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Flat Earth Theory / Why UA Violates the Equivalence Principle
« on: June 11, 2021, 12:15:05 AM »
I decided to use my time out to do some reading and put together some thoughts that have been floating around in my mind for awhile now.

Tom and I have been down the path of how GR resolves the “mystery” the equality of inertial and gravitational mass before. This issue is at the heart of what is wrong with FET reliance on the EP to justify both UA and a flat earth, but he refused to accept any source on the subject other than a “physicist”.

So I went straight to the horse’s mouth on the issue. Hopefully, Einstein is enough of a physicist for him.

The wiki claim that GR doesn’t explain the equivalence of gravitational and inertial mass isn’t just wrong, it exposes a basic lack of understanding of the theory. The whole theory of GR is founded on the unity of inertial and gravitational mass, along with the principle of relativity.

According to GR, there is no substantive difference between “gravitational mass” and “inertial mass”. There is just “mass”, and whether or not it is identified as gravitational or inertial is wholly dependent upon its state of motion and/or frame of reference.

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What is important is only that one is justified at any instant and at will (depending upon the choice of a system of reference) to explain the mechanical behavior of a material point either by gravitation or by inertia. More is not needed; to achieve the essential equivalence of inertia and gravitation

http://einsteinpapers.press.princeton.edu/vol7-trans/220 
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It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognize the following fact: The same quality of a body manifests itself according to circumstances as "inertia" or as "weight" (lit."heaviness").

Volume 6: The Berlin Years: Writings, 1914-1917 (English translation supplement) page 317 (princeton.edu)

Albert Einstein’s book: The Meaning of Relativity, pg 58
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“…In fact, through this conception we arrive at the unity of the nature of inertia and gravitation. For according to our way of looking at it, the same masses may appear to be either under the action of inertia alone (with respect to K) or under the combined action of inertia and gravitation (with respect to K’).

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Kottler claims I had abandoned in my later papers the "principle of equivalence" which I did introduce in order to unify the concepts of "inertial mass"and "gravitational mass”

https://einsteinpapers.press.princeton.edu/vol6-trans/249

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In an example worth considering, the gravitational field has a relative existence only in a manner similar to the electric field generated by electro-magnetic induction….

The thought that one is dealing here with two fundamentally different cases was, for me, unbearable. The difference between these two cases could not be a real difference, but rather, in my conviction, could be only a difference in the choice of reference point. Judged from the magnet there certainty were no electric fields; judged from the conducting circuit there certainly was one. The existence of an electric field was therefore a relative one, depending on the state of motion of the coordinate system being used, and a kind of objective reality could be granted only to the electric and magnetic field together, quite apart from the state of relative motion of the observer or the coordinate system

https://einsteinpapers.press.princeton.edu/vol7-trans/151

The significance of understanding the EP this way is that it unifies gravity and inertia into one field, much like the electromagnetic field. One field is responsible for both inertial and gravitational effects as opposed to two different types of mass resulting in two different effects.  It also follows that whenever there is acceleration, a gravitational field exists relative to it. Acceleration produces inertial effects, inertial effects and gravitational effects are both governed by the gravitational field, therefore, whenever there is acceleration, there is a gravitational field relative to it. The existence of the field is relative and its presence depends on the frame of reference. However, by considering both frames together the field always exists in objective reality.

The relative nature of the gravitational field also means that the EP requires that whenever you consider an accelerating system at rest, you must also assume the presence of a gravitational field relative to it.

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The Principle of Equivalence.

Do the laws of nature, known to us in some approximation, allow us to consider a reference system K' as being at rest if it is in uniform acceleration with respect to K. Or, somewhat more generally: Can the principle of relativity be extended such as to encompass reference systems that are in (uniform) accelerated motion relative to one another. The answer is: insofar as we really know the laws of nature, nothing prevents us from considering a system K' as at rest, provided we assume a gravitational field (homogeneous in first approximation) relative to K'. Because in a homogeneous gravitational field, as with regard to our system K', all bodies fall with the same acceleration independent of their physical nature. I call "principle of equivalence"the assumption that K' can be treated with all rigor as being at rest, such that no law of nature fails to be satisfied relative to K'.

https://einsteinpapers.press.princeton.edu/vol6-trans/250

So what does all this mean? Using the often used analogy of jumping off a chair, it means, according the EP, the jumper can
1) Consider the accelerating earth at rest but only if he assumes a gravitational field relative to it exists . In that case, the jumper is subject to the field and is falling from that perspective Or
2) Consider the earth accelerating and he is at rest above the ground with no gravitational field present. That violates the requirement of the EP that whenever there is acceleration, a gravitational field exists relative to it.

It isn’t enough that a field is produced once the ground and the jumper meet.  The concept of a gravitational field being “relative” to the accelerating system implies that there are (at least) two different perspectives.  One in which the field exists, and one in which it doesn’t. If an object is on the surface of the earth and the field only exists on the surface, there is no perspective in which a gravitational field doesn’t exist for that object. There is nothing “relative” about the gravitational field.

All this adds up to mean that there is no scenario in which the jumper can consider himself at rest but not in a gravitational field with an accelerating earth without violating the Equivalence Principle.

RE, however is perfectly consistent with the EP as stated in 1) above because in RE, the earth does accelerate centripetally.

So whatever basis you use to justify UA, you can’t use the EP. There is no “earth rising up to meet” anything.

EDIT: One more thing I forgot to mention.  There is an inherent contradiction in using the EP/UA to argue for a flat earth.  Supposedly, the FET position is that the EP can be applied because the effects of gravity caused by UA and the effects of gravity by GR are indistinguishable.

Except that GR gravity results in massive objects collapsing into spheres and UA gravity doesn’t.  The effects are distinguishable
.


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Flat Earth Theory / Question about the Vomit Comet
« on: April 27, 2021, 09:57:51 PM »
Hoping one of you good people who are familiar with how the Vomit Comet works can clear something up for me.

My understanding is that during parabolic motion, thrust and drag cancel each other out and lift is reduced to zero because of the angle. That leaves just gravity working on the plane and since the plane and the occupants are falling together, there is a sensation of weightlessness.

I don't see how this could work with FE/UA.  Without any other forces to counteract it, the UA force should continue to accelerate the plane up, pushing the floor of the plane up and creating the sensation of weight.

Essentially, no different than our friend in the enclosed rocket ship that can't tell if he's being accelerated up or gravity is pulling him down.

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Flat Earth Theory / The equivalence principle and non-uniform motion
« on: April 19, 2021, 07:29:56 PM »
UA starts with the EP as its foundation as a theory for gravity.  Uniformly accelerated motion is the equivalent of being at rest in a gravitational field, therefore it follows that what we experience as gravity is actually the uniform acceleration of the earth. (Please correct if I have misrepresented)

But why can they be considered equivalent?  Because the situations are symmetrical. In both cases, the observer experiences the same forces (or lack of them).  But non-uniform motion is not the equivalent of being at rest in a gravitational field. The forces experienced by an observer in uniform motion are not the same as the forces experienced by an observer in non-uniform motion.

I think that is where using the EP, in isolation, as a foundation for a theory of gravity breaks down.  It doesn’t explain how gravity works with respect to non-uniform motion.  As long as it is limited to objects that “are at rest in a gravitational” field it works fine, but it doesn’t explain how gravity works with respect to objects that are not at rest in a gravitational field.

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Flat Earth Theory / My Happiest Thought
« on: April 07, 2021, 02:05:29 PM »
Ever since finding this site, I have had this nagging thought that there was something fundamentally wrong with the logic behind relying on the equivalence principle to justify UA, but couldn’t  quite put my finger on it.

I wasn’t thinking about people falling off a roof, but it finally dawned on me.  Special Relativity tells us that accelerated motion warps spacetime. The faster you go, the slower time moves and objects will contract.  The equivalence principle tells us that accelerated motion and gravity are indistinguishable.  The logical conclusion then is that gravity is the warping of spacetime.

Instead, the UA crowd concludes that the EP means there is some mysterious force that is accelerating the earth (and maybe, but maybe not, everything else.) upwards. 

I couldn’t find anything in the wiki that justifies this leap (no pun intended) in logic. Maybe if you took SR out of the equation, it would make some sense but that creates even more problems for UA.  Not to mention the fact that part of what makes the EP so important is that it serves a bridge between SR and GR so that SR is consistent with gravity.

Why should UA be considered a better theory for gravity when it doesn’t even logically follow from the very premise it is based on?  Not to mention the fact that it leaves so many questions unanswered that GR very elegantly solves.

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Flat Earth Theory / Water is always level?
« on: November 03, 2020, 12:40:40 AM »
I read that quite often and it is true enough, but "level" is a relative term.  In RET, it means level with respect to the center of gravity.

In FET, with respect to what is water "level"?

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Flat Earth Theory / UA and Gravitational Time Dilation
« on: October 16, 2020, 06:32:18 PM »
The wiki says about GTD:
Quote
Gravitational time dilation is a phenomenon in which the difference of elapsed time manifests between two events as measured by observers situated at varying distances from the Earth. Time is seen to dilate in accord with the Equivalence Principle, which predicts that all physical effects which would occur in an upwardly accelerating rocket ship should also happen in a gravitational field. Since the time dilation of clocks would occur at different elevations inside of an upwardly accelerating rocket, it must occur at different elevations in the Earth's gravitational field as well. Supposedly only a 'local' effect, the Equivalence Principle and its uniform nature[1] has been confirmed over various elevations

This is all true, but it seems to be used as evidence for universal acceleration, when in fact, it’s the opposite and is pretty convincing evidence against it.

General Relativity says that time dilation is due to a difference in gravitational potential.  According to UA, there shouldn’t be any difference in gravitational potential.at various elevations across the surface of the earth.  The point is repeatedly made on this forum that there is no evidence of that the strength of gravity varies.  Ironically, the wiki itself provides evidence that it does.

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NIST Pair of Aluminum Atomic Clocks Reveal Einstein's Relativity at a Personal Scale (Archive)
  “ BOULDER, Colo. – Scientists have known for decades that time passes faster at higher elevations—a curious aspect of Einstein's theories of relativity that previously has been measured by comparing clocks on the Earth's surface and a high-flying rocket.
Now, physicists at the National Institute of Standards and Technology (NIST) have measured this effect at a more down-to-earth scale of 33 centimeters, or about 1 foot, demonstrating, for instance, that you age faster when you stand a couple of steps higher on a staircase.

If you age faster at the top of the stairs than the bottom of the stairs due to gravitational time dilation, that means there is a difference in the gravitational potential between the top and bottom of the stairs.  Something, that FE/UA consistently denies is possible.

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The wiki makes the equivalence principle the foundation of the FE argument for universal acceleration, but it misrepresents what the equivalence principle says and what it means in the context of general relativity.

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The equivalence principle demands that that mi = mg. Why should this be true in our universe? It has been about 85 years since the discovery of the Einstein equivalence principle, and hundreds of years since the discovery of Newton’s mass equivalence principle. Yet, it is still not understood why inertial mass exists in the first place, or why a mass opposes acceleration with a back acting inertial force. More importantly, it is also not known why there are two totally different physical definitions for inertial and gravitational mass (instead of just one).

The first problem with this statement is that according to the equivalence principle, inertial mass and gravitational mass don’t have two different physical definitions.  In fact, it explicitly says they are the same thing.

The second is that the equivalence principle offers an explanation as to why inertial mass exists in the first place. 

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We then have the following law: The gravitational mass of a body is equal to its inertial mass. It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as “inertia” or as “weight” (lit. “heaviness”). In the following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate of relativity.

Pg 77-78  The Meaning of Relativity by Albert Einstein

The unification of inertia and gravity is expressed in the geodesic equation:

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Formally, the unity between inertia and gravity is expressed by the fact that the entire left side of d2 xν ds2 þ αβ ν ( )dxα ds dxβ ds ¼ 0 is tensorial (with respect to arbitrary coordinate transformations), whereas the two terms separately are not. In analogy to the Newtonian equations one would have to view the first as an expression for inertia, the second as an expression for the gravitational force.

https://einsteinpapers.press.princeton.edu/vol7-trans/358?highlightText=Formally

In other words, according to the geodesic equation inertia and gravity are the same thing because the two elements transform as tensors only when considered as a single entity.

In short, the wiki relies on the equivalence principle, which states that inertial mass and gravitational mass are the same thing, and explains why that's true, to make the argument that inertial mass and gravitational mass are not the same thing and there is no explanation for their equivalence.

That’s pretty much the mother of logical fallacies.

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Flat Earth Theory / Does Flat Earth/UA reject the concept of spacetime?
« on: October 08, 2020, 04:18:35 PM »
The reason I ask is because UA rises and falls (pun intended) on the equivalence principle, but the equivalence principle logically leads (at least according to Einstein) to the gravitational and inertial effects of falling bodies as determined by spacetime...or as he calls it in the quote below the "g-field"

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Inertia and gravity are phenomena identical in nature.  From this and from the special theory of relativity it follows necessarily that the symmetric "fundamental tensor" determines the metric properties of space, the inertial behavior of bodies in space, as well as the gravitational effects.  We shall call the state of space which is described by this fundamental tensor, the "g-field"


https://einsteinpapers.press.princeton.edu/vol7-trans/49?highlightText=metric

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Flat Earth Theory / Center of gravity of objects on a flat earth
« on: August 19, 2020, 07:09:02 PM »
I’ve been reading about universal acceleration in the wiki and it’s a good alternative explanation for gravity for objects that are free falling.  But not everything that falls is in free fall.  Things that are already on the ground or supported in some way topple over, or fall, or drop all the time. According to conventional physics, it is because an objects center of gravity shifts or isn’t low enough to keep it upright.  Something with a low center of gravity is much more stable than something with a higher center of gravity and is less likely to fall.

Is there an FE explanation for why somethings are more stable than others since the conventional “center of gravity” concept wouldn’t apply (I’m assuming)?  What would cause something to be balanced or unbalanced on the flat earth?

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