Shown solutions to physics problems in lucid dream

[BertBonsai]

I looked at your "solution" to the dark energy problem, and it requires SR to be applied to a non-uniform gravitational field over a distance of many billion light years.

It doesn't require that. It doesn't do that or imply that.

For example, show how your methodology differentiates between the cases of:

a) a uniform gravitational field throughout the universe
b) a non-uniform inverse-square law field centered on the Earth

The solution uses SR in only a small region, one that can be arbitrarily small. Even a micrometer-sized region will do.

No, go look up the Schwarzschild metric, it's not just some multiple of the Minkowski (flat space) metric.

I'm looking right at those two metrics now. The Schwarzschild metric is indeed nothing more than the metric for flat spacetime with a gamma factor incorporated into it. The SR metric I’m looking at is for a plane with polar coordinates. The Schwarzschild metric I’m looking at is for a plane bisecting a center of gravitational attraction.

If you do the proper GR calculation, for the case of the Schwarzschild metric, an Earthbound observer will see distant objects being accelerated towards the Earth and either returning, or else asymptoting down to some fixed velocity. Plus nowhere are you accounting for the fact that two clocks ticking simultaneously in one reference frame need no be doing so in another.

No calculation changes the fact that the Schwarzschild metric is nothing more than the metric for flat spacetime with a gamma factor incorporated into it. My equations do account for differences in rates of clocks.

Now your turn, show me how you derived your result, because I think it's mistaken.

See below.

Sorry, but that's a very non-rigorous and effortless attempt you give here.

There’s no need for me to go crazy with rigor for a side topic in a forum discussion. What is logical (leads to correct conclusions) is often considered non-rigorous, for no good reason.

For a guy who complains so much about not getting fair access to peer review, this was a chance for you to show some initiative.

This isn't the thread for that. No journal has seen my work; the whole issue with them that I pointed out is based only on a question I posed to them, so the rigor of my work has nothing to do with it. If you want to point out a problem with my stuff re the issue of peer review you should do it in the other thread. I’m not going to do rigorous calculations for one person in a forum, where I can make my points using simple logic instead.

I did some calculations, and I'll need to double check them at some point, but it appears that if the equations I've used so far are correct, the effect would be noticeable for launch velocities equal to or greater than $$c/2$$.

Before you said "I'm pretty confident the apparent acceleration of the projectile is an effect that will be observed at any launch velocity". That's a lot different what you're saying now. I wouldn't have disagreed with your latter notion. My logic is correct about what you originally said.

No, my calculations indicate that the effect is immediate, and occurs for any projectile launched at half the speed of light or more.

I don’t disagree. I hadn’t figured out at what speed the effect occurs. I just knew it wasn’t at any launch speed. If the effect occurs at c/2 or greater, rather than just at closer to c (like I said), that doesn’t affect any of my major claims in this thread.

The rocket observer does not see the projectile's instantaneous position, they see the light emitted from it at some point in the past when it was closer to Earth.

The measurements that the equations predict ignore the delay in the transmission of light that affects what is seen. The predictions at the rocket site do that too. Such delay does not somehow prove that the projectile isn’t accelerating away as the accelerating observer measures. Any decent book on relativity discusses that delay and how to account for it.

In the example I gave to you, where you pass by a star and come to rest with respect to it, there is no such delay issue; that was by design. When you’ve come to rest with respect to the star you can in principle make an accurate measurement of its distance in an arbitrarily small time, using the parallax method. If between passing nearby the star at less than c and, when you’re at rest with respect to it, measuring it to be 10000 light years away from you after just one year on your clock, it must have accelerated away from you. No other conclusion is logical.

You forget that in SR, the accelerating observer can always be taken to be inertial at that very instant, as if they turned their rockets off for an infinitesimal moment in time. That's how you treat accelerations in SR when doing actual calculations in the real world, as opposed to calculations in the dream world where you can make up whatever the heck you want.

Alright, we’re done. You won’t get that derivation now that you’ve resorted to ad hom attacks. I thought you could hold a decent discussion. It’s too bad this forum isn’t better moderated.

 

[CptBork]

The solution uses SR in only a small region, one that can be arbitrarily small. Even a micrometer-sized region will do.

You have yet to show any such solution. A micrometer-sized region isn't good enough to explain an effect occurring over billions of light years.

I'm looking right at those two metrics now. The Schwarzschild metric is indeed nothing more than the metric for flat spacetime with a gamma factor incorporated into it. The SR metric I’m looking at is for a plane with polar coordinates. The Schwarzschild metric I’m looking at is for a plane bisecting a center of gravitational attraction.

Wrong once again. One is not merely a multiple of the other.

My equations do account for differences in rates of clocks.

They don't account for the differences in simultaneity.

I’m not going to do rigorous calculations for one person in a forum, where I can make my points using simple logic instead.

Your logic is off, that's why you need the math to back it up.

I don’t disagree. I hadn’t figured out at what speed the effect occurs. I just knew it wasn’t at any launch speed. If the effect occurs at c/2 or greater, rather than just at closer to c (like I said), that doesn’t affect any of my major claims in this thread.

All you did was look at the graphs and guess that there would be some flatlining at low enough launch velocities. I also haven't tried for cases where the projectile is launched from other locations, but it's not worth bothering over.

The measurements that the equations predict ignore the delay in the transmission of light that affects what is seen. The predictions at the rocket site do that too.

I never said whether it matters or not. I said the instantaneous position of the projectile is not what the rocket is interested in, they only measure where the projectile was when it gave off the light they're seeing. It really doesn't matter anyhow- the rocket knows it's accelerating, they know their yardstick is changing. As soon as they stop accelerating and make inertial measurements of the projectile, they will see that it was indeed travelling faster away from them when it was first launched.

In the example I gave to you, where you pass by a star and come to rest with respect to it, there is no such delay issue; that was by design. When you’ve come to rest with respect to the star you can in principle make an accurate measurement of its distance in an arbitrarily small time, using the parallax method. If between passing nearby the star at less than c and, when you’re at rest with respect to it, measuring it to be 10000 light years away from you after just one year on your clock, it must have accelerated away from you. No other conclusion is logical.

The logical conclusion reached from studying SR from an actual book (while physically awake) is that the rocket's yardstick is changing. If a rocket is travelling near lightspeed towards a distant star, and hits the brakes, the star appears to jump a great distance forward (along with everything else in the area), and subsequent measurements will then show that it's stationary, hence it didn't accelerate at all. Measurements made from an inertial frame are different from measurements made by an observer who is switching frames.

Alright, we’re done. You won’t get that derivation now that you’ve resorted to ad hom attacks. I thought you could hold a decent discussion. It’s too bad this forum isn’t better moderated.

1) You never had a derivation, because your result doesn't follow from correctly using the Lorentz transformations

2) I agree we're done here, I've seen more than enough misuse of relativity from you based on a dream

I personally recommend the mods should come lock this thing up, and we'll never speak of this subject on this forum ever again.