Why Einstein was wrong
Introduction
1 The start point is existence. But nothing other than our own existence is knowable, since we cannot transcend it. So we can only know a particular form of existence, ie what is potentially detectable by any sensory processes, as these are what enable awareness. Our reality therefore comprises those existent phenomena which are potentially sensorially detectable by any organism, and the phenomena then proven to have caused them (normally referred to as reality). The caveat of potentiality relates to physical issues with the sensory processes, which means that some aspects of physical existence have to be hypothesised. However, that procedure must remain subservient to validated direct experience, otherwise it will be belief, not knowledge.
2 That emphasises the importance of first understanding how existence is detected, and then how that (ie our reality) must occur. We know that our form of existence:
-exists independently of the processes which detect it, ie while awareness is limited to these processes generically, within that sensory systems receive specific input.
-involves difference, ie what exists alters, as comparison of inputs reveals difference, and therefore that there is change.
3 Our reality is therefore existential sequence. The entirety of whatever comprises it can only exist within that sequence in one definitive physically existent state at a time, as the predecessor must cease to exist so that the successor can exist. Any such state (ie a physical reality of our reality) could be conceptualised into its constituent states, for example by association with 'things' with the proviso that these are abstract concepts. That is, they result from the differentiation of physical existence at a higher level than the existential, and therefore involve duration and more than one physically existent state in sequence. The differentiation between the substance of physical existence, and its physically existent state at any given time is critical, because it is existent states which need to be identified when defining what physically existed.
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Distance/space/dimension
4 Distance is solely determined by physically existent states, since it is the difference between them in respect of spatial attributes, and differences do not exist physically. So distance can only involve physically existent states which exist at the same time. It is not possible to establish a distance, as opposed to some form of conceptual spatial relationship, between something which exists and something else which does not.
5 Therefore, any given distance is always unique, since it reflects a definitive physically existent circumstance at a given time. Notions which relate to the quantification of it in terms of space, or duration, and the comparison of one way with the other, are a fallacy, if they involve the presumption that there could be a difference. Whatever quantification methodology, there can only be one result.
6 Indeed, any notion of duration in a physically existent state is incorrect, because to be physically existent, by definition, entails no form of change or indefiniteness. Put another way, whatever constitutes the elementary components of physical existence must be in a specific physically existent state at any given time, and cannot be in more than one such state each at that time. Like a film, physical existence only appears to be continuous because of the rate of change. And this is occurring at such a speed that differentiation which could enable identification of a physically existent state is nearly always, if not always, impossible. Leaving aside also identifying other physically existent states which occurred at the same given time. However, any solution to that issue must be based on an understanding of the actual circumstance.
7 The exception to this is that distance could be conceived as a single example of change, ie a difference. So it can be expressed, conceptually, in terms of duration incurred. The concept being that instead of expressing distance as the fixed spatial quantity which it is, it can alternatively be quantified as the duration which would have been incurred had any given entity been able to travel along it, either way. But it must be understood that there is no duration as such, this is just an alternative to, and the equivalent of, a spatial measure, ie a singular quantity. Failure to understand the absence of elapsed time in a physical reality results in the flawed application of the equation x = vt. Making this mistake reifies change, and hence duration.
8 In establishing what constitutes dimension, distance and space in our reality, we are using a reference which conceives of any given physical reality being divided into a grid of spatial positions. And the constituent physically existent states have definitive dimension/size/shape (ie spatial footprint), which can be defined as spatial positions 'occupied' at the given time of existence. 'Mapping' other states that were existent at the same given time, would reveal not only both the spatial footprint of those states and their comparability with each other, but also, distance. Which is usually measured between the two nearest dimensions of the existent states, but could include any combination of dimensions. And depending on the spatial relationship of the states involved, distance could involve a relationship in terms of separation of the states, or one within another, that again being with respect to specified dimensions.
9 Dimension is a specific aspect of spatial footprint, relating to the distance along any possible axis of that 'occupation'. So, three is the minimum number of spatial dimensions that is ontologically correct at the highest level of conceptualisation of any given physical reality. But is not what is physically existent. At that existential level, the number of possible dimensions is half the number of possible directions that the smallest substance in physical existence could travel from any single spatial point.
The misconception of time and timing (the AB example)
10 The misconception of time and timing revolved around the incorrect application of local time, and the flawed concept of simultaneity, by Poincaré in particular. Einstein: On the electrodynamics of moving bodies (1905), Section 1 Part 1, Definition of Simultaneity, provides an explanation of the argument, so is used as the reference.
11 A and B are each attributed a time (local) of existence, ie t(a) and t(b). Either there is a relationship between these timings, or not. If there is a relationship, then there is no timing issue to resolve. If there is no relationship, then nothing further can be discerned from this information, since they are variables defined on the basis of different references with no known relationship.
12 So there must have been a presumption that the timing devices were synchronised (ie working properly). Which reveals that the actual reference against which all timings are compared is the concept of a constant rate of change (while spatial attributes are referenced to the concept of a spatial grid). Timing devices just 'tell' the time, and are therefore only valid if they are all related to this one reference. This must be so, otherwise there can be no basis upon which to compare timings and progress an analysis. That is, if timing devices are set arbitrarily, and/or are not operating properly, then the time, as 'told', is meaningless. Measuring devices just enable quantification, but that is only valid when it correlates with the single reference for the attribute, which is synchronisation of timing devices, and consistent calibration of spatial devices.
13 The whole raison d'ĂȘtre of any measuring system is comparison and the identification of difference, which necessitates a reference. Obviously a reference is chosen usually on the basis of its characteristics being commensurate with the role, ie it being the best practical manifestation of the conceptual constant, which in timing is constancy, and rapid, frequency of change. The key point is that once something is used as the reference, then it must be used consistently, so that other results are comparable (ie differences are identified with respect to the same reference). Which means either using the same reference, or ensuring variance is discounted.
14 By definition then, the timing relationship which supposedly needed to be inferred, ie local times to a common time, was known already. That is, the timing devices were working properly. And presumption of the distance AB meant that A and B must have been existent at the same time, ie t(a) equalled t(b). Alternatively, had the times been different, then A could not have been compared to B, and distance established, because one was non existent.
15 The comparison of AB to BA, which is unnecessary anyway, is effected in terms of time incurred with consecutive, not concurrent, timings. This is incorrect. Not only is there no duration in a spatial circumstance, even if each duration incurred had been properly understood as just an alternative fixed quantity to a spatial quantity, AB cannot be compared to BA on the basis of subsequent timings. Because any subsequent timing cannot be presumed to relate to AB, as either A and/or B could have ceased to exist. Such measurements can only represent whatever was deemed to constitute A and B, and therefore AB, at the time it was effected. Whether physically existent states, and/or the distance between them, remain the same over time is irrelevant to the quantification of a unique difference which occurred at a given time.
16 The use of light speed (and the presumption that it was constant) as a method for quantifying distance was not the issue. Neither was the quantification of distance in terms of a conceptual duration incurred, had it been understood. Any method, involving any direction, would suffice, if the calculation had been carried out properly. The error was assuming that physical existence, and hence any artefact dependent thereon, exists over time, rather than only in one existent state at a time.
Light
17 Before progressing with the argument, it is necessary to highlight certain fundamental characteristics of light. Light is a physical effect in photons which enables sight. That effect results from an atomic interaction, therefore, unlike in a collision, the start speed of any given light is always the same, and as with any existent phenomenon, it will continue to move at that speed unless impeded. Also, there is a relentless sequence of such interactions, and light travels in all directions. So when reference is made to light, it is usually in respect of many different physically existent phenomena, ie different physically existent lights may be the same from the perspective of recipient observers. Again, there is a danger of simplification resulting in reification and misconceptions. Light as a physically existent state in its own right, and light as in what sensory systems decode upon reception, need to be differentiated. The other consequences of this process are that observers receive, in the context of sight, a photon based representation of any given physically existent state (ie a light reality of reality), and there is always a delay between time of existence, and the time of observation of that existence.
The misconception of the role of observation
18 It is argued that the AB example is explainable in terms of observation. So time of existence, and time of observation, were asserted to be the same if whatever existed was in the "immediate proximity". This is correct as an approximation, though would need definition. The issue then was establishing a relationship between two such times when they were not in the "immediate proximity".
19 But, introducing the differential between timing of existence, and timing of observation of existence, is irrelevant. As before, the timing devices must be synchronised, otherwise these timings are meaningless, and if the distance AB is presumed, then A and B must have existed at the same time. Alternatively, if A and B did not exist at the same time, then there could not be a distance AB to observe.
20 Therefore, in the context of observation, assuming a simplification of the real conditions, any difference in these times can only be a function of the time delay for light to travel from B to A, or vice versa, and not a reflection of some other variance. That is, again there is no issue to be resolved. The difference in timing is because they were observations of reality, not reality. The simplification of equating timings of existence and observation in the "immediate proximity" is a symptom of the underlying conflation of reality and light reality. Physically, there is always a distance and therefore a delay whilst light travels; and there must always be light in order to observe. Indeed, what was the spatial relationship between the observer and the light as at the time of existence, could alter with respect to the light whilst the light is travelling. Neither is physical existence affected by observation, because it occurred before that, and involved no physical interaction with reality, but with a physically existent representation (from the perspective of the sensory system) of that reality (ie light reality). Constant light speed and no relative motion were presumed, which whilst further complicating calculations, would not affect the logic.
21 By substituting c for v, ie a specific velocity of a particular entity, c is asserted to be: 2AB/(t'(a) - t(a)). Which is both incorrect as a generic definition, but more importantly, wrong because that time involves duration incurred from subsequent timings, apart from being deemed an elapsed time in both cases anyway, which it is not. Assuming the quantity is doubled, it should be either twice A to B or B to A, or the sum of A to B and B to A incurred at the same time. So it should be, when specifically considering light speed: c = 2AB/2(t(a) - t(b)). Or simply, as considering either direction is superfluous, c = AB/(t(a) - t(b)). Which, although correct, is a statement of the obvious. That is, the velocity of light is a ratio of total distance travelled to the time taken to do so, ie the definition of velocity. Light is just another entity, which can be presumed to travel at a constant speed. But it is not a conceptual constant like rate of change, or spatial grid, its importance is in enabling sight.
22 The book: 'why does E=mc2' by Cox & Forshaw will now also be used as a reference, as this is a standard and readable exposition of the argument. That is, it is acknowledged that this is a repetition of certain accepted assertions which underpin the argument.
The train example
23 In general, the situation is seen as (page 43): "In order for the clock to tick at the same rate as it does when it stands still the light must travel a little bit faster...but... applying Einstein's logic means that the light cannot speed up because the speed of light must be the same to everyone". And later: "...time ticks at different rates depending on how we are moving relative to someone else. In other words, absolute time is not consistent with the notion of a universal light speed".
24 The issues arising from this general overview are:
1 Light, as in observation, has been conflated the use of light as the clock beam.
2 Originally (1905) Einstein correctly postulated that observational light always had the same starting speed, and unless impeded would continue at that speed. [SR is not 1905. It is a hypothetical circumstance with fixed shape bodies, only uniform rectilinear and non-rotary movement, and light which travels in straight lines (unlike 1905 when there was dimension alteration), because there is no gravitational force in SR on either matter or light. The contradictory circumstance was noted by Einstein in 1905 when he stated that the two postulates were "only apparently irreconcilable"].
3 Existence, and the sensory representation of that existence, have been conflated.
4 Timing is misconceived. It actually involves quantifying the rate of change, irrespective of type, by comparing the number of changes over the same duration. There can only be one absolute reference for this measuring system. Indeed, the beam is the time reference, which is why it has an independent constant velocity, and should be differentiated from observational light speed, since the only reason they are the 'same' is because of the particular choice of a beam of light as the tick mechanism. Neither is time a timing device, it just 'tells' the time, and must be in accord with the absolute rate of change reference to be valid.
5 The asserted dichotomy between light speed and rate of change is non existent, light speed is rate of change (timing) in this example.
25 The example (Fig 2, pages 42-48) involves two mirrors moving at v in parallel on a train, a distance apart. A beam of light is the tick mechanism of a timing device moving independently at a velocity c. The tick being defined as the beam travelling in both directions of the same distance between the mirrors. There is a stationary observer on the train (intrinsic reference) and another one who is stationary but not on the train (extrinsic reference). The aim is to establish the duration of the tick with respect to (wrt) the extrinsic observer, compared to the intrinsic one.
26 The configuration of this example involves complexity which disguises basic mistakes, since there are two different mirrors travelling in parallel a distance apart, a beam of light which moves independently, and a tick which involves a return. To ensure consistency of referencing the beam velocity will be a constant Vfast (Vf), the mirror velocity Vslow (Vs). These being generic velocities with VfËVs and Vfâ€c, where c is a specific (theoretically constant) velocity of a specific entity, ie light.
26.1 First, even as just an intrinsic reference (ie not an observer), wrt the intrinsic reference the beam is not the return over the vertical, because the beam is independent of the mirrors which move wrt the beam. The beam always travels the transversal, unless the mirrors do not move, ie they are moving backwards at -Vs to counteract the train velocity, or the train is stationary, and the beam is set to travel the perpendicular. This again emphasises the point that the beam is the time reference, ie it is a constant and independent. The mirrors and intrinsic reference are 'of the train', extrinsic reference 'of the earth', as is train movement. Whereas the beam is 'of nothing' because it is a conceptual concept, its manifestation (eg timing device) is irrelevant, so long as it 'tells' the proper time.
26.2 If two entities moving at different velocities start and finish at the same points, and do so in the same duration, then the faster entity must move laterally more than the other whilst travelling to the finish. The example uses one particular possibility which entails the faster entity (beam) moving over two equal distances, whilst the slower entity (bottom mirror) moves in a direct line, between the start and finish. That lateral shift, which is dependent on the velocities, is: (Vf - Vs)t. An alternative expression of this is that if the entities travel in the same direction, then the slower entity would need a headstart distance of (Vf - Vs)t for both to able to reach the same finish point in the same duration, having started at the same time.
Since the durations are the same, the ratio of the distance travelled by the faster entity (H, hypotenuse/transversal) to its velocity (Vf), ie H/Vf, is equal to the ratio of the distance travelled by the slower entity (L, lateral) to its velocity (Vs), ie L/Vs. That is, H = (Vf/Vs)L, or L = (Vs/Vf)H.
In other words, given a specified spatial relationship of the start and finish, a specified configuration for the beam to travel, the requirement for the duration to be the same, and a specified beam velocity (ie Vf = c), then the distance X (which in this example is the distance between the mirrors) cannot be arbitrarily stated. It must remain unknown as X. Otherwise, specifying it, as was done in this example (as 1) solves Vs, ie it can then only have a unique value and is no longer a generic V. Though in the expression of some ratios this does not have an effect, which disguises the error.
26.3 The other issue arising from this particular configuration is in the context of observation. That is, for the intrinsic reference as an observer, there are two different effects. First, when the beam is moving away from the observer, the half tick incurs a duration of H/Vf. But, subsequently, the light which enables an observation of this will take an additional duration of Z/c to travel back to the observer, wherever that might be, which is dependent on the speed of light. In other words, if there is a difference between the velocities of the beam and observational light, then that light will not travel the same path as the beam. So the duration for observation of the first half of the tick is H/Vf + Z/c. However, return of the beam will happen concurrently with the travel of that light. So, allowing for simplification of the real conditions, the elapsed time for observation of the complete tick is 2H/Vf. Because even if the observer receives observation of the first half of the tick before reaching the finish, for an observation of the second half of the tick, the observer must reach the finish. This again stresses the importance of differentiating observational light from a beam of light which is being used as a tick mechanism, ie this time is as stated, but not the right reasons. That outcome being a function of the tick configuration, and using a beam which travels at the same speed as the light which enables sight.
The extrinsic observer remains at the start. So observation of the first half of the tick involves the time taken for the beam to travel to the top mirror, H/Vf, plus the time taken for the observational light to return, H/c, ie H/Vf + H/c, which could be less that 2H/Vf if light is faster than the beam. However, again, it is the finish that is critical for elapsed time, and the finish occurs after a duration of 2H/Vf. Then light takes a duration of 2L/c to return to the extrinsic observer, who remains at the start. So the elapsed time for the extrinsic observer of the complete tick is 2H/Vf + 2L/c.
27 In the example, the following actually occurs:
1 Time for actual perpendicular tick: 2X/Vf (book states 2/c)
2 Time for actual transversal tick: 2H/Vf (book states 2ct/c)
3 Time wrt both intrinsic and extrinsic reference: 2H/Vf ( book states 2/c for intrinsic, ie perpendicular, and 2ct/c for extrinsic, ie transversal)
4 Time for observation by intrinsic observer: 2H/Vf (book states 2/c, ie same as actual perpendicular)
5 Time for observation by extrinsic observer: 2H/Vf + 2L/c (book states:2/â(c2 - v2).
28 The tick being a return masks certain effects, the times for a half tick are:
1 Actual perpendicular: X/Vf
2 Actual transversal: H/Vf (or L/Vs)
3 Intrinsic observer observation: H/Vf (or L/Vs) + Z/c
4 Extrinsic observer observation: H/Vf (or L/Vs) + H/c
This reveals the effect that: transversal/perpendicular = H/X, and that the duration of an observation takes Z/c longer if the observer moves in parallel and thereby maintains a perpendicular relationship with the top mirror, but then maintains momentum. The observer who remains stationary has an observation time which is wrt the actual, a longer duration of H/c.
29 Ratio of transversal to vertical tick time: H/X. This is Îł.
Book derives: 1/â(1 - v2/c2) from: (Vft)2 = X2 + (Vst)2, ie t = Xâ(Vf2 - Vs2).
But as explained at para 26.2 above, H and V are in a mathematical relationship which therefore determines the relationship between H and X:
t = H/Vf = L/Vs, so: H = (Vf/Vs)L, or L = (Vs/Vf)H and (H)2 = L2 + (X)2
So: X = Lâ[(Vf)2/(Vs)2- 1] = Hâ[1 - (Vs)2/Vf)2].
Therefore: H/X = H/{Hâ[1 - (Vs)2/(Vf)2]}, which is 1/â[1 - (Vs)2/Vf)2], which is Îł.
30 From consideration of the half tick only, which is ultimately what t relates to, Îł is immediately apparent. Especially if what constitutes the actual (and differentiates perpendicular from transversal) and what constitutes observation, and for whom, is properly analysed. Deeming X as 1 fixes the value of V, but this has no effect from the perspective of Îł. That set of conditions results in Îł being expressed as: 1/â(1 - v2/c2). The proper expression of Îł is:1/â(1-V(lateral)2/V(transversal)2) or just H/X, ie transversal/perpendicular.
31 The point is not about intrinsic vrs extrinsic reference, or observation, the pre-conditions determine the ratios. The hypotenuse (H) and the lateral (L) sides of a triangle depicting the event represent constant velocities which start at points vertically above each other, ie distance X, and must reach the same point after the same duration. The shortest time possible is over is X, ie the perpendicular, but this is when the mirrors do not move wrt the beam, ie L = 0. Otherwise, in all other cases, and as defined in the example, the transversal, ie the distance travelled by the beam, is greater than the vertical by a factor which reflects the relationship between the two velocities. The two extremes being when V = 0 (ie Vf involves perpendicular travel), or when Vf = Vs (ie both continue to travel in parallel and there is no transversal).
32 So the time taken for "someone sitting on the train next to the clock" is not 2/c because "for them the light simply travels 2 meters at a speed c" (page 48), neither as a reference nor an obsever, because the beam velocity is independent, and the mirrors move wrt it. 2/c, or more precisely, 2X/Vf is the actual time incurred when the mirrors do not move wrt the beam. The beam is not 'of the train', it has an independent velocity wrt everything since it is time. By definition, the time taken for the tick wrt to both intrinsic and extrinsic references is the same, one just stays at the start, the other moves to the finish. Neither, is 2/c the time taken for observation of "someone sitting". Neither is the time taken for a complete tick wrt the extrinsic reference, as a reference, the observation time, ie "as determined by someone on the platform". That takes longer (2L/c) because the observational light has to return.
33 The configuration of the tick, ie involving a return, the deeming of X as 1 for simplicity, and the deeming of Vf as c, which is the same speed as observational light, disguises the mistakes. That is, the conflation of beam and light, and the failure to understand that the beam velocity is independent because it represents time. This is self perpetuating in that the underlying misconceptions result in the configuration and its flawed analysis based on those misconceptions, proves the incorrect presumptions.
34 This is not the clock "running slow". Neither is it a function of observation. It is just because of the extra distance that the entity with the faster velocity must travel, as the velocity of the slower entity increases wrt to the faster velocity, starting with a base reference of zero (the perpendicular). Whilst in observation, the determinant is the spatial relationship between the observer and the finish, at the time of the finish. In addition to any distance moved after that, and the direction thereof, wrt light.
35 The commonality of Îł, and reification of observation, ie the involvement of c, rather than a proper generic time constant (though dimension alteration may occur as the result of force applied) is illustrated by:
- Einstein (1916 Section 12): "It therefore follows that the length of a rigid metre-rod moving in the direction of its length with a velocity v is â(1-v2/c2) of a metre. The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod". [&] "As judged from K, the clock is moving with the velocity v; as judged from this reference-body, the time which elapses between two strokes of the clock is not one second, but 1/ â(1-v2/c2) seconds, ie a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest".
36 Comparison of a tick without a return, in linear travel, reveals:
36.1 Actuality: a tick incurs a duration of X/Vf, where X equals the distance travelled during each tick, ie Vst + (Vf-Vs)t.
36.2 Observation wrt intrinsic observer: the time taken for an observation is the sum of the time taken for the event, plus the time taken for the observational light to return over the distance from where the event finished to the intrinsic observer, who in the meantime continues to move. Total distance moved by the intrinsic observer is: distance moved by the time the occurrence happened, ie Vst, plus distance then moved before observational light returns, ie: [Vs/(c + Vs)][(Vf -Vs)t]. The total duration is: time taken for the tick, plus time taken for observational light to return to the moving observer, ie t + {[c/(c + Vs)][(Vf -Vs)t]}/c.
36.3 Observation wrt extrinsic observer: the time taken for an observation is the sum of the time taken for the event, plus the time taken for the observational light to return from where the event finished to the extrinsic observer, who remains stationary.
That is: t + Vft/c.
36.4 The point being that, in the simplest of terms, the relationship between an event and observation of that event is a function of the original distance (X) between the event and observer, ie at the time of the event, and then the relationship between the two velocities, ie light (c) and observer (v), and whether they are moving towards or away from each other.
Moving away: for light and observer to arrive at same point over the same duration, observer has headstart distance of (c-v)t (ie X), then v travels distance of vt
Moving towards each other: light takes [c/(c + v)] of total time or total distance (ie X), or observer [v/(c + v)] of total time or total distance (ie X)
37 In both cases of observation the increment is constant, ie it is a per t increase in the duration. This is because the velocities, whilst different, remain constant. However, if one or both of these velocities is altering, then an optical illusion occurs with the observed rate of change (ie a sequence of ticks):
There is always a delay between time of physical existence, and time of observation of that existence, as light has to travel. The duration will vary as a function of the distance involved, and the speed at which any given light travels (or is presumed to do so). Assuming a constancy of light speed for the sake of simplicity, then the perceived (ie received) rate of change of any given sequence will remain the same, so long as the relative spatial position of whatever is involved remains constant. But, when relative distance is altering (ie there is changing relative movement), then the perceived (ie received) rate of change alters, because the delay is ever increasing (or decreasing) at a rate which depends on the rate at which the distances are altering. To the observer this gives the impression that the rate of change is slowing/speeding up, over time, but is an optical illusion, as the actual rate of change does not alter.
38 [Note: The recipient observer will be in a different physically existent state from that when existence occurred, so too will light. But this is irrelevant, because the physically existent state of the observer is not relevant, and the characteristic of light that resulted in its use in the evolution of sight in the first place is that fundamentally, from the perspective of the recipient sensory system, it varies very little, if at all, over time. Whether light has a rate of change which is equivalent/faster/slower than reality is another issue. And unless there was a particular form of interference, then the perceived (ie received) order of sequence will never vary from what occurred].
The Einstein version of the train
39 The key point here is that the beam is not observational light, and its speed is independent and constant because it is the time reference. So the same mistake was made by Einstein (or more precisely, everybody is replicating the same mistake, which probably originates with Poincaré. Apart from a more general underlying failure to understand the nature of physical existence). Einstein 1916, section 7: "It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage". Actually, it is obvious that this is incorrect. The man is, in terms of referencing, 'of the train', because he is on it and therefore has any velocity it has, in combination with any he may generate by walking, when that velocity is then compared wrt a stationary extrinsic reference, ie one not 'of the train'.
40 Whereas the ray of light was independent. Einstein defined it as such: "We shall imagine the air above it to have been removed. If a ray of light be sent along the embankment, we see from the above that the tip of the ray will be transmitted with the velocity c relative to the embankment". The reference here is "the above", not 'of the earth', nor 'of the embankment', but a conceptual position, ie the same as deeming a beam of light as the timing device mechanism. That is, an independent time reference. After describing the 'man on train' form of this example in the previous section (6), Einstein incorrectly concludes: "We shall see later that this result, which expresses the theorem of the addition of velocities employed in classical mechanics, cannot be maintained; in other words, the law that we have just written down does not hold in reality. For the time being, however, we shall assume its correctness".
41 This is not some form of deficiency in classical mechanics, but the result of a mistake with references, which itself reflects an underlying problem with the reification of change, and the attributation of this variance to timing differences in reality which is rationalised with the conflation of reality, and light reality. The latter being a separate existent reality based on light, and since there is always a delay as observational light travels, then there are potentially timing differences between existence and various observations of that existence.
42 Nothing is physically altering as a result of observation, ie timing devices are not ticking at different rates, nobody is aging faster, etc, etc. Observation is just that, observation. Physical existence occurs independently of that, before observation, and is dependent on interaction with a light based representation of reality anyway. For example: page 43: "applying Einstein's logic means that light cannot speed up because the speed of light must be the same to everyone. This has the disturbing consequence that the moving clock must genuinely take longer to tick, simply because the light has farther to travel, from the perspective of the person on the platform". "From the perspective" are the key words if translated as referring to observation, "genuinely" being redundant, and "disturbing" reveals misunderstanding.
The circular argument for spacetime
43 The next step is seen as calculating 'distance' between existent and non existent (previously existent) physical states, ie their supposed spatial separation in terms of a combination of physical distance and elapsed time. That is, their distance in spacetime. But physical distance over time is a contradiction, by definition. Something cannot be a distance from something else when they do not exist at the same time. So really the question is: can physically existent states which existed at different times be compared in terms of some conceptual relative spatial position? That involves consideration of the concept of a spatial grid, as explained in para 8.
44 A key error is revealed on page 74: "...because they are not of the same type of quantity. We can, however, convert distances into times and vice versa if we use the equation...v = xt...distance and time can be interchanged using something that has the currency of a speed. Let us therefore introduce a calibrating speed; call it c". This is only correct if, as explained in para 7, it is understood that it is not actually duration. And whilst it is explicitly stated that this velocity could represent anything, in fact it represents light speed, by virtue of the conflation of reality and light reality in the ensuing analysis. Indeed, the next sentence gives an example of light years. The issue was seen as best resolved by assuming homogeneity. Distance is Euclidean, and in order to "add time" the presumption is made that "our spacetime is unchanging and the same everywhere".
45 So the 'distance' in terms of a combination of space and time, known as s, was therefore deemed to be the hypotenuse of an imaginary triangle relating the two entities, with physical distance and elapsed time representing the other sides. Hence the two possibilities were: s2 = (ct) 2 + x2 or s2 = (ct) 2 - x2. The decision on which option is correct is based on causality, which is correct as such, in that effect must exist after cause. The 'negative' option was therefore chosen. This issue is with the presumptions and the analysis.
46 The argument is circular, because (page 89) it is asserted in relation to an examination of causality that: "Nothing can travel faster than c because if it did it could be used to transmit information that could violate the principle of cause and effect". And hence "we have finally managed to interpret the speed c: It is the cosmic speed limit". Then: "No matter how two different observers are moving, they must always measure c to be the same." and "The speed c is beginning to look a lot like another special speed we have encountered in this book: the speed of light, but we haven't proved the connection yet". And: "Certainly the existence of a universal speed limit offers promise, especially if we can interpret it as the speed of light".
47 But the assertion about 'nothing can travel faster' is incorrect. Because if there is something which can travel faster than light, it is irrelevant, as by definition, it is not the information transmitter. In respect of sight, evolution has utilised light, an effect in photons, as the information transmitter.
48 This presumption is only true in the context of a light based experience (eg sight) of physical existence, it is not necessarily true of physical existence. Since it is light that is enabling that experience, its speed and other innate properties impinge upon what is observable, and how that occurs. In other words, physical existence is not defined by light, observation of physical existence is. So the conflation of reality and light reality results in c, as in light speed, being seen as proven to be the constant, whereas it is just an inevitable outcome of the flawed analysis.
49 More generally, this applies to all phenomena involved in transmitting information to the sensory systems. They are physically existent, ie have intrinsic physical properties, so it has to be assumed until proven otherwise, that these could impinge upon their ability to fulfil this acquired sensory function. That results in potential practical problems which could arise in effecting direct sensory detection. That is, leaving aside the capabilities of the sensory systems to process what is received (both in terms of generic and individual capability), there are three types of issue:
-non receipt: eg no recipient sentient organism was in the line of travel of the effect, or it ceased to exist en route due to interaction with another existent phenomenon first, or it has not yet reached any known organism. Another possibility is that the reality has a property which does not interact with the phenomena involved, ie nothing is generated as a result of the interaction.
-alteration: the effect has been altered in some way, en route, ie it is not in its original state when received. This could involve delay, distortion, partial elimination, diversion from the original line of travel, etc.
-deficiency: this could revolve around the occurrences within any given physically existent state being too much, or too small, or changes being too frequent, or some properties not detectable, etc, so the physical phenomena involved cannot cope, ie they are unable to properly differentiate all that existed.
50 Unless proven to the contrary, it must not be assumed that what is received by the sensory systems, which is not the reality anyway, is an entirely accurate, and/or comprehensive, representation of that reality. It is only the result of a physical interaction, which sensory systems have evolved to take advantage of, thereby enabling awareness of reality to organisms. Whether any given recipient sensory system could process all that information, if it is, or could be, available, is another issue. Sensory systems evolved to enhance survival, not analyse reality.
51 So, the argument is circular, and incorrect. The final part of this being a reference back to the apparent effect on time with moving clocks. Which is also incorrect. But the proof is seen in the fact that (page 91): "the [derived] enhancement factor is equal to c/â(c2 - v2) or 1/â(1 - v2/c2), which is exactly what we got in the last chapter but only if we interpret c as speed of light...We have deduced the same formula...". With the added statement that: "We didn't even need to give light a special role". The only two presumptions are seen as: an invariant distance between events, and cause and effect are not to be violated. Then it is argued that the speed, and hence distance, through spacetime must be universal and that the variance is in observation, in that time varies with movement. Page 95: "...but there is something special about the motorcyclist's watch, because the motorcyclist does not move relative to himself". And then: "...a moving clock doesn't move so fast through time as a stationary one, which is just another way of saying it ticks more slowly".
52 Finally, on (page 103): "We haven't proved that c has anything to do with the speed of light yet...in the spacetime way of looking at things, light is not so special...everything hurtles through spacetime at the same speed, c...Light just happens to use up all its spacetime speed quota on motion through space and in doing so travels at the cosmic speed limit: The apparent specialness of light is an artifact of our human tendency to think of time and space as different things" . This is incorrect. In light reality, light speed is the speed limit, but not necessarily in physical reality. Light just enables sight.
What should happen
53 There is no distance between physically existent states that exist at a different time. So establishing some form of conceptual spatial relationship entails comparing spatial positions 'occupied' when they did exist. That is, in effect, relating where one of the entities would have been on the spatial grid of the other (para 8 refers). Put simply, calculating where the entities would have been wrt to one another, if the factors which resulted in the variance are discounted (speed, direction, environmental conditions, time elapsed between their respective existences, etc).
And the rest is history
52 Page 103: "There is in fact a reason why light is forced to use up its quota [ie spacetime speed] in this way [ie on motion], and this is intimately related to our goal of understanding E=mc2".
53 A summary of the final phase of the argument is:
Because change (and hence time) has been reified, Îł is introduced, since Îł is supposedly the factor which accounts for the 'effect of time', and c replaces v, as it is the speed of light, which is by now being deemed as the time constant against which physical existence is referenced. So, the energy that must be conserved becomes Îłmc, instead of mv. Then Îł as 1 + œ(v2/c2) replaces 1/â(1 - v2/c2), as the former is approximately correct for Îł at low values of v. Hence, ymc becomes equivalent to:
mc + œ( mv2/c). The second part of this quantity, ie œ( mv2/c), being defined as the "time component of the momentum spacetime vector" (page 133). Finally, to derive E=mc2 , this quantity, ie mc + œ( mv2/c), is multiplied by c, as if Îłmc is conserved then so too is Îłmc2, because c is a constant. The resulting energy quantity then becomes more "illuminating" because it is then expressed as: mc2 + œmv2, which is kinetic energy (œmv2), plus mc2.
Conclusion
54 The fundamental failure is to presume there is duration in physical existence. This particularly manifests as the expression of distance in terms of elapsed duration, and the concept that what is physically existent involves change, and hence time. That is, a variable is reified. The rationalisation of the consequences of this is effected with the conflation of physical reality and light reality. Thus light, and its speed, becomes attributed with an influence in physical existence which it does not have. Or more precisely, may only coincidentally have, if light speed is the fastest rate of change in physical existence, ie can be deemed to be the absolute timing reference for physical existence. This needs to be proven, without the conflation of physical reality and light reality. Obviously, light and light speed in particular, have the asserted influence in what is observable, because light enables sight.
Paul Reed © November 2012
Reference:
Why does E=mc2 By Brian Cox and Jeff Forshaw, Da Capo Press © 2009