Shown solutions to physics problems in lucid dream

[AlphaNumeric]

Your distance scales are in multiples of $$5 \times 10^{-6}$$ light years. That's around 50 million kilometres, which is half the distance to the Sun. Gravity most certainly is not constant over such distances.

If you're right then you shouldn't be needing to make simplifications and assumptions, you should be able to obtain the motion of projectiles by solving the full, non-simplified equations of motion. Newtonian physics makes it easy, $$F = m\ddot{r} = \frac{GMm}{r^{2}}$$. For relativity you solve the geodesic equation for the Schwarzchild metric. If you're right then you should be right for the full theories and it means you can exclude the possibility you're making assumptions about GR to SR or constant gravity which may turn out to be wrong.

I'll again comment that the effect of projectiles under gravitational forces and their accelerations are well tested via Gravity Probe A, Gravity Probe B and the GPS network. GR has correctly predicted the outcomes in all of them, which are sufficiently sensitive to detect the kind of errors you're claiming. You can't hide behind "Well no one has done a high velocity experiment", because the same deviations would appear in low velocity experiments provided you're doing sensitive enough experiments and Gravity Probe B and the GPS network are.

If you claim the mainstream has gotten it wrong then you need to obtain the data from those experiments, derive the GR predictions, demonstrate there's a disagreement with the results and then demonstrate your idea doesn't have said disagreement. Presently all you've demonstrated is you make assumptions which aren't valid and then blame relativity.

 

[Ophiolite]

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.

I'm taking this as an invitation. AlphaNumeric, bless his heart, has systematically skinned, gutted and stuffed you. Your ignorance has been demonstrated, not by his dissection of your arguments, but by your failure to respond to them in any meaningful way.

His posts are replete with calculations and references to established theory. Your are filled with handwaving and third rate rhetoric. Any casual lurker with a brain a smattering of an education reached a conclusion about you and your 'theory' a long time ago.

So we have to be polite if we want an answer to physics' biggest problems, do we? Well, **** off you dumb prat.

 

[BertBonsai]

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?

No, time in the SR graph is measured by a clock on the ground. T is the time elapsed in the accelerating frame. Your frame, as you read this, is accelerating as if you were in a rocket accelerating at 1 Earth gravity. The t is the time elapsed in the projectile's non-accelerating (freely falling) frame.

 

[Crunchy Cat]

Nah, it comes right from the physics books. So does relative expansion. I can give examples if you ask nicely.

Books and page numbers please.

No, interweb only.

Evasion from the get-go... sigh.

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:

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).

None of this supports your assertion that "space doesn't expand".

 

[BertBonsai]

None of this supports your assertion that "space doesn't expand".

I didn't say it did. It was your assertion we were addressing. Those are university-level sites, just as good as the books they agree with.

 

[BertBonsai]

Your distance scales are in multiples of $$5 \times 10^{-6}$$ light years. That's around 50 million kilometres, which is half the distance to the Sun. Gravity most certainly is not constant over such distances.

I didn't say these experiments are taking place on Earth, or even in our solar system. In the text I am clear about choosing a planet that’s a good lab for these experiments.

My calculator (Excel) has issues dealing with very small numbers, so I chose a larger planet. Matlab could do the calculations for Earth for small heights, and would still show acceleration away for an initial velocity close to c. It’s clear from the equations and the plot that it would.

For relativity you solve the geodesic equation for the Schwarzchild metric.

That's unnecessary according to the principle of equivalence. Google for: "For sufficiently small regions, the special theory of relativity is correct!!"" I chose a sufficiently small region, which can be any particular size (even a light year across or more) given a sufficiently large planet.

I'll again comment that the effect of projectiles under gravitational forces and their accelerations are well tested via Gravity Probe A, Gravity Probe B and the GPS network. GR has correctly predicted the outcomes in all of them, which are sufficiently sensitive to detect the kind of errors you're claiming. You can't hide behind "Well no one has done a high velocity experiment", because the same deviations would appear in low velocity experiments provided you're doing sensitive enough experiments and Gravity Probe B and the GPS network are.

The deviations could be unnoticeable in low-velocity experiments, as the first SR plot shows. The difference could be not until the 100th significant digit, say, beyond the precision of even those experiments you mention. But in any case it doesn't matter that others haven't noticed it yet in experimental data. Your point here is irrelevant. The equations predict what they predict, regardless of any experiment, and according to the principle of equivalence my application of SR is perfectly valid.

If you claim the mainstream has gotten it wrong then you need to obtain the data from those experiments, derive the GR predictions, demonstrate there's a disagreement with the results and then demonstrate your idea doesn't have said disagreement.

Nope! I’ve proven that SR predicts acceleration away. I’ve pointed out the existing equations so that anybody else can prove it. My work is done on that. It doesn’t matter what experiments show--experiments are completely irrelevant to this finding. That said, there exists one high-velocity experiment, and that is the high-redshift supernovae that make up the finding of accelerating cosmic expansion. That experiment shows acceleration away.

Presently all you've demonstrated is you make assumptions which aren't valid and then blame relativity.

Nope, didn't blame relativity. I'm obviously depending on relativity here. Presently I have demonstrated one of the greatest findings in physics of the last 50 years at least. (Thank you, dream physicist!) Objects thrown upward at close to c measurably accelerate away, according to GR. Who would've thunk it?

 

[BertBonsai]

AlphaNumeric, bless his heart, has systematically skinned, gutted and stuffed you. ...

Too bad physics disagrees!

 

[Pete]

No, time in the SR graph is measured by a clock on the ground. T is the time elapsed in the accelerating frame. Your frame, as you read this, is accelerating as if you were in a rocket accelerating at 1 Earth gravity. The t is the time elapsed in the projectile's non-accelerating (freely falling) frame.

Yes, my mistake.
I notice that distance is measured in the non-accelerating frame. Have you considered the distance that will be measured in the ground frame?

Can you upload your spreadsheet somewhere (eg Skydrive)?

 

[BertBonsai]

Yes, my mistake.
I notice that distance is measured in the non-accelerating frame. Have you considered the distance that will be measured in the ground frame?

Distance in the SR graph is measured in the ground frame. D is the distance (height) in the accelerating frame. (D and T are the axes of the graph.) The d is the distance in the projectile's non-accelerating frame, and is calculated only as a means to get D. Note that the time increment d_T is also in the accelerating frame, as it should be.

Can you upload your spreadsheet somewhere (eg Skydrive)?

For you, yes. I'll take a look at that site later, maybe tonight.

 

[Pete]

Distance in the SR graph is measured in the ground frame. D is the distance (height) in the accelerating frame. (D and T are the axes of the graph.) The d is the distance in the projectile's non-accelerating frame, and is calculated only as a means to get D. Note that the time increment d_T is also in the accelerating frame, as it should be.

Ha. I should read more carefully before posting. So, you're saying that according to SR, a uniformly accelerating observer chasing a relatively high speed inertial object will never catch that object? I'm thinking there is something wrong with your equations. I'll nut it out if and when I find time.

 

[AlphaNumeric]

That's unnecessary according to the principle of equivalence. Google for: "For sufficiently small regions, the special theory of relativity is correct!!"" I chose a sufficiently small region, which can be any particular size (even a light year across or more) given a sufficiently large planet.

You're incorrect. Yes, for sufficiently small regions SR is a decent approximation but not over light years! Are you telling me that the gravitational acceleration felt by someone on the Earth right now is the same as they would feel if they were trillions of miles away?!

If you can't justify your simplifications clearly and correctly then you should be using the full theories so that you completely avoid the issue of what simplifications are valid. I've already told you this but I suspect you're not going to do it because you know you don't understand full GR and you've convinced yourself you do understand SR well enough to make claims about it. You're wrong.

Nope, didn't blame relativity. I'm obviously depending on relativity here.

I'm certain you can't do relativity to the level of a university exam. If you think I'm wrong on this then I'll be happy to provide you with some questions. The fact you don't know GR and so you think other people you talk to don't know GR, thus allowing you to make shit up is a flawed line of logic. Some of us do know GR and see that you do not.

Presently I have demonstrated one of the greatest findings in physics of the last 50 years at least.

Either you're very stupid or very egotistical. Probably both.

Objects thrown upward at close to c measurably accelerate away, according to GR. Who would've thunk it?

Considering you haven't used GR only an idiot would 'thunk' you've done it. And only a very very stupid person would believe they got it from their dreams.

I'm trying to work out if you're spinning the whole "It came to me in a dream" nonsense to try and get people's attention or you really are so laughably stupid and delusional you honestly believe it.

 

[BertBonsai]

Yes, for sufficiently small regions SR is a decent approximation but not over light years! Are you telling me that the gravitational acceleration felt by someone on the Earth right now is the same as they would feel if they were trillions of miles away?!

It's not the Earth, as I've said three times now.

If you can't justify your simplifications clearly and correctly...

It's clear and correct. You just didn't read it.

I'm certain you can't do relativity to the level of a university exam.

Keep wondering. What we do know is you haven't admitted you're wrong like you said you would. I've proven acceleration away and now you're making excuses.

Considering you haven't used GR only an idiot would 'thunk' you've done it.

GR would return the same result to the same number of significant digits. That's implied by "For sufficiently small regions, the special theory of relativity is correct!!" If you really are a post-grad in a science field, I suggest you do lots of logic problems to help you see the forest for the trees. That's meant to be constructive. A good book for that is Thinking Physics.

 

[BertBonsai]

So, you're saying that according to SR, a uniformly accelerating observer chasing a relatively high speed inertial object will never catch that object?

The accelerating pursuer could still catch up to and pass the high speed inertial object. As measured from the ground of some planet, either of them could in principle recede at more than one light year per year, with no limit. Replace the ground observer with a spaceship's crew, and let the ship pass by an inertial object at high speed, decelerating relative to it. (The principle of equivalence allows this replacement.) An example would be a floating flag that stays halfway between two galaxies. You know that SR allows travel between galaxies in a human lifetime. Ask yourself at what average rate the flag would recede when you've passed it and are decelerating to arrive at the destination galaxy at low speed, perhaps 15 years later on your clock, at which point the flag will be perhaps a million light years away. Ask yourself if, considering that you passed the flag at less than c, it must subsequently accelerate away for that average rate of recession to occur. Ask yourself if, after passing the flag, a shuttle launched from the ship could catch up to the flag.

I'll let you know when I've got the spreadsheet uploaded.

 

[Pete]

The accelerating pursuer could still catch up to and pass the high speed inertial object.

But your graph indicates that in the accelerating pursuer's frame, the inertial object will only recede faster as they accelerate.

Replace the ground observer with a spaceship's crew, and let the ship pass by an inertial object at high speed, decelerating relative to it. (The principle of equivalence allows this replacement.)

And the principle of relative says that this is exactly the same as the ship accelerating and pursuing a high speed inertial object.

An example would be a floating flag that stays halfway between two galaxies. You know that SR allows travel between galaxies in a human lifetime. Ask yourself at what average rate the flag would recede when you've passed it and are decelerating to arrive at the destination galaxy at low speed, perhaps 15 years later on your clock, at which point the flag will be perhaps a million light years away. Ask yourself if, considering that you passed the flag at less than c, it must subsequently accelerate away for that average rate of recession to occur.

Yes, I see where you're going with this. But, there seem to be are complications that you (and I) don't fully understand or haven't considered, because there are inconsistencies.

I suspect that changes in length contraction in the instantaneous inertial frame are getting in the way - that said changes in distance are not in fact a useful measure of relative velocity, that the increasing distance is actually a consequence of decreasing relative velocity.

 

[AlphaNumeric]

It's not the Earth, as I've said three times now.

It shouldn't matter. If your claims are correct then you should be able to obtain the results for any sized object. Smaller objects mean you consider smaller regions as you're simply reducing the 'local approximation' region. Of course if you start considering truly enormous and massive objects such that GR would consider them doomed to collapse into black holes then you introduce another thing you're having to approximate.

It's clear and correct. You just didn't read it.

Yes, its my fault you can't translate your dreams into physics.

Keep wondering. What we do know is you haven't admitted you're wrong like you said you would. I've proven acceleration away and now you're making excuses.

Tell you what, you type up your work into a lengthy clear document, send it to me, I'll convert it into the appropriate LaTeX typesetting for a reputable GR journal and then you can submit it. If you think you've got something submit to a journal.

This is a point I make again and again and again on these forums to cranks who ignore anything anyone says and who profess they are right. If you're so sure you're right why are you wasting time on a forum? Why not just go directly to journals? That's what I and everyone else in the physics community does. Ben, Guest, QuarkHead, myself, Prometheus, we're all in the academic community and despite being regular posters here we don't post our work on forums. If you believe you're right why post on forums? Is it to convince people on forums who don't know any physics? I know a fair bit of physics, are you trying to convince people like me? Posting on a forum implies you do but the fact you ignore anyone who disagrees with you implies you don't. What's the purpose of you posting? The only people you'll convince are those who don't know any physics, so what's the point? Science isn't a popularity contest, you have to support your claims and retort any criticisms. Posting on forums and ignoring everyone who knows any physics smacks of you knowing you're a hack and you simply trying to sucker people who don't know any physics.

GR would return the same result to the same number of significant digits.

Go on, prove it. Just do it for one example, work through the full GR calculation and then repeat it but making various simplifications, making it clear what simplifications you're doing and why. If you're right and you understand the physics you're talking about surely this isn't too much to ask? It's the kind of thing you'd be expected to do if you submitted to a journal.

That's implied by "For sufficiently small regions, the special theory of relativity is correct!!"

I am not disagreeing with the equivalence principle, I'm questioning your application of it. I am well aware certain GR calculations are simplified by picking 'normal coordinates' and derivations of such things as gravitational waves through the use of perturbation theory in the metric. If you're aware of these things also, in a way which is more than just you skimming the Wiki page on 'Bianchi Identities' then you know the manner in which such simplifications are applied to GR models. The applications are done by writing down the full GR theory and then clearly and carefully stating what assumptions/simplifications are made and why and how valid they are. Instead you're brushing over all of this.

I'd like to see you construct the relevant curvature tensors and show that you can apply a Taylor expansion in a curvature dependent parameter such that you formally define the 'local region' in your calculations. Without such formalising you'll struggle to justify your claims in any way other than simply repeating them.

If you really are a post-grad in a science field, I suggest you do lots of logic problems to help you see the forest for the trees. That's meant to be constructive. A good book for that is Thinking Physics.

Ah, nice deflection. Rather than you demonstrating you know relativity to the level you'd like people to believe or retort my comments of a technical nature to do with normal coordinates you're saying that its my grasp of logic which is the issue. You have failed to justify your claims, you have failed to demonstrate the assumptions you make about the GR -> SR reduction in your analysis are valid. I'd say that logic of mine is fairly sound, in that if you fail to justify your claims people shouldn't put too much faith in them.

I also like how you've changed your tune over this thread. Initially you were putting yourself forth as little more than an interested layperson whose had a dream and now you're arguing you have an in depth grasp of gravity, cosmology and logic with people who do happen to have demonstrable in depth grasps of gravity, cosmology and logic.

And for the record, since you wonder if I'm telling the truth and you're a relatively new poster here, I've a masters in applied mathematics from Cambridge (covering GR, black holes and string theory) and a PhD in aspects of differential geometry arising from GR's role in string theory. To use your analogy, clearly the people who planted the forest think I can tell the woods from the trees.

 

[BertBonsai]

But your graph indicates that in the accelerating pursuer's frame, the inertial object will only recede faster as they accelerate.

You haven't seen the whole graph! If the inertial object's recession velocity falls enough (so that it's no longer close to the speed of light as locally measured), it does decelerate as measured from the ground, eventually reaching an apex if it didn't have escape speed to begin with. The whole graph can look a lot like a bell curve, with tails at either end. (Which means that an object that falls at close to the speed of light decelerates toward the ground as measured from the ground.)

Yes, I see where you're going with this. But, there seem to be are complications that you (and I) don't fully understand or haven't considered, because there are inconsistencies.

I suspect that changes in length contraction in the instantaneous inertial frame are getting in the way - that said changes in distance are not in fact a useful measure of relative velocity, that the increasing distance is actually a consequence of decreasing relative velocity.

What other inconsistencies than your sentence above? You should let the equations be the guide. Assuming they are correctly applied they tell us what would be measured according to SR, as strange as it may seem. The velocity equation takes into account the acceleration. I'm not using change in distance per unit time to get the velocity.

As the flag decelerates relative to the ship as locally measured (i.e. as v decreases), and as long as v is close to c, in the ship's frame space between the ship and the flag expands (this is length uncontraction) to such a degree that it overtakes that deceleration to make the flag measurably accelerate away. The principle of equivalence tells us that the same behavior occurs in a ground observer's frame.

 

[BertBonsai]

And for the record, since you wonder if I'm telling the truth and you're a relatively new poster here, I've a masters in applied mathematics from Cambridge (covering GR, black holes and string theory) and a PhD in aspects of differential geometry arising from GR's role in string theory.

Congrats, but it means nothing here. Here, you’re making logic gaffes galore.

It shouldn't matter. If your claims are correct then you should be able to obtain the results for any sized object.

I said that my calculator (Excel) has problems dealing with very small numbers, hence the larger planet used. A physicist who can see the forest for the trees can look at those equations and the chart showing acceleration away and immediately realize that a chart for a region small enough for the Earth would likewise show acceleration away.

Go on, prove it. Just do it for one example, work through the full GR calculation and then repeat it but making various simplifications, making it clear what simplifications you're doing and why.

I have proven it. You have a false understanding of what an approximation is. When I’m using a region small enough that SR returns correct results at a given precision, GR could return a different result at the same precision only if the theory is invalid.

If you're right and you understand the physics you're talking about surely this isn't too much to ask? It's the kind of thing you'd be expected to do if you submitted to a journal.

Yes it’s too much to ask (that’s been proven) and I don’t care that journals require superfluous stuff.

I am not disagreeing with the equivalence principle, I'm questioning your application of it.

Then you should go back to your texts until you truly understand it. It really is as simple as: "For sufficiently small regions, the special theory of relativity is correct!!" You haven't shown a problem with that.

If you're so sure you're right why are you wasting time on a forum? Why not just go directly to journals? That's what I and everyone else in the physics community does.

It’s a discussion, which I like. I’m here to find people like Pete, and even you if you’d stop throwing out the red herrings (like this one) and be a bit willing to learn something. I’m willing to learn as well but I’m not going to accept something refutable. What would a journal do for me? The dream physicist told me solutions to many of physics’ greatest problems. I already have that knowledge.

 

[Pete]

You haven't seen the whole graph! If the inertial object's recession velocity falls enough (so that it's no longer close to the speed of light as locally measured)...

But your graph indicates that in the pursuing observer's frame, the inertial object is accelerating away. How can it's recession velocity be falling?
If you plot the object's recession velocity against time, what do you expect to find?
Do you see the inconsistency?
Do you see that the graph is misleading, that the inertial object is not, in fact, accelerating away?

It’s a discussion, which I like. I’m here to find people like Pete, and even you if you’d stop throwing out the red herrings (like this one) and be a bit willing to learn something. I’m willing to learn as well but I’m not going to accept something refutable. What would a journal do for me? The dream physicist told me solutions to many of physics’ greatest problems. I already have that knowledge.

You know, imagining that you have "solutions to many of physics' greatest problems" based on some basic reading and a dream is breathtakingly arrogant. I think that "dream guy" is simply projecting your own misunderstandings. If I was the cynical type, I might suspect that you made up the dream story to give your thread a story hook.

I think you should forget gravity for the moment, and focus on uniform acceleration. Take one step at a time, ask questions, listen to what people say, and when your understanding disagrees with well-polished and fire-tempered mainstream, you should assume that you're missing something until proven otherwise. Then you won't look so arrogant, and very bright people who know what they're talking about (like AlphaNumeric) will find it easier to be polite.

 

[funkstar]

I said that my calculator (Excel) has problems dealing with very small numbers, hence the larger planet used.

Make an analytical analysis, then.

When I’m using a region small enough that SR returns correct results at a given precision, GR could return a different result at the same precision only if the theory is invalid.

How do you know that SR returns correct results for your region?

 

[BertBonsai]

But your graph indicates that in the pursuing observer's frame, the inertial object is accelerating away. How can it's recession velocity be falling?

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.

If you plot the object's recession velocity against time, what do you expect to find?
Do you see the inconsistency?
Do you see that the graph is misleading, that the inertial object is not, in fact, accelerating away?

It does accelerate away as the ground observer measures, the equations show, and there's no inconsistency. Just like how, in the example of the ship traveling between galaxies, there's no inconsistency when a flag that passed you at less than c subsequently moves a million light years away as you measure, in 15 years on your clock. The only way the flag can do that is if it accelerates away (otherwise it'd move less than 15 light years as you measure, in those 15 years on your clock). But v (relative to the flag) decreases during that entire scenario. Play with the equations to see that.

I think you should forget gravity for the moment, and focus on uniform acceleration. Take one step at a time, ask questions, listen to what people say, and when your understanding disagrees with well-polished and fire-tempered mainstream, you should assume that you're missing something until proven otherwise. Then you won't look so arrogant, and very bright people who know what they're talking about (like AlphaNumeric) will find it easier to be polite.

I've amply shown that Alpha is wrong, which predictably resulted in a dump of red herrings and even a CV to look superior no matter what. People like Alpha are satisified only when you kowtow to them. I'm the one being scientific here, besides the dream itself. I've read & responded to the objections. It's natural human reaction to accuse those with new ideas of arrogance.