Tag: einstein

Abstract

An attempt is made to understand Einstein’s theories of relativity, particularly with respect to the central idea of an inertial frame of reference. Available descriptions are confusing and contradictory with definitions of the basic concepts either ambiguous or absent. Einstein himself voiced similar concerns. Some of Einstein’s fundamental errors are pointed out and alternative ideas proposed. The experimental results that are claimed to be explained by the theory of relativity are insufficient to prove the theory of relativity and in many cases, alternative explanations are available.

Inertial frames of reference

The idea of an inertial reference frame is key to Einstein’s theories of relativity, both ‘special’ and ‘general’. It follows that:

• If we can’t understand inertial frames of reference then we can’t understand relativity
• If a text doesn’t explain inertial frames properly then it hasn’t explained relativity
• If reference frames have no consistent, unambiguous definition then relativity is likewise undefined

We take Wikipedia as a respected source of information on this and try to understand the main ideas.

What is a ‘frame of reference’?

In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system, whose origin, orientation, and scale have been specified in physical space. It is based on a set of reference points, defined as geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signalled by conventional markers). – Wikipedia

So a frame of reference is just a coordinate system and as such we can use it to define such a thing as ‘position’. If we now integrate the concept of ‘time’ somehow, we can define the change of position over time and call it ‘movement’ or ‘velocity’.

‘Velocity’ is the rate of change in position respect to a specified coordinate system and agreed time metric.

Likewise we can define the concept of ‘acceleration’ as the rate of change in velocity with respect to a specific coordinate system and agreed time metric.

Coordinate systems (frames of reference) are described as frameworks for the specification of position, velocity and acceleration and that is all.

Conversely, if we are to describe such things as position, velocity and acceleration, then the framework with respect to which they are defined is deserving of the term ‘frame of reference’.

To reiterate: All position and movement is defined with respect to frame of reference (coordinate system).

A first inconsistency?

In the same paragraph, Wikipedia goes on to say:

An important special case is that of an inertial reference frame, a stationary or uniformly moving frame. – Wikipedia

Ouch!

What is a ‘stationary or uniformly moving frame’? Such uniform movement (or otherwise) is only defined with respect to some coordinate system (reference frame), but which one?

We are talking here about the movement of a reference frame itself, not objects within it. Such a movement is nevertheless ‘movement’ and hence must be measured in some coordinate system in order to have any meaning at all. The moving framework cannot be described with reference to itself (it would always be stationary!) and so some other ‘higher’ or ‘universal'(?) framework is assumed here but not explicitly stated.

I would suggest that the reason such a framework is not discussed is because the eventual aim is to give justification to the idea, from Einstein, that no coordinate system is preferred over any other; everything is ‘relative’.

What is an inertial frame of reference?

The abstract idea of a frame of reference was introduced above, but Wikipedia has a whole separate entry now on the definition of a specifically ‘inertial’ frame of reference:

An inertial reference frame is a frame of reference in which Newton’s first law of motion holds true without any corrections. This means that an object either remains at rest or continues to move with constant velocity in a straight line unless an external force acts on it. In such a frame, there are no fictitious or pseudo forces required to explain the motion of objects. – Wikipedia

Compare with the first definition above, where an inertial reference frame is described as a “stationary or uniformly moving frame”.

The first definition is in terms of coordinates, of position, distance, velocity and acceleration (change of velocity over time) but the second is in terms of Newton’s laws of physical motion.

These two concepts are worlds apart and should never, ever, be assigned to the same terminology. There is no concept of ‘force’ within a coordinate system, nor of an ‘object’, ‘inertia’ or even ‘mass’; these are separate entities that need their own definitions.

Note that the first definition of an inertial frame contains no mention of the word ‘inertia’ – and so why refer to it as ‘inertial’? This tends to conflate the idea of inertia with that of acceleration. They are obviously different entities but later descriptions of relativity require that they be effectively the same thing, and so describing a stationary frame as ‘inertial’ makes it a practical certainty that such a conclusion should eventually be reached.

Again, from the same article in Wikipedia:

Inertial reference frames are either at rest or move with constant velocity relative to one another.  – Wikipedia

What does this mean? Two possibilities:

1. This is a definition. Inertial frames are now defined as those that are at rest relative to one another
2. This is a theoretical consequence of the definition in terms of Newton’s first law.
   
   In all likelihood, the second possibility is intended, but it needs some justification. The attempt here is to define the basis of special or general relativity and so accuracy is required.
   
   What does sit mean to: “move with a constant velocity relative to one another“? Remember that velocity is always defined with respect to the elements of a coordinate system and so the relevant coordinate system here should be specified. We can guess here that each coordinate system is to be regarded as an element of the other but this has the consequence that each system ultimately contains a reference to itself!
   
   If the only qualifications of an inertial system are those to do with relative velocity, then why are they described as ‘inertial’?
   
   This is a perfect example of definition creep which seems ubiquitous in attempts to describe relativity. Descriptions start off talking about velocity and acceleration, i.e. events within a pure coordinate system, but soon turn to forces and inertia and after a while the reader becomes hypnotised into believing the central tenets of the theory with no real justification at all.

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Special relativity

From the Wikipedia entry on special relativity:

In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein’s 1905 paper, “On the Electrodynamics of Moving Bodies”, the theory is presented as being based on just two postulates:

1. The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration). This is known as the principle of relativity.
2. The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance.

Read again: “The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration).“

So we are now describing inertial frames as those with no acceleration again. Fine, but acceleration with respect to what exactly? If this question cannot be answered then there is no acceptable definition of special relativity.

Note that this definition of inertial frames is both convenient and necessary here, as if we accept the alternative definition of a frame of reference where Newton’s law holds true then we have something like: “The laws of physics are invariant (identical) in all frames of reference where Newton’s first law holds“. This is not entirely vacuous but note that it cuts out the idea of acceleration altogether and if all we are concerned about is Newton’s law then we get: “Newton’s first law holds in all frames of reference where Newton’s first law holds“. This is vacuous now and nothing of any meaning has been said about Newton’s law, gravity or acceleration.

From the same Wikipedia article:

In relativity theory, ‘proper acceleration’ is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured.

And there you have it! The transformation is complete! We have moved seamlessly from a definition of acceleration that everybody understands to one that is convenient for the theory of relativity.

Accelerometers do not measure acceleration in the conventional sense of the word but instead record the displacement of a weight owing to either inertial or gravitational forces.

We started with ‘acceleration’ meaning a change of velocity within a specific coordinate system and ended up with a definition in terms of forces, inertia and gravitational attraction. We have now seemingly described inertial reference frames without the need of velocity or position, or in other words, without any of the qualities that identify a reference frame as a coordinate system.

A non-accelerating frame has become synonymous with a force-free frame simply by linguistic trickery.

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Einstein’s concerns

This conflation of ‘inertial’, ‘non-accelerating’, ‘force free’ and ‘Newtonian’ has not gone unnoticed:

All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton’s first law of motion holds. – Wikipedia

What is meant by ‘zero acceleration’ in the above?

If you do not have an absolute frame of reference then how can you ever say that something is moving with constant velocity (zero acceleration)? You clearly can’t and so they are trying to define constant velocity as relative to other frames that are also moving with constant velocity relative to each other. This is gibberish.

Einstein himself was aware of the problem:

The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration.

— Albert Einstein: The Meaning of Relativity, p. 58

Zero acceleration is now defined, not with reference to a coordinate system but by the lack of gravitational attraction from other bodies.

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Example: Two falling weights

Inertial reference frames are either at rest or move with constant velocity relative to one another.  – Wikipedia

As an example consider two astronauts positioned a thousand miles above the Earth, a hundred miles apart and falling freely towards the plant’s surface.

A stationary observer at the surface will see these astronauts accelerating with respect to himself and also with respect to each other as they converge. Furthermore, the astronauts see themselves as accelerating towards each other and towards the Earth.

By the discussion above, we cannot have all of these as being stationary within inertial frames at the same time – so which ones are inertial and which ones are not? How do we tell?

Which of these bodies is moving ‘without acceleration‘? Physicists will no doubt say: “The freely falling bodies are in an inertial frame because they experience no force and Newton’s first law holds”, but the question was about acceleration and replying in terms of forces like this pretty much assumes the conclusion that Einstein was trying to reach.

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Why is all this happening?

Newton’s theory of gravitation is based upon the ideas of mass, gravity, force, inertia and acceleration. However, whilst it is clear that there is some relationship between these quantities, it isn’t quite clear precisely what this is and nor is there any basic mechanism described for the phenomenon of either inertia or gravitational attraction.

Einstein has seen this and conceived the idea that inertia and gravity are one and the same thing but viewed according to different coordinate systems. The acceleration caused by gravity is now nothing more than the acceleration of a body perceived according to an accelerating frame of reference, nothing more and nothing less.

Einstein has thereby obviated the need to describe a mechanism for gravity by simply relabelling it as ‘acceleration’. He has declined to provide a physical mechanism for gravity and instead reframed it a, very simply, a change in position relative to something else! An observation (measurement) has been elevated to the status of a physical law.

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The equivalence principle

A version of the equivalence principle consistent with special relativity was introduced by Albert Einstein in 1907, when he observed that identical physical laws are observed in two systems, one subject to a constant gravitational field causing acceleration and the other subject to constant acceleration, like a rocket far from any gravitational field. Since the physical laws are the same, Einstein assumed the gravitational field and the acceleration were “physically equivalent”. – Wikipedia

Einstein stated this hypothesis by saying he would:

“…assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.”

— Einstein, 1907

This is obviously two big mistakes rolled into one short phrase.

First, Albert refers to an “acceleration of the reference system“, but again we can ask: “With respect to what?”

Second, the phrase “complete physical equivalence” is surely a massive overreach? The text above claims that Einstein: “observed that identical physical laws are observed in two systems.. like a rocket far from any gravitational field.”. Really? How did he observe this? A complete characterisation of the laws of physics is not available at the present and was not available in 1907. There is therefore no way of testing for complete physical equivalence. This is a meaningless phrase.

The available laws at the time were Newton’s laws of gravity and since these were proving to be inadequate, alternatives should have been considered. Instead what has happened is that Einstein has tried to ‘fix’ the paradoxes of Newton by the simple means of equating all acceleration with gravitational acceleration. By this means he can do without any explanation for a physical mechanism of gravity and just say that it is ‘acceleration of the reference system’.

We can say that no additional physics is being proposed here, merely the same Newtonian laws but described from different perspectives. Indeed, the proposed equivalence of acceleration and gravity actually stifles further enquiry into the topic as there is nothing further to research, with any further anomaly resulting in attempted explanations by manipulation of the reference system only.

Out of necessity now, Einstein will go on to explain the laws of physics purely in terms of outlandish frames of reference, resulting in the concept of 4-dimensional curved space time with shrinking lengths and clocks that run a different rates.

A model of the fundamental nature of space and time has arisen purely from considerations of gravity and acceleration, and much of that mere conjecture. It is no surprise then that the new theory says nothing about the forces of electromagnetism and is unlikely to do so for the foreseeable future.

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The gravitational field

The conflation of a gravitational field with mere acceleration effectively rules out the investigation of any characteristic of a gravitational field that is not relevant to acceleration; the theoretical framework is simply not able to express such properties.

Gravitation is now synonymous with acceleration and has no other function than to move objects and no other measurable or theoretical properties other than those pertaining to with acceleration.

This is clear bunk. We have, in a gravitational field, several properties which are likely to have effects other than pure acceleration:

• A diminishing of strength according to an inverse square law
• A divergence of the ‘field lines’
• A reduction of curvature of the isobars according to an inverse square law
• Some fine grained structure arising from the atomic structure of the Earth
• A directional accelerative propensity towards the Earth
• An aligning effect on a ship’s gyroscopic compass
• A mechanism for inertia
• Some other global structure aside from a simple ‘sink’ (e.g. a vortex structure)
• Something to explain the precession of the perihelion of Mercury

Some of these are already measurable and others may be measurable in the future or calculable from other measurables. To say that they don’t exist or aren’t relevant is positively deranged and for a theoretical framework which rules these out to survive for a whole century is just inexplicable.

Gravitational attraction is not just acceleration, there is a mechanism producing such an acceleration which needs explaining. Indeed, acceleration itself is not a mechanism but the resultant effect of such a mechanism, whatever that may be.

Example: elevator gravity

An example below from the Wikipedia entry on General relativity:

According to general relativity, objects in a gravitational field behave similarly to objects within an accelerating enclosure. For example, an observer will see a ball fall the same way in a rocket (left) as it does on Earth (right), provided that the acceleration of the rocket is equal to 9.8 m/s² (the acceleration due to gravity on the surface of the Earth). – Wikipedia

So now objects in a gravitational field only behave similarly to objects within an accelerating enclosure, whereas before, the laws of physics were identical.

What is an accelerating enclosure accelerating relative to? If the rocket is at the surface of the Earth then it does not need to accelerate as the effects are already there from the gravitational field.

We are intended to imagine the rocket in space far away from any gravitational field. However, there is no such place in the universe and so no such experiment has been performed and never will be performed.

We have, from the same article:

..it is impossible to decide, by mapping the trajectory of bodies such as a dropped ball, whether the room is stationary in a gravitational field and the ball accelerating, or in free space aboard a rocket that is accelerating at a rate equal to that of the gravitational field versus the ball which upon release has nil acceleration.

This is pure conjecture. This is a thought experiment, the result has been assumed and a theory has been developed with no empirical data or foundational definitions.

There is no such thing as ‘free space’, the whole of space is permeated by a gravitational field. What is the meaning of: “stationary in a gravitational field“? Again, another use of the word ‘stationary’ without reference to a well-defined coordinate system.

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What is the solution?

We can go on like this almost indefinitely but the fundamental problem always remains which is the lack of a well-defined coordinate system in which these events take place. Without this we have no way of defining acceleration or even velocity and since the whole point of the Theory of Relativity is to describe gravitational effects in terms such metrics, it can be regarded as a failure.

It is all very well to criticise something, but such comments will simply fall upon deaf ears unless some sort of alternative is at least suggested.

The ‘Inertial Field Theory’ (IFT)

The post: Gravity as an inertial field outlines an idea that gravity is in fact an ‘accelerating’ inertial field with mechanisms and characteristics of itself that explain the local movement of matter in the cosmos.

Consider that:

• A gravitational field has fine grained structure on the scale of the atom
• A horizontal component is present
• The local structure provides for inertial effects
• An accelerative component provides for gravitational attraction via ‘movement’ of the inertial mechanism
• The accelerative component derives from the global structure whether it be purely radial or vortex-like in nature
• The idea of a ‘uniform’ gravitational field is probably bunk

We can now describe a plausible and at least consistent foundation for a theory of gravitation and provide answers for Einstein’s thought experiments.

What is an ‘inertial frame’?

If a gravitational field has both horizontal and vertical components that are roughly isotropic then we may use this as as the basis of an actual physical coordinate system. The system is uniform only locally and theoretically varies from point to point across the whole universe.

This aspect of the gravitational field is insensitive to ‘uniform’ motion of matter but has a certain accelerative resistance thereby providing for both inertia and gravitational acceleration.

The gravitational field has a fine grained structure of a certain scale and this may be used as a basis for a metric of length and hence velocity and thereby acceleration. We therefore have a coordinate system that is:

• Highly local – not global
• ‘Absolute’ in a sense as opposed to arbitrary or relative
• Defined by characteristic physical processes, whatever they may be
• Responsible for both defining and implementing the laws of gravity and inertia

Free-falling objects move according to local field conditions only and can be said to be following an ‘inertially straight’ path. This is not a geodesic in space-time as there is no need to suppose a distinct space-time as separate from the local field. This is not necessarily the shortest distance between any two points but is a path determined by local field interaction at every point on the path.

Free falling objects in close proximity form an equivalence class of objects which may be said to be in ‘uniform motion’ relative to each other. Their velocities are all constant relative to the local inertial field and constant relative to each other by definition.

There is no need for an abstract coordinate system anywhere as the idea, maybe surprisingly, doesn’t make any sense. Physical objects are moved around by physical field phenomena and that is all. Any idea of a metric must come from emergent properties of the field characteristics itself. In stark contrast to Einstein’s approach where coordinates and ‘space’ are ‘fundamental’, we have a system where the physical gravitational field is the fundamental and any coordinate or metric is defined in terms of local field characteristics or their effect on ‘matter’.

The field forms an inward spiralling vortex system around the Earth where the rotation at the Earth’s surface is synchronous with the Earth’s rotation, thereby forming a ‘gravitational-inertial layer’ at the surface of the Earth which provides for laboratory conditions. Almost all experiments performed by physicists have been within this layer, thereby giving the impression that such conditions are representative of the cosmos as a whole and that all discoveries have been ‘fundamental’ and universal. The Michelson-Morley experiment was performed within this layer.

The horizontal components of the field give rise to inertia and centrifugal forces. Objects at the Earth’s surface can be said to be accelerating upwards relative to the Earth’s gravitational field, where such acceleration is relative to the downward accelerative component of the (physical) gravitational field.

Any experiment carried out in a free-falling rocket is nevertheless within a gravitational field somewhere and this field provides a physical reference frame for measurements, movement, acceleration and the behaviour of rotating bodies.

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What would Einstein say?

I think Albert would approve, he was obviously trying to:

• Remove the need for a global coordinate system
• Define physical laws locally
• Somehow unify gravity, inertia and acceleration
• Explain the Michelson-Morley result
• Explain rotational motion and centrifugal forces
• Come to terms with his own discomfort with the foundational ideas

Unification of inertial and gravitational fields

The gravitational and inertial fields are different components of the same field:

Even in generally-covariant reformulations of these older theories, there will be an inertial field and a gravitational field existing side by side. The unification of these two fields into one inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems (not necessarily associated with observers in different states of motion) is one of Einstein’s central achievements with general relativity – Michel Janssen

The motivation is good but the unnecessary introduction of different coordinate systems spoils the idea. The accelerative effect of the gravitational field is always present even if it is not measured. If an observer is freely falling towards Earth, they will not experience any accelerative effect from the gravitational field as they are moving along with the field acceleration. However, there must be some sort of mechanism producing this effect and that physical mechanism is not going to disappear just because the observer is moving along with it.

One idea might be that it is the radial convergence of the gravitational field lines towards the planet which produce such acceleration, in which case an observer can accelerate all they like towards the Earth but the field lines have their own ontology within the theoretical framework and are not going to vanish just because they are being ignored.

Another idea is that it is the ‘curvature’ of the field which produces such acceleration. This curvature diminishes with the inverse square of the distance from the Earth and so can be thought of as producing less acceleration the further out in orbit we are.

Some texts talk about a ‘uniform gravitational field’ in an attempt to simplify the ideas of special relativity, but if either of the above two hypotheses are true then there is no such thing as a ‘uniform gravitational field’, since the acceleration comes from phenomena that derive directly from the radial or curved nature of the field. Try to think that the centripetal effect of a tornado has nothing to do with the rotational nature of the wind! Try to simplify to a flat tornado!

The removal of a global frame of reference

After the development of General Relativity, Einstein wrote:

Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that co-ordinates must have an immediate metrical meaning

(Einstein, 1949, p. 67).

Einstein failed to do this:

As we will see .., the coordinates that Einstein actually used in his accounts of the twins and the bucket in the 1910s have essentially the same status as those in special relativity. They still have direct metrical significance and still identify and individuate space-time points uniquely. – Michel Janssen

The scheme that Einstein settled upon was to identify ‘space-time’ as representing a global and somewhat ‘absolute’ reference frame but at the same time to allow such a coordinate system to have a curved geometry and to allow such curvature to be produced by some physical (although unspecified) process involving something called ‘mass’.

Thinking about this in a quiet place, we realise that this is just a rephrasing of all the ambiguities and double-speak that plagued the early formulations of special relativity.

Properly handling accelerating frames does require some care, however. The difference between special and general relativity is that (1) In special relativity, all velocities are relative, but acceleration is absolute. (2) In general relativity, all motion is relative, whether inertial, accelerating, or rotating. To accommodate this difference, general relativity uses curved spacetime.

— Albert Einstein: The Meaning of Relativity, p. 58

The idea is ostensibly to use a coordinate system (reference frame) as a basis for defining acceleration as before, but the coupling of ‘mass’ to the geometry of space-time performs the same linguistic trickery as before and effectively re-defines an inertial frame by its propensity to accelerate an object. This is just a rehash of Newton’s force = mass x acceleration but with ‘Force’ replaced by ‘space-time curvature‘, ‘mass’ replaced with ‘the propensity to curve space-time‘ and acceleration with ‘movement caused by space-time curvature‘.

Again, no new physics has been produced and all we are left with is a more complicated way of looking at Newtonian gravitation.

Moreover, the formulation of acceleration as being something like the natural propensity of a mass to move through space-time effectively removes the need to provide any other explanation for such a phenomenon. A physical law is replaced with a ‘natural propensity‘. This is not a new physics but a way of avoiding doing any physics at all!

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Example: a geo-stationary space station

Imagine a geo-stationary space station hovering above a laboratory on Earth. The relative velocity of the laboratory and station is zero. There is no relative movement, so are they both in the same inertial frame of reference or not?

Although there is no obvious relative acceleration I think that most physicists would say that they are in different inertial frames and the reason given would be that the station is in free-fall whereas the laboratory is not.

So although frames of reference are theoretically defined in terms of spatial acceleration, none of this really matters when it comes to actual examples and we find again that inertial frames are described in terms of what physicists imagine is happening in physical space.

How do we know that an orbiting station is in free-fall when it has no relative movement let alone acceleration? How do we know that conditions at the surface are different? Not by any observed acceleration between the laboratories that is for sure, but by the overall geometry of the situation and observed difference of behaviours of masses within each room.

Such behaviours are clearly independent of each other and decoupled from any relative acceleration that may exist between the laboratories. Experiments within each room unfold according to the local field conditions within that room and that is all. What does the idea of variable reference frames of reference add to all of this?

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Special relativity as an engineering model

Special relativity is defined in the absence of gravity. For practical applications, it is a suitable model whenever gravity can be neglected. – Wikipedia

There is no place in the universe that is without gravity and so we can disregard special relativity as a reliable representation of actual reality. It is not a law of physics, it is not a law of nature and it is not a fundamental principle. It is at best a collection of useful rules of thumb that can be used to address specific physical problems.

As a theoretical framework it is riddled with ambiguities and deficiencies as we have seen and in particular it has failed to define either gravity or acceleration.

Even the idea that it can be used to perform useful calculations where gravity is negligible is surely a joke? How do we know if we can ignore gravity when gravity has not even been defined properly? The equivalence principle says that gravity is indistinguishable from acceleration and is therefore, along with acceleration, effectively unmeasurable and undefinable. We are therefore left asking: “What it is exactly, that can be neglected?”.

General relativity is no better and suffers the same fundamental problem which is that of defining acceleration, gravity, inertia, frames of reference and a global coordinate system.

Attempts to identify gravitational attraction with pure acceleration have failed and at the same time effectively prevent any further enquiry into the nature of the gravitational field, having given the impression that the problem has already been solved in terms of bendy space-time.

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The Michelson-Morley experiment

It turns out that light is measured as having the same speed travelling with the Earth’s rotation or against it. This was a surprise at the time and is said to be the motivation behind the development of special relativity.

So how did Einstein solve the problem? Put simply, he just declared the result to be a fundamental principle of physics and manipulated everything else to fit the result that he wanted.

From the definition of special relativity:

2. The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance.

This is just garbage, just a crude forcing of the result that was required based upon one experimental result only.

There is no such thing as an inert and empty vacuum as normally conceived since all areas of space are permeated by a gravitational-inertial field. Moreover, since it is precisely these fields that are of relevance here, this should be explicitly acknowledged rather than brushed under the carpet as ‘vacuum’.

One consideration is that the gravitational field at the surface of the Earth rotates with the Earth thereby providing a stable reference frame for the movement of both mass and light. However, the formulation of gravity as synonymous with acceleration effectively excludes this hypothesis from the model and leaves us bereft of any other means of explaining the experimental result apart from declaring a new principle of nature.

A principle is declared and not just for the local conditions in the Earthly laboratory, but for the whole of space everywhere and at all times!

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Experimental evidence

Aficionados are adamant that there are many experiments that confirm the truth of the theories of relativity, to great precision. However, closer examination reveals things to be a little more complicated.

The precession of Mercury

The orbit of Mercury is elliptical, but the axes of such an ellipse are not static and rotate over time. This is contrary to the assumed action of a simply radial Newtonian force and needs some explanation.

The ‘solution’ from General relativity is to assume that gravitational effects do not propagate instantly through the space-time framework but do so at a finite speed: the speed of gravity: Wikipedia This allows calculations to be made that seem to explain the motion of the planet.

Note that again the term ‘space-time’ has moved from defining a mere coordinate system to becoming a complete, all-pervasive physical entity which is causal in directing events at a cosmic scale. It is responsible for moving around ‘mass’ through physical space and is in turn responsive to the presence of such mass, thereby altering its curvature.. in order to move such a mass!

John Wheeler summarises:

Matter tells spacetime how to curve, and curved spacetime tells matter how to move – John Wheeler

This should be a massive red flag. The language of causation is used but the causal chain is circular! How do you preserve your own sanity with such an attitude? How does the ‘telling’ happen? What is the mechanism please? How does anything happen at all?

Returning to the precession of Mercury, we need to do some actual calculations within the framework of general relativity in order to prove our point. It turns out that the calculations for the altered orbital were actually performed within the framework of parameterised post Newtonian formalism (Wikipedia).

This framework is in Newtonian in spirit, Newtonian in name and uses the very Newtonian concepts of:

• Newtonian gravitational potential
• Momentum
• Angular momentum
• Gravitational potential energy
• Kinetic energy

Parameterised post Newtonian formalism is therefore a de facto extension of Newtonian physics. The Wiki post tries to squirm out of this by claiming that is a Newtonian approximation to general relativity, but if all of the computation requires Newtonian type quantities within a Newtonian framework, then what has been gained by calling it General Relativity?

The idea that effects travel through Einstein space-time at the speed of gravity (speed of light) is a MacGuffin employed to distract and give validation to the fashionable theory of the day. We could just as well have said that Newton’s gravity propagates at the speed of light and come up with exactly the same results using exactly the same post Newtonian formalism.

Once again, the theory of relativity is just a more complicated way of doing the same Newtonian physics.

The theory of general relativity is still not well-defined and so no amount of accurate predictions can confirm such a theory as: there is no theory!

Why have things gone so wrong?

Reading back through the post it is evident that the same themes crop up time and time again and that the same basic mistakes are responsible for leading the aspiring theorist astray. Einstein himself started off with good intentions but still thought in the same basic patterns and so ended up in the same blind alleys.

The mistakes arise from a few fundamental assumptions which seemed fine at the time but have proved to be crippling in the development of a consistent cosmology:

Error 1: Physics is downstream of mathematics

Almost all physicists believe this, but it just isn’t true. The idea of a reference frame upon which to hang physical events started out fine but we ended up with a space-time that was physical, curved, dynamic and ultimately causative. This seems inevitable in hindsight as physical reality must always somehow reference such a system in order to travel in a straight line for example and so the coordinate system ends up partaking of physical reality even if only passively.

The solution is to take observed physical events as the basis for a science and any apparent order in the form of a consistent coordinate system to be regarded as emergent from these observations.

Error 2: The world is not ‘Newtonian’

The Newtonian world consists of ‘objects’ moving around in space that is empty apart from a few gravitational forces emanating from those objects themselves. A ‘separation’ is built into reality of space, distance, force and object. Forces emanate from ‘matter’, matter takes prime place in the causal chain and matter is somehow aware of a separate coordinate system. Each element of reality is subject to different laws.

In terms of a solution from field physics, the cosmos consists solely of field interactions at every point in the cosmos, with matter, mass and forces constituting observable and measurable effects which, by virtue of their salience, attain an undeserved prominence in our cosmology. To regard such emergent effects as ‘fundamental’ will clearly result in failure.

Error 3: The innate properties of objects

Mass and inertia are held to be ‘innate’ properties of matter and this distortion percolates down even into relativity. The idea should be considered that both are emergent properties arising from the interaction between matter and field structures, rather than immutable properties of matter itself. This becomes evident in John Wheeler’s statement above where mass and space-time curvature are obviously precisely the same thing, but he can’t quite bring himself to say so for some reason.

Nobody regards ‘friction’ for example as an innate property of matter and so so why regard ‘inertia’ as an innate property of matter?

Error 4: Locality bias

The idea that an experimental result in a laboratory is somehow representative of physics at all points in the universe for all time is a clear bias.

Error 5: The fixation on causality

This is another Newtonian concept, that events proceed in a ‘causal’ chain from some original cause (Big Bang) to the complexity we see at the present. In reality, the entire cosmos evolves as a whole and any perceived ‘events’ are merely emergent and observable effects of such an evolution. To describe such events as ‘fundamental’ and such causal chains as controlled by ‘fundamental’ laws is misleading and again crippling in the formulation of a consistent cosmology.

As an example, consider Wheeler’s statement that “Matter tells spacetime how to curve, and curved spacetime tells matter how to move“. It is evident from this that matter and spacetime move in concert with each other and are effectively synonymous, but the conceptualisation of the two as fundamentally different entities necessitates some sort of physical coupling and the abstract idea of ‘causality’ has been roped in as yet another MacGuffin to cement over the cracks, with no mention of an actual physical mechanism. Such a thing is not thought necessary because the abstract idea of ‘causality’ is so readily accepted.

Error 6: Inability to assimilate an existing paradigm

An alternative to ‘causality’ had already been discovered in the form of the Navier-Stokes equations governing the flow of fluids and gases. Here, there are no separate objects as such to exert forces upon each other, and no distinct ‘events’ to delineate causality. Instead fluids and gases are treated as a continuum whose behaviour is in accordance with a set of partial differential equations. This is as about as far from intuitive as we can get, but nevertheless avoids all of the problems we are seeing. Reality evolves at each point in the continuum according to certain rules and that is all that happens. Any perceived order within the resulting activity is not a fundamental law but an emergent effect only.

Error 7: The Laws of physics are not ‘reality’ and are not fundamental

The laws of physics belong in the right hand column below. They are twice removed from reality and take the form of abstract mathematical equations constructed in order to explain a finite number of measurements derived from a limited number of physical processes. They are not fundamental in any way, shape or form.

Contrast this self-evident truth with the attitude of physicists who are prone to declaring almost any new theory going as ‘fundamental’. Note that Einstein’s framework for relativity started off as merely an abstract coordinate system but quickly morphed into an actual physical process that shaped the entire universe by its causative properties.

Error 8: Linguistic overloading of the term ‘straight line’

The term ‘straight line’ can have several meanings:

1. Geometrically straight – with reference to a coordinate system
2. Inertially straight – the unimpeded path of a mass through space
3. Electromagnetically straight – the path of a light beam

There is no reason that these should all be the same and no evidence that they are. Newton’s 2nd law is the assertion that 1 and 2 are equivalent but without reference to a specific coordinate system. Einstein was so keen on the idea that all 3 were equivalent that he allowed for a curved geometry in order that it be so. The reality is that neither mass nor light are moving through space along a coordinate system but instead moving through a gravitational field and driven only by local physical processes.

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Energy conservation

The conservation of energy is widely held to be a fundamental principle of nature (of course it is!) However:

• Energy as an abstract quantity is poorly defined
• Many physicists will admit that it is not in fact conserved
• Energy is frame-dependent in relativity and hence not absolute
• In Newtonian physics it is relative to a reference frame which is fixed but undefined
• No mechanism is provided for the transmutation of energy from one type to another

Consider two objects in space:

For example, if two objects are attracting each other in space through their gravitational field, the attraction force accelerates the objects, increasing their velocity, which converts their potential energy (gravity) into kinetic energy. – Wikipedia

We need a reference frame to describe acceleration, so imagine yourself as object A whilst object B accelerates towards you. You don’t feel yourself accelerating and you don’t perceive yourself as having potential energy or of converting it to kinetic energy. This immediately adds an asymmetry to the situation.

This is fine from the point of view of gravity and acceleration, but the claim here is that there is now some energy conversion, some physical process, happening at one place but not the other. Even this may be considered valid, but an observer at B will imagine the same situation but this time with the energy conversion happening at A. There is a disagreement as to what actual physical processes are taking place.

The doctrine of relativity will be fine with the velocity and acceleration disappearing at one observer as this is all frame dependent, but if the transmutation of potential to kinetic energy consists of some actual physical process then we are forced to concede that this physical process only ever happens in the other guy’s framework. This sounds like nonsense and so it probably is.

Physicists don’t notice this happening as they have no physical definition of ‘energy’ or energy ‘conversion’ and so have no requirement to say why it only seems to happen to somebody else. However, we do not need to specify a mechanism in order to suppose that one might exist, and that if it does exist, then it must exist in some ‘absolute’ sense if energy is to be transmuted.

To see what sort of mechanism might be in play we note that kinetic energy is really just velocity squared and ‘potential’ is just the position in a gravitational field. The conversion of potential to kinetic energy is now equivalent to that of a mass acquiring velocity within a gravitational field.

This is now an identical argument to the one above concerning acceleration under a gravitational field. There must be some mechanism by which this happens and it must be in effect locally to make objects move. It must therefore be in effect even in the rest frame of the observer, i.e. even when the observer appears to himself to be not accelerating.

The theory of relativity, then, seeks to explain away all mechanisms which may be dependent upon acceleration by simply pretending that they don’t exist or at least will vanish in an appropriate reference frame. This has the effect of limiting, rather than expanding, the number of phenomena that can be explained by such a theory.

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Rotational movement

Newton put some water in a bucket, spun it on a rope and watched the water climb the sides of the bucket. He then spent decades arguing with Ernst Mach as to why this should happen, but without satisfactory resolution.

Einstein described what he thought was an equivalent situation but with a globe spinning in space:

Following Einstein’s (1914, pp. 1031–1032) lead, [..] we consider a globe, held together by non-gravitational forces, rotating with respect to the fixed stars, [..] In this case, the centrifugal forces, rather than giving the surface of the water in the bucket its tell-tale concave shape, make the globe bulge out at its equator. – Michel Janssen

Ouch! There is a big assumption here which is that centrifugal forces exist at the cosmic scale in the same way that they do in a laboratory within a strong gravitational field at the Earth’s surface . Observational evidence, however, shows that the bulge of a planet is not uniquely determined by its size, mass and rate of rotation. Our sun, for example has almost no bulge at the equator whilst our moon has a noticeable bulge but little rotation.

Gravitational fields are thought to have some inertial component even by Einstein and so it should be considered that the inertia experienced by Newton’s water could possibly arise from the fact that it is being dragged trough the inertial field of the Earth’s gravity and that it is this inertial drag that gives rise to the centrifugal forces causing the water to climb the sides of the bucket. The water may have its own gravitational field but the Earth’s field dominates the experiment whilst the bucket spins within it.

The situation of a planet in space is completely different. The Earth is not spinning within a strong enclosing field, but its own field spins with it and again dominates proceedings. There is no reason at all to suppose that centrifugal forces will arise during this situation and no reason to connect the rate of spin with an equatorial bulge.

The whole system forms a spinning vortex field and the resulting activity conforms to the laws and patterns of vortex physics.; see the barred galaxy depicted below. The field spirals inwards in a manner similar to a hurricane before stabilising at a fixed radius, within which solid-body rotation occurs.

In the system of the Earth, the planet engages in solid body rotation whilst the gravitational field spirals inwards. A zero-slip condition at the surface gives us the inertial framework we are familiar with and easily explains the Michelson-Morley results if we allow that the propagation of light is not through empty ‘space’ but through the gravitational field itself.

Any equatorial bulge is determined by the dynamics of the vortex system as a whole.

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E = mc²

By now, this equation can simply be treated as a joke!

There is no physical definition of ‘energy’ and no direct way of measuring it, merely inferences made from an as yet unproven and undefined theory. There is only a circular definition of mass and again, no consistent method of measuring it (The gravitational ‘constant’). The E in the equation does not mean what most people think and is something called Einstein’s ‘rest energy’; the ‘m’ here is similarly a ‘rest mass’. These are novel, imaginary quantities arising as artefacts of the theoretical framework.

These are quantities derived from a theory which is rooted in:

• Considerations of imaginary experiments whose outcomes were invented
• An arbitrary decision to set the speed of light to constant with insufficient experimental evidence
• Goal-oriented attempts to eliminate any physical differences between acceleration and gravity
• A failure to define acceleration, gravity or mass

In popular imagination, the energy described in this equation is real energy that is somehow bound up in the structure of an atom and can be somehow harnessed for the purposes of atomic energy or bombs. However, note that none of the foundational elements of the theory or any of the equations have anything at all do do with the structure of an atom. How then can the theory say anything at all about the energy contained in such an object?

Practical examples of E = mc²

Wikipedia gives some ‘practical examples’ in support of the mass-energy equivalence:

• A spring acquires extra mass when it is compressed
• A weight acquires extra mass when heated
• A spinning ball has greater mass than when it is not spinning

We should expect, given the iconic status of the equation, that they have done due diligence, checked the sources and provided good references to support their claims.

The language used suggests that these experiments have actually been performed and the results measured, however, no citations are given and a quick AI search can find no actual experimental results in support of a single one of these claims!

In addition, the same article contains the following statement:

The “gadget”-style bomb used in the Trinity test and the bombing of Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, after cooling. The electromagnetic radiation and kinetic energy released in this explosion carried the missing gram of mass. – Wikipedia

The language suggests that they actually performed the experiment, that they actually measured the mass and energy of the end results of an atomic bomb explosion!

Accurate measurements of such quantities are clearly impossible. The reference supplied gives an estimated ‘yield’ of 21 kt, but to within an accuracy of 10% only! (Malik) This is not the impression given by the Wikipedia article. To cite this experiment as evidence of the mass-energy equivalence is wholly dishonest.

We still have no experimental evidence for the famous equation.

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The constancy of the speed of light

Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant and is independent of the motion of the light source. – Wikipedia

.. and..

The speed of light is the same for all observers, no matter their relative velocity. It is the upper limit for the speed at which information, matter, or energy can travel through space. – Wikipedia

These both seem like massive overreach given the experimental evidence or lack thereof.

Alternative hypotheses should be sought.

Alternative hypothesis: The ideas described as the Inertial Field Theory (Gravity as an inertial field) are correct and should be explored as possible explanations for the various effects purporting to support Einstein’s proposal.

This theory proposes that gravity is an accelerating moving inertial field which adopts a vortex structure in space and centres upon the Earth. Both matter and light move within this field even in a vacuum and the movements of both are affected by local field conditions. In the case of matter, the field imbues objects with both inertia and gravitational mass, and in the case of light, the speed and direction are very possibly altered.

Laboratory conditions: This field rotates along with our planet and thus there exists a thin layer at the surface of the Earth where a stable field condition provides the laboratory conditions that we are familiar with and within which almost all experiments are performed. The field is roughly isotropic as far as inertia is concerned and ‘accelerates’ towards the Earth to provide gravity. If a beam of light travels the same speed in all directions within any laboratory, then this is not surprising. The light uses the gravitational field as a ‘carrier medium’ and will inherit the velocity of such a field. This is the Michelson-Morley experiment.

The solar system: The stars are said to move according to the precession of the Earth’s axis, but the planets are not seen to do the same, which implies that the whole of the solar system is rotating and tilting along with the Earth’s axis. This is consistent with the notion that the solar system is the centre of a giant cosmic vortex and is undergoing ‘solid body’ rotation similar to that of the centre of barred galaxies (see image below).

The gravity of the solar system therefore forms its own ‘inertial frame’ (literally now) and all movement of matter and light will be in relation to this roughly isotropic field.

Deep space: A free falling laboratory in deep space is not moving relative to any gravitational field, being dragged along by it, and so we expect the speed of light to be constant in all directions.

Gravitational lensing: Light is said to bend around massive objects and this surely implies some sort of interaction between light and a gravitational field. There is therefore some physical process at work as a result of this interaction and it is this which needs a thorough investigation. Simply saying ‘the light is bending because space is curved‘ is again avoiding the question and discouraging further inquiry. Light has a physical ‘nature’ and so does gravity and to investigate these is the duty of the physicist.

No surprise: In all the cases above, we expect light to travel the same speed in each direction, but not for the reasons stated by Einstein but for other, more prosaic considerations, which are specific to the local conditions and arise from some, as yet, unspecified laws of physics that control the interaction between light and gravity.

Geo-stationary orbit: This is more interesting. A geostationary space station is moving at speed transversely to the radial field lines of the gravitational field but is stationary with respect to the radius and thus is subject to an inward accelerating flux of such a field. What do we expect light to do in this situation? Will we see the same speed in each direction? Has anybody measured this?

According to Einstein, the speed of light will be the same again.. because he has declared it to be so! However, the mechanics of the situation are different here and so why should we not expect a different outcome? This does not seem unreasonable.

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Summary

This is obviously a real mess, with the whole theory having flawed foundations, undefined terms and insufficient empirical evidence to support the claims. In particular the idea of an ‘inertial frame of reference’ is ambiguous at the very least. This is unforgivable since inertial frames of reference lie at the very heart of the theoretical framework and without them there is simply no theory.

Einstein failed to show that gravity is equivalent to acceleration and failed to justify the constancy of the speed of light in any meaningful way.

We have:

• No properly defined coordinate system
• Velocity and acceleration are therefore undefined
• ‘Mass’ is ultimately undefined
• No new physics
• No mechanisms described
• Ambiguous terms
• Definition creep
• Conclusions drawn from ‘thought experiments’

In addition, if we look for empirical evidence we find:

• Exaggerated claims made from little evidence
• Too much weight placed upon Michelson-Morley experiment
• Failure to consider alternative solutions
• Failure to explain the precession of Mercury
• Failure to explain or even define rotary motion (Newton’s bucket)
• Bad results in the Hafele – Keating experiment claimed as good results
• Failure to explain own thought experiments

Conclusion: Gravitational fields exist and act via a specific mechanism but the central idea of Einstein is to explain away the effects of gravity by rephrasing it as simply ‘acceleration’, thereby removing any need to describe the mechanism.

The other idea, to simply declare the speed of light to be constant, similarly circumvents the need to describe any physical process by which this might happen. No new physics has been proposed, merely some arbitrary restrictions on how we may interpret measurements.

These are fundamentally flawed ideas and hence the theory can never, ever, amount to anything useful.

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