My gravity theory

Student Project A, Global Positioning System, from Exploring Black Holes. Edwin Taylor and John Wheeler
http://www.eftaylor.com/pub/projecta.pdf

 

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brucep, I noticed in the link you posted that it describes the least-action principle. What's that all about? Was Newton wrong? A quote from your link:

http://www.eftaylor.com/leastaction.html

 

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Everything you need to answer your question is right in the link you posted. I would suggest reading Prof Taylor's "Call to action" to start. Note that they derive Newton from the principle of least action:

Simple derivation of Newtonian mechanics from the principle of least action
http://www.eftaylor.com/pub/NewtonFromAction.pdf

Read Prof Taylor's call to action. See if you can 'get the gist' of Figure 1.

 

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Just so you know Tom Van Flandern, may he rest in peace, was a 'card carrying' crackpot. He thought the GPS didn't need the relativistic corrections. He knew lots of physics and worked for NASA in Celestial Mechanics. His main flaw was he thought the local coordinate speed of light could be much > c. He also felt this wouldn't be a drawback for relativistic physics. Over at Google forums sciphysicsrelativity they're some classic, long running, arguments between Steve Carlip, and others, trying to get Tom to come to grips with reality. They're all archived.

From: Living Reviews in Relativity [click pdf}
Relativity in the Global Positioning System. Neil Ashby
http://relativity.livingreviews.org/Articles/lrr-2003-1/

The other Project A I posted is for a simple derivation accounting for relativistic effects from the Schwarzschild metric.

 

Obviously Special Relativity is needed. It’s needed anywhere there is ‘sufficient’ inertial motion that can be measured from any one frame, toward any other. It is interesting that so many would try convincing one person to come to reality. This sounds vaguely familiar.

I suppose we could decide a minimum relative velocity threshold shouldn’t we? Just something that states, “at ‘X’ Km/s, time dilation is immeasurable, incalculable, or otherwise not observable.” Perhaps someone has their name on this number, but it would be good to have it handy I think. To find the number mathematically, might we use the inverse square of “distance”, (divergence) from zero state? Meaning that the further we are from the speed of light the less time dilation is observed; exponentially. Might this be same equation as gravity’s effect is at a certain distance from a central mass? I like it.

The document you provided covers pretty much all the variables to be considered with the GPS system. The depth of what Relativity means to systems like this, or ANY coordinate system, is astounding.

Relativity is no mumbo jumbo, and it is what is truest to our understanding of all things large and small at any serious level. Either light speed has to give, or time must give. So far, as uncomfortable as it may be to some, time submits to light, every time. Time also submits to gravity, because light is our ‘Daddy’ (lol), but Gravity is our Mama, apparently. Everything else has to fall in line from there I think.

 

Hi Scott;

Thanls for the reply. I haven't yet read the article you linked, but seeing as it isn't ridiculously long, has no math, etc, I have downloaded it to read soon. In the meantime ..

This is getting curiouser and curiouser (to borrow from Alice).

Hitherto we've been told that the time dilation effect would be only metres over a much longer period - not 10 miles a day as you say above. Nor has it ever been pointed out by relativity proponets, that the satelites are reset once a day !

Reset ONCE A DAY ? That's incredible !

Why not then dispense with what must be an incredibly complex and expensive process .. dispense with 24 atomic clock altogether, and simply broadcast the time to the satelites every second ? Or perhaps every hour, and have a simple 60 pulse mechanism within them that divides that one hour span into 60 equal parts ?

Something smells fishy about this whole 'GPS proves relativity' thing.

 

PS - and why are we told that prior to launch, the satelites are calibrated (or slowed) to take into account the time dilation they will experience ? Why then the need to reset them once a day ?

 

In order to know what he did not say, you would first need to know what he did say. Principia Mathematica is free on Google Books. Read it and find out some of what he did say and you'll be one step closer to declaring what he did not say.

You are asking how power relates to vehicle acceleration. You should have gotten to this question way, way back when you first brought it up (although it's off track from gravity. Note, Principia will cure you of all of your doubts about gravity.)

If you doubt that power increases acceleration, then you need only understand that F = ma. (And yes, Sir Isaac Newton did say that and a whole lot more). Next you need only admit that the force we are talking about here is the force parallel to the pavement as the power in the wheels is spent pushing the car forward. The force of the tire pushing against the pavement is governed by τ = r×F. That is, rear wheel torque equals wheel radius (normal to the pavement) cross Force (opposite the direction of travel). The car reacts (Newton) with an equal and opposite force, F = ma, accelerating the car.

Reversing this, and collapsing to scalar: a = F/m and F = τ/r so a = τ/(rm). Wheel radius and mass of the car are constant. Therefore this simply says that vehicle acceleration is proportional to rear wheel torque. Increase the rear wheel torque and the vehicle accelerates. Similarly, the car with the greatest rear wheel torque gets greater acceleration.

Rear wheel torque is proportional to engine torque, since you didn't change gears. Therefore the greater the engine torque the higher the acceleration of the vehicle. However, the car with the higher gear ratio gets a mechanical advantage; it will accelerate more for the same amount of engine torque. But it's revving higher at a higher gear ratio which means it's at a higher power level. This is governed by P = τ · ω, or engine power equals engine torque times tach (use rad/s and Nm to get Watts, it's so much easier, that's why I converted your numbers to SI). This simply confirms that the car with the higher gear ratio develops more power at a given torque. On the other hand, I have just demonstrated that higher power (at a given tach) increases engine torque, increased engine torque increases rear wheel torque, increased rear wheel torque increases vehicle acceleration, so, as I said before, an engine with more power accelerates the vehicle more. Similarly, for two engines of the same power capacity, the one running in higher gear or same gear higher gear ratio develops more power and thus accelerates faster.

Bear in mind that you can quickly confuse this by talking about the engine's power capacity as opposed to the power developed. In your example, two cars leading off at the same slow speed are developing only a fraction of their capacity. When they hit the accelerator, the power developed quickly reaches the maximum capacity. In this case the more powerful engine wins regardless of gear ratio. For example, a space shuttle in any conceivable gear ratio will still leave you at the intersection wondering what that blur was as you peel off in your hopped up dragster.

That's putting it in words since you don't do math. The simplest and most concise way to say this is P = F·v, that is, for a given velocity the car with the greatest power will develop the greatest force of acceleration.

As a homework assignment, I'm going to task you with finding the gear ratio that an engine with the capacity of the space shuttle would have to have in order for you to win the race in your A vs B question. You can pick any stock car you like. Part two of my question is: how many freight cars of full of lead the shuttle engine drag behind itself and still beat you, using the same gear you're using.

The day I need to turn to you for help is the day I put a gun to my head, to put myself out of my misery, since that will be the day I am drooling, incontinent, and unable to add up the change in my pocket.

What's to understand? This is beginner's math and science. And how can you help anyone in math or physics when you've never gotten past the junior high level? You should respect your elders. And especially you should try to learn from them. Sure, it's not easy. But remember this: idleness is the devil's playground. Now go wash behind your ears before the oatmeal gets crusty. And next time use a spoon.

Shaft velocity is irrelevant to this question. You need only understand that input torque times gear ratio equals output torque. That's putting it in words since you don't do math. The simplest and most concise way to say this is P = F·v, that is, for a given velocity the car with the greatest power will develop the greatest force of acceleration. The answer is obviously 10. Notice, if you were working in SI, we could easily get the power in Watts by taking the torque in N·m times the shaft velocity in rad/s. In physics we speak of instantaneous velocity. This means that the velocity can be changing, but we recognize that at every instant the laws of physics still apply. Newton was very good at this, recognizing that motion can be broken down into differentials which he called fluxions. Of course he said it in Latin, so we can just as well call them differentials. You'll discover differentials (not gears but mathematical concepts) if your math persona ever grows up and goes off to college. Right now it's stuck in the terrible twos, throwing its bowl of pap at every intelligent person that comes along, even the ones we keep inviting over for dinner, such as good doctors Newton and Einstein.

You've not been a good boy, so I won't give you a lollipop, but I will give you an admonishment from the good Sir Isaac as he went out of the door brushing the globs of Malt-O-Meal off his waistcoat. He wanted you to know that your claim about gravitating to the core of an object is proven wrong. He directs you bend over and take your spankings from his work in Principia:

Proposition LXXXIX. Theorem XLVI. If there be several bodies consisting of equal particles whose forces are as the distances of the places from each ; the force compounded of all the forces by which any corpuscle is attracted, will tend to the common centre of gravity of the attracting bodies and will be the same, as if those attracting bodies, preserving their common centre of gravity, should unite there and be formed into a whole.

Don't make me put you in the corner writing that over and over on your slate until you've got it memorized. Now finish your homework and I'll let you go out and play with your Tonka trucks. And next time, stop bragging about how you've learned to feed yourself. This whole thread is a wreck, with your dinner splattered all over the walls. Next time just sit still and hold your mouth open, and we'll take care of getting the porridge down your starving little beak.

And I want you to sit down and write an apology to the good Sir Isaac for being such a nuisance and for bearing false witness against him.

 

An error of 1 ns is an error of 1 m. However in geolocation a geometrical problem has to be solved (the intersection of pairs of hyperbolas of rotation) so this one meter blows up into a 3D region of uncertainty that's even larger. If the two surfaces are very flat and parallel at the intersection, you get a long thin box of uncertainty which can be too far off. Without calibrating for time warp, you would indeed be kilometers off.

You misunderstand how GPS works. Time dilation is cumulative, and it's thousands of meters per day in error per hyperbola. Hence the calibration for relativity.

High precision clocks are required to keep the phase between them from walking away. GPS works by measuring time difference of arrival between clock edges from pairs of sats, so without very precise clock edges it would be useless. Hence the highly stable references for the clocks.

The satellites broadcast, that's how your receiver is able to measure the time difference of arrival. The time difference describes a hyperbola, with each of the two sats at the foci. You are somewhere on the hyperbola. Find another pair of sats, do it again, and where the hyperbolas intersect is where you are. But this only works if they are accurately synchronized, transmitting their position and the time of day. This is why time dilation must be calibrated out of the measurements

They do in fact transmit periodically. Your receiver has to average over many readings, and won't finish until the standard deviation converges. But it's time difference of arrival, that's the method used.

Not at all. You need only learn how it works. It is in fact conclusive proof that the sats are in time warp.

 

Well like I said, I debated this topic with a serious mathematician for over 2 years. That mathematician was representing Newton's views, so that mathematician was teaching me what Newton had to say. I was not in agreement with that mathematician, so I was not agreeing with Newton.

I know how torque and HP work, I am asking you questions to see if you too know how they work, as you don't appear to have any understating at all on the subject.

So what you are saying is that I should continue to believe a magical attraction between masses causes them to come together, because Newton said so? Are you suggesting that I should believe magical attractions are real because Newton said so?

Power increases acceleration? So let me get this straight. An engine is operating at 2500 RPM. It was previously on a dyno and measured to produce 200 lb-ft at 2500 RPM. HP=torque*RPM/5252. The HP at 2500 RPM is 95.2 HP.

So according to your statement, the 95.2 HP at 2500 will increase the acceleration. Would you like to stand by that belief?

Did you understand the hint I gave you? Your mind is closed to what I am telling you. That is because you believe that I am an idiot, and that you are correct. You're wrong on both counts. When you are honest with yourself then you may start to understand this, but until then it's not going to happen. You are not honest with yourself and you are not open to learning.

 

Hey Newton, you're full of it. Stop talking about magical attractions and come down to reality.

 

I don't think you are characterizing Newton's beliefs accurately. In the Newton quote note the words "as if".

"Proposition LXXXIX. Theorem XLVI. If there be several bodies consisting of equal particles whose forces are as the distances of the places from each ; the force compounded of all the forces by which any corpuscle is attracted, will tend to the common centre of gravity of the attracting bodies and will be the same, as if those attracting bodies, preserving their common centre of gravity, should unite there and be formed into a whole."​

Newton was not too fond of the idea of magical action at a distance either. He wrote in a letter (see http://plato.stanford.edu/entries/newton-philosophy/#ActDis):

"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it (Janiak 2004, 102)."​

So you and Newton shared the notion that action at a distance was a problem.

 

Another astute observation on your part. And add me to the list of those who share that notion.

 

He was wrong again, wasn't he?

 

No, his theory of gravity was correct. He knew it was correct. He knew how gravity acted, but he didn't know what it was.

From wikipedia:

"Newton's postulate of an invisible force able to act over vast distances led to him being criticised for introducing "occult agencies" into science.[52] Later, in the second edition of the Principia (1713), Newton firmly rejected such criticisms in a concluding General Scholium, writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena. (Here Newton used what became his famous expression "hypotheses non fingo"[53])."​

We still don't know what gravity is. Just as we don't know what mass is or what energy is or what space is. We do have a pretty good idea how they all act and interact.

 

Thanks for all that. Yes, I know the satelites broadcast, etc.

Here is my simple question, which I don't think has been addressed here yet.

The satelites have a critical requirement to have the exact time, right ? All of them, and synchronised. Thus they have the dizzying array of atomic clocks, time dilation calculations, pre-calibrations, etc.

Then why not simply broadcast the exact time to them, from earth, at suitable intervals, say every second or minute ? Would that not do away with all the aforementioned clocks, calculations, etc ?

 

Is anyone able to elucidate on this ? It's a fairly straight forward question.

 

That is done periodically. GPS time in each satellite is resynchronized every few days. This allows ground stations to have problems (i.e. they were blown up, power went out etc) and still have navigation systems work well for several days. To be accurate enough in the interim, atomic clocks are used.

 

Hi and thanks for the reply.

Ground stations being blown up, mal functioning, etc, is a moot point. So can GPS satelites, and there are a lot more ground stations than satelites. And just as there are four spare satelites for mal function contingencies, etc, there could be 40 (or whatever) spare ground stations / simple transmitters.

I continue to wonder; WHY isn't the precise time relayed to the GPS satelites at suitable intervals (one second, one minute, etc) so as to obviate the need for all the highly complex and expensive atomic clock stuff, paricularly with the inherent complexities of the so called time dilation effect ?