believed? If we simply accepted anything without justification we wouldn't be further developed, we'd be less developed. Remember the Dark Ages? That's when religion ruled and accepting without evidence was the norm. And you aren't doing anything new, you're simply showing us all you have no experience with SR by making a fuss about a basic result your intuition doesn't like.

I don’t care if rudeness is rampant in your industry. I can take it, I just don’t tolerate it. Do you see the difference? If you want to know solutions to some of physics’ biggest problems, don’t be rude to me.
Without even having seen your 'solutions' I'll be you money you couldn't pass peer review in a reputable journal because your work is nonsense. Your comment about peer review suggests this has already happened.
 
I gotta do 2 more posts to get to post links, so I'll do some of these:

Its not. I explained in my previous post what it is you're doing, you're talking about from the point of view of the projectile which is not in inertial motion.
No, in the accelerated frame; i.e. an observer on the ground. The projectile is in inertial-enough motion. There always exists a sufficiently small frame in which the variations of gravitational acceleration can be neglected.

This is what you're referring to, that B decelerates yet gets further away. This is not a contradiction, ...
I can't follow you completely in this scenario. B gets further away from what? A? In A's frame? If you fill in details I could follow you.

Such basic mechanics are covered in any SR course and there's no contradiction.
I'll show acceleration away that is measurable. That's all that matters.
 
Without even having seen your 'solutions' I'll be you money you couldn't pass peer review in a reputable journal because your work is nonsense.
Highly doubtful that a genuine solution to a major physics problem could pass peer review. It hurts, not helps the progress of physics. I've already given one solution here, to the flatness problem. The observations that supposedly confirm the notion of expanding space are being misinterpreted because of spatial expansion that is relative (depends on frame), which makes objects thrown upward at close to the speed of light accelerate away as an observer on the ground measures.
 
Here we go. Below are Newton's vs. Einstein's predictions for the height that a projectile launched upward from the ground at a specified speed reaches over time, as measured by an observer on the ground (accelerating frame). First a control prediction at relatively low launch speed (0.007c), showing that SR matches Newton. I chose -1.03 ly/yr^2 (light year / year^2) for gravitational acceleration, which is -9.8 m/s^2. However, I’m assuming a planet for which g is sufficiently constant over the whole experiment, so that SR gives high-enough precision results. (I could always choose a planet such that SR is accurate to, say, a thousand significant digits, no matter the height the projectile reaches.) The equations that are shown I found at this site. I set c = 1 to simplify them (which I can do when using units of light years and years). I added a trend line to the plot:

suL0n.png


Next, the launch speed is set to 0.99c. Now SR predicts acceleration away, made clear by the trend line:

dZHDx.png


I knew I would find this result after what the physicist in the dream showed me.

Even though I chose a planet for which g is sufficiently constant over the whole experiment, SR predicts acceleration away for any part of the plot you see, no matter how small. That means that a projectile launched upward from the Earth at that speed also accelerates away, initially at least, and measurably so. There is a logical explanation for that of course, and there is also a logical explanation for why this means that any free object receding from the Earth at a speed sufficiently close to c accelerates away as we measure, including the supernovae that make up the observation of accelerating cosmic expansion. In other words the second plot above is part of the solution to the dark energy problem, showing that dark energy need not exist to explain what we observe. I’ll explain the rest later if I still have an audience; I’m out of time now.
 
I'm only going to show that SR predicts that an object thrown upward at close to the speed of light accelerates away as measured from the ground. (To be clear, by "accelerate away" I mean that its change in distance per unit time increases.) The experiment is obvious from that.
In your graph, you have distance measured by ground rulers, and time measured by moving clocks.

To get acceleration as measured from the ground, should you not have t on the horizontal axis, rather than T?
 
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