Gravitational Mass = Inertial Mass: Einstein or Galileo?

Einstein takes as postulate of his general theory of relativity that

• gravitational mass = inertial mass.  

To Einstein this represented a deep insight into the inner nature of things, which he named the Equivalence Principle. To Galileo the same thing was a most natural consequence of his theoretical insight from experiments of dropping objects from the Tower of Pisa noting that all objects fall in the same way (modulo air resistance) and reflecting over the connection between force and motion.

Let us see if we can understand what to Einstein was beyond comprehension and to Galileo more or less self-evident. Newton's second law states that 

• $m_i\frac{dv_i}{dt}=F_i$, 

where $m_i$ is the inertial mass of a body showing acceleration $\frac{dv_i}{dt}$ with $v_i$ velocity and $t$ time when subject to a force $F_i$. On the other hand, the same body when subject to a gravitational force $F_g$, shows an acceleration $\frac{dv_g}{dt}$ satisfying 

•   $m_g\frac{dv_g}{dt}=F_g$,

where $m_g$ is the gravitational mass. 

To find out if $m_i=m_g$, let us consider the following experiment: Consider two identical bodies,  a body $A$ at rest on a frictionless table and another body $B$ in your hand with the two bodies connected by a weightless string stretched over a frictionless wheel attached at the end of the table, see picture in earlier version of this post. Then remove your hand and observe the action of the two-body-string system.  Observe that $A$ is acted upon by the horisontal string force $F_s$, while $B$ is acted upon by $F_g-F_s$ with $F_g$ the gravitational force acting on $B$. Since A and B have the same acceleration, we have

• $\frac{F_s}{m_i}=\frac{F_g-F_s}{m_g}$.  

If we now observe that 

• $F_s=\frac{F_g}{2}$,    (1)

then we can conclude that $m_g=m_i$ as a simple experimental verification of the Equivalence Principle. We can also argue that (1) must be true according to Leibniz' principle of sufficient reason, since there is no reason that the two-body-string system should not show this form of symmetry. We can also argue that (1) must hold if we re-orient the system to be all horisontal and pull $B$ with a certain force $F$ which must result in a string force $\frac{F}{2}$. 

Summing up, we have given simple evidence that gravitational mass = inertial mass, based on the insight that there is only one type of mass, namely inertial mass as a measure of acceleration vs force. Since gravitation is a force the measure of acceleration vs gravitational force as gravitational mass is necessarily the same as inertial mass. This is captured in the experiment with $B$ subject to (vertical) gravitational force (minus vertical string force) and $A$ to horizontal string force. 

The Equivalence Principle is thus a direct consequence of Newtonian mechanics, and as such a most questionable empty Basic Postulate for general relativity. As usual Einstein managed to create confusion rather than clarification. For more reason to this verdict see earlier posts on the Equivalence Principle.    

Special Theory of Relativity: Empty of Real Physics 2

Modern physics is supposed to be based on in particular on Einstein's special theory of relativity SR. In discussions with theoretical physicist Ulf Danielson recorded in a previous post, and in an upcoming post with physics philosopher Lars-Göran Johansson, my position is that SR is empty of real physics because the two basic Postulates of SR are definitions or analytic propositions true by definition (or stipulations without truth value), and not synthetic propositions about physics which may be false. To see this, recall the two basic Postulates of SR:

1. Laws of physics have the same formal expression in different inertial systems.
2. Measurements in different inertial systems (must) give the same constant speed of light.  

Inertial systems are space-time coordinate systems traveling with constant speed with respect to each other. 

Is Postulate 1 a synthetic proposition stating something about physical reality which may be false? No! It only states that a "law of physics" must meet a requirement of looking the same in all inertial systems.  It does not say what a "law of physics" is, nor gives any example, only states that it must look precisely the same in all inertial systems. It is thus a stipulation like a legal law, which has no truth value, or definition true by semantic construction. No physics in Postulate 1.

Postulate 2 is also a stipulation about the result of measurement of the speed of light by different observers using different inertial systems. Since speed is measured in terms of measures in space and time, Postulate 2 says that measures in space (meter) and time (seconds) must be chosen so that the speed of light comes out the same in all inertial systems. This is the SI standard since 1983 where the meter is defined as the distance traveled by light over a certain length of time as measured by a cesium atom clock.

Is Postulate 2 a synthetic proposition stating something about physical reality which may be false. No! It is a definition of the length scale to be used in different inertial systems, a stipulation or legal law to follow a certain standard, which again has no truth value. No physics in Postulate 2.

We arrive at the conclusion that since the Postulates of SR contain no physics, neither does SR.  Empty of physics = pseudo-physics!

Further evidence on the strange unphysical form the Postulates of SR is obtained from the observation that Postulate 2 appears to be a consequence of Postulate 1 using the following reasoning: If there is a law of propagation of light it must be viewed to be a "law of physics" and as such it must take the same form in all inertial systems by Postulate 1 and thus in particular express the same constant speed of light = the statement of Postulate 2. 

In fact, Postulate 1 is ridiculous and as such unphysical: Laws of physics in general have different formal expressions in different coordinate systems and so very few, if any, satisfy Postulate 1. Not even Maxwell's equations for the propagation of light waves in vacuum take the same form in different inertial systems since initial conditions change form and waves are extended in space and thus require initial values as wave forms extended in space at a specific time.  

Modern physics is thus based on empty physics, and so it is no surprise to meet modern physics empty of physics, such as multiversa and string theory. 

PS1 Recall Leibniz strict separation between space and time, in direct contradiction to the mixing of space and time in SR, with 

• space = order of coexistence  (connecting to initial value),
• time = order of succession.

PS2 In the upcoming discussion with philosopher Lars-Göran Johansson the question of analytic vs synthetic statement and Kant's synthetic a priori, will come up. LGJ will argue that the distinction between analytic and synthetic cannot be made and that there are propositions which are both analytic and synthetic, or neither. This can be a tricky debate, and to avoid getting bogged down in sophistry, I will seek to focus on the question which real physics is expressed in the Postulates of SR, if any.

PS3 Modern physics is based on Einstein's mechanics including SR, and not Newton's mechanics,  and thus it would seem to be one of the fundamental missions of education and practice of modern physics to subject SR to a critical analysis concerning form and physical meaning, right?

This is anyway the objective of the book Many-Minds Relativity. My conclusion is that SR is empty pseudo-science or fake-physics, which does not say anything of interest concerning the real physics of the world. But this is viewed simply as crackpot heretics, which a modern theoretical physicist can dismisses without any argument from a position that a critical analysis of SR is not needed nor possible, as shown in the discussion with Ulf Danielson.

The True Twin Paradox

Two twins C and S, Clever (Salviati) and Stupid (Simplicio), decide to part with mutually agreed speed $v$ equipped with identical cesium clocks and so decide to compare the readings of the two clocks, to test the validity of Einstein’s special theory of relativity SR, by exchanging light signals with the clock frequency. Both twins then record a redshift of frequency of the other clock of size $\frac{1}{1+v}$ (with light speed normalised to 1).

C says that this is just what is to expected from laws of physics and it does not say that the clock of S runs slow; it is only a red-shift effect. 

S says that the reduction in frequency,  which he records carefully, shows that the clock of C runs slow compared to that of S, and S becomes convinced that C ages more slowly as evidence of SR, which makes S unhappy.

Who is right then? C or S? Is the reason for S to get unhappy, reasonable?

A symmetrical situtation has turned into an unsymmetrical and this is the true twin paradox. What is your solution?

Speed of Gravity? Newton or Einstein?

Tom Van Flandern (1940-2009) was a free-thinking physicist who with perplexion made the observation (along with Laplace and also Newton of course) that the Earth on its path around the Sun at every instant in time accelerates in the direction of the actual position of the Sun, which is about 20 arc seconds ahead of the position of the Sun as seen in the sky from the Earth, because of the 8 minutes it takes for light to travel the distance from the Sun to the Earth. See also this review of Van Flandern’s work.

This observation is in accordance with Newtonian gravitation, which is assumed to propagate with infinite speed. If gravitation propagated with the speed of light, the acceleration would be instead in the direction of the visible Sun, but this is not what is observed (because it would be unstable).

I have discussed this observation in various posts with conclusion that the connection between mass density $\rho (x,t)$ and gravitational potential $\phi (x,t)$ as given by Poisson's equation in Newtonian gravitation

• $\Delta\phi (x,t)=\rho (x,t)$      

with $\Delta$ the Laplacian with respect to a space coordinate $x$ and $t$ being a time coordinate, is to be interpreted as a relation where mass $\rho (x,t)$ somehow is "created" at $x$ at time $t$ by the local operation of differentiation through the Laplacian $\Delta$ acting on the gravitational potential $\phi (x,t)$. 

This is different from the standard interpretation where instead the presence of mass $\rho (x,t)$ at a specific point in space at time $t$ contributes to $\phi (x,t)$ for all points $x$ somehow through instant action at distance. Like Tom Van Flandern I view instant action at distance as physically impossible, while local instant action may be physical. The creation of mass from gravitational potential through the Laplacian thus may be possible, while its detailed physics remains to be discovered...

In any case the observation of the acceleration of the Earth towards the actual position of the Sun is only compatible with a speed of propagation of gravitational waves (if they exist), which is much bigger than the speed of light. This observation is in accordance with Newton's mechanics (with both the new and old interpretations of the mass-potential connection), but not with Einstein's mechanics.

What is your conclusion concerning who describes physics of gravitation best? Newton or Einstein? Be careful when you look at the Sun for answer.

The current wisdom among physicists is that despite the above Earth-Sun observation, for sure there are gravitational waves because Einsteins so says, waves which propagate with the speed of light and that these waves can be detected, not gravitational waves from the Sun, but from distant mergers of black holes and stuff. Do you buy this?

Sorry to say Tom passed away in 2009, but his ideas live.

PS Of course there is a cover up suggesting that also in Einstein's mechanics does the Earth accelerate in the direction of the current position of the Sun, even if the speed of gravitational waves is the finite speed of light,  because there is a subtle cancellation of the effect of the 8 minute delay from another effect, a most happy and welcome cancellation which allows a stable observable planetary system not only according to Newton but also for Einstein. But why Einstein if Newton explains what is observed? No wonder that Einstein begged for pardon in his: "Newton, forgive me!".

Einstein: The Illusionist

What would Einstein answer to this question: Is the time dilation and space contraction of special relativity real physics or only illusionary physics?

Here is his answer published in Physik Zeitschrift 12, p 509, 1911:

• The question whether the Lorentz contraction (time dilation and space contraction) does or does not exist is confusing. It does not really exist in so far as it does not exist for an observer who moves (with the rod); it really exists, however, in the sense that it can as a matter of principle be demonstrated by a resting observer.

This ambiguous answer is typical of Einstein and makes discussion so difficult. One way to interpret Einstein's statement is that time dilation and space contraction are both real and illusionary physics at the same time and one can always choose whatever fits the discussion best. 

If a skeptic says that the physics is contradictory a physicist can say that the contradiction is only an illusion so it is no real contradiction, and if the skeptic complains that it is illusion the physicist can say that this is only a misinterpretation of something which is real physics.

This is why the discussion becomes so confusing, even to Einstein, and all his followers as thousands and thousands of modern physicists.

An example of illusion of contradiction connecting to space contraction, is to consider two twins looking at each other at distance both stating according to physical input that the other appears to be smaller.  Of course you say that the smaller size is only an illusion depending on view at distance and that the twins in fact remain physically equally tall.  

It is like two twins both appearing to age slower than the other which could be an illusion of similar form if the twins are equipped with identical clocks and are traveling with a mutual velocity difference $v$ each one able to record the frequency of the other clock through a light signal subject to Doppler shift scaling with $\frac{1}{1+v}$ with the speed of light normalised to 1. Both twins would then be able to record a redshift when parting and blueshift in approach and state that their instruments record a different rate of ageing. All illusion of course, depending on Doppler shift.

A discussion with Swedish media physicist Ulf Danielson can be followed in comments to the previous post. This is hot topic so follow closely! Is it confusing or illuminating?

Note that Danielson immediately plays the following card suggesting that I am a crackpot representing pseudoscience:

• In a time when theories that the Earth is flat and conspirations around moon landings are flooding the net, it is not so surprising that questions like this (my questions) come up.
• (I en tid när teorier om att att jorden är platt och konspirationer kring månlandningen florerar på nätet tillsammans med pseudovetenskap av olika slag är det kanske inte så överraskande att en fråga av detta slag dyker upp.)

This is one approach to debate. Let us see how effective it is this time. Danielson's professional work concerns string theory, by many viewed today as illusionary physics rather than real physics. This may explain why Danielson is not sensitive to a distinction between illusion and reality, or definition and fact as discussed in previous posts.

Dingle Destroyed as Scientist by Questioning Relativity Theory

   It is ironical that, in the very field in which Science has claimed superiority to Theology, for example—in the abandoning of dogma and the granting of absolute freedom to criticism—the positions are now reversed. Science will not tolerate criticism of special relativity, while Theology talks freely about the death of God, religionless Christianity, and so on.

Herbert Dingle (1890-1978) was a prominent English physicist who came to question Einstein's special theory of relativity in an intense scientific controversy in late 1950s, see Questioning Relativity 1 with more as 2-20.

Dingle pointed to the logical contradiction of two traveling twins both ageing more slowly than the other.  Dingle concluded that since physics cannot be contradictory, the special theory of relativity with its Lorentz time dilation and different twin ageing cannot be a theory about physics. This is also my standpoint 60 years later.

The reaction from the physics community to Dingle's heretics was harsh and Dingle was destroyed as scientist, like Bruno in 1600. Dingle recorded his experience of this process in Science at the Crossroads:

• They are, briefly, that the great majority of physical scientists, including practically all those who conduct experiments in physics and are best known to the world as leaders in science, when pressed to answer allegedly fatal criticism of the theory, confess either that they regard the theory as nonsensical but accept it because the few mathematical specialists in the subject say they should do so, or that they do not pretend to understand the subject at all, but, again, accept the theory as fully established by others and therefore a safe basis for their experiments. 
• The response of the comparatively few specialists to the criticism is either complete silence or a variety of evasions couched in mystical language which succeeds in convincing the experimenters that they are quite right in believing that the theory is too abstruse for their comprehension and that they may safely trust men endowed with the metaphysical and mathematical talents that enable them to write confidently in such profound terms. 
• What no one does is to answer the criticism.

The situation today 60 years later is the same: The accepted truth is that Einstein's special/general theory of relativity is correct and experimentally verified over and over again, but this cannot be questioned because no real physicist can understand the theory nor the experiments. Only crackpots like Dingle can understand that something is wrong.

I have asked Ulf Danielson as a Swedish media physicist about his view.

PS1 Read Tom van Flandern on the (non)use of SR in GPS.

PS2 For a detailed presentation of my criticism of special relativity theory, see Many-Minds Relativity (download)

PS3 Listen to Louis Essen, designer of the atomic clock:

• No one has attempted to refute my arguments, but I was warned that if I persisted I was likely to spoil my career prospects. …the continued acceptance and teaching of relativity hinders the development of a rational extension of electromagnetic theory." - Louis Essen F.R.S., "Relativity and time signals", Wireless World, oct78, p44. ‘Students are told that the theory must be accepted although they cannot expect to understand it. They are encouraged right at the beginning of their careers to forsake science in favor of dogma.’

PS4 More Dingle from the Crossroads:

• Lorentz, in order to justify his transformation equations, saw the necessity of postulating a physical effect of interaction between moving matter and æther, to give the mathematics meaning. Physics still had de jure authority over mathematics: it was Einstein, who had no qualms about abolishing the æther and still retaining light waves whose properties were expressed by formulae that were meaningless without it, who was the first to discard physics altogether and propose a wholly mathematical theory...

PS5 Here is short summary of the exchange of comments with Ulf Danielson:

CJ Question1: What is the real physics of the Postulates of SR? Are the Postulates only definitions empty of physics?

UD Answer:??

CJ Question2: In what way does GPS depend on the special and general theory of relativity?

UD Answer:??

CJ Question3: Are there any physical laws that are Lorentz invariant, when not even Maxwell's are so with respect to initial conditions and presence of charges? If yes, which?

UD Answer:??

CJ Question4: Does translation with constant velocity influence the physical action of a pendulum or atomic clock?  If so, what is the physics of the influence? 

UD Answer:??

There are many more questions, but with this poor result we both felt that continued discussion was meaningless. UD appears in media as an authority on modern physics and so it would have been very interesting, for me in particular but maybe also for the world, to get some illuminating answers on pressing questions, and so we have to wait for answers with patience. The questions remain and authorities on physics must be expected to have some form of answers.

PS6 Dingle pointed to an apparent physical contradiction in SR (asymmetry of symmetric twins), but that argument did not bite on modern physicists used to view contradictions as signs of deep physics. So the contradiction did not kill SR, but Dingle instead.

I try with another approach pointing to the fact that SR is empty of physics, and as such does not contain contradictions of physics. Maybe it is more difficult for a modern physicist to dismiss emptiness than contradiction. We shall see.

Dingle's analysis and conclusion of incompatibility/contradiction of SR could be dismissed because the physics of the postulates of SR is so murky that it could twisted to support any claim ("event", "rigid measuring rod", "clock", "reading of a moving clock", "time" et cet).  The only way to get out of this swamp is to show that the postulates contain no physics at all, in which case twisting of physics no longer is possible.  

(Postulates of) Special Relativity Empty of Physics 1

The postulates of Einstein's special theory of relativity are:

1. The laws of physics are the same in all inertial frames of reference.
2. The speed of light in free space has the same value c in all inertial frames of reference.

In the light of the discussion in recent posts on relativity theory, we make the observations that the postulates state that:

• It is necessary for a law to be a law of physics (but not sufficient) that it takes the same form in all inertial systems.
• It is necessary for different observers to measure the same speed of light. 

We understand that neither 1. nor 2. contains any actual real physics, since they do not specify any law of physics,  only stipulate a necessary requirement to be satisfied by a physical law (invariance in the sense of taking the same form in all inertial systems) and stipulate what the result of a measurement of the speed of light must be. The postulates of special relativity thus are not postulates (assumptions) about real physics, but instead are stipulations or definitions concerning form (invariance) or procedure (measurement of the speed of light).  But form and procedure do not contain any real physics, and therefore special relativity has nothing to say about real physics. If the postulates of special relativity are empty of physics, this must be the case for any logical derivation from the postulates, and so the whole special theory of relativity is empty of physics. 

In particular, it is not enough to note invariance of a law to allow declaration that it is a law of physics.

Special relativity is a corner stone of modern physics, and if special relativity is empty of physics, this means that modern physics rests on emptiness. Viewing the result in the form of string theory and multiversa gives further evidence of this unfortunate state of affairs.

PS As stated in my comments to the next post, postulate 2. is a convention since by definition according to the 1983 SI standard the speed of light is specified to be exactly 299792458  meter per second, which is used to define the meter. Postulate 2 is thus a definition without physical content. Likewise, postulate 1 is void of real physics, since it is only a specification of what can be called a physical law. 

Special Relativity: Physics without Physical Laws

Unphysics of sawing a woman into two pieces.

The focus of both the special and general theory of relativity is coordinate systems with the idea that  coordinate systems hide truths about the world. Special relativity concerns Euclidean space coordinate systems moving with constant velocity with respect to each other, so-called inertial systems, while general relativity is expressed in general curvi-linear space-time coordinate systems with Einstein's equations expressing a connection between space-time curvature and mass-energy distribution.

Einstein's contribution to physics with the special theory is the postulate that physical laws have the same formal expression in all inertial systems connected by the Lorentz transformation, in other words are Lorentz invariant. Einstein thus postulates a formal requirement on what is allowed to be called a physical law: It must be Lorentz invariant.

Recall that the Lorentz transformation connecting two inertial space-time coordinate systems $(x,t)$ and $(x^\prime ,t^\prime )$ moving with velocity $v$ with respect to each other, read:

• $x^\prime =\gamma (x - vt)$, $t^\prime =\gamma (t - vx)$,
• $x =\gamma (x^\prime + vt^\prime )$, $t =\gamma (t^\prime + vx^\prime )$,

where $\gamma = \frac{1}{\sqrt{1-v^2}}$ assuming the speed of light is 1.

Einstein's contribution to physics with the general theory is Einstein's equations which express a physical law satisfying the invariance requirement by being covariant in the sense of having the same formal expression in different space-time coordinates as if allowing a coordinate-free representation in terms of curvature and mass-energy.

Which physical laws are then Lorentz invariant?  Does Newton's 2nd law $\frac{d^2x}{dt^2}=F(x)$ for a body of unit mass moving under the force $F(x)$ in the $(x,t)$ system take the same form in the the $(x^\prime ,t^\prime )$ system? Let us check out: By the chain law, we have

• $\frac{\partial}{\partial x}=\gamma (\frac{\partial}{\partial x^\prime}-v\frac{\partial}{\partial t^\prime})$,
• $\frac{\partial}{\partial t}=\gamma (\frac{\partial}{\partial t^\prime}-v\frac{\partial}{\partial x^\prime})$,

and conclude that 

• $\frac{\partial^2}{\partial t^2}=\gamma^2(\frac{\partial}{\partial t^\prime}-v\frac{\partial}{\partial x^\prime})^2$.    

Does this show that Newton's 2nd law takes the same form in the two systems? Does not seem so, but to be sure let's take an even simpler case, that of a body moving with constant velocity $V$ in the $(x,t)$ system, with motion satisfying the physical law $x=Vt$ (with the initial condition $x=0$ for $t=0$), which in the $(x^\prime ,t^\prime )$ takes the form

• $x^\prime =\frac{1-Vv}{V -v}t^\prime$.  

We conclude that only for $V=1$ does the physical law $\frac{dx}{dt}=V$ take the same form in the $(x^\prime ,t^\prime )$ system. In other words, the physical law of propagation with constant velocity $x=Vt$ is Lorentz invariant only if $V=1$, that is only if the physical law of propagation is the law of propagation of light. Of course you can save the situation by simply defining $V^\prime =\frac{1-Vv}{V-v}$ and then claim the $x=Vt$ and $x^\prime =V^\prime t^\prime$ have the same formal appearance (with and without prime), but opening this possibility would loose the meaning of Lorentz invariance in the sense that any law could be made Lorentz invariant by suitable manipulation of symbols. 

Einstein thus says that the physical law of propagation with constant speed less than 1 is not a physical law. The only physical law compatible with Lorentz invariance is the law of propagation of light at speed 1.  This means that special relativity is empty of almost all physics as a physics with the only physical law being that of propagation light.  That this is so, is clear from the only hypothesis of special relativity, which is constant speed of propagation of light. With (close to) zero real input the real output can only be (close to) zero.

Special theory thus does not contain even the most basic physics as Lorentz invariant physics, but instead a lot of unphysics such as time dilation and space contraction as a consequence of postulated Lorentz invariance.

General relativity is supposed to be a generalisation of the special theory and if the special theory is zero so is the general theory. More precisely general relativity is not Lorentz invariant, so there is a possibility that the general theory contains some physics such as Newton's 2nd law and gravitation, but without special relativity the rationale of replacing Galilean invariant Newtonian mechanics with new Einstein mechanics is missing. See Many-Minds Relativity for a generalisation of Newtonian mechanics different from Einstein's reaching into speeds comparable to the speed of light.

PS1 What about Maxwell's equations? Yes, they are Lorentz invariant insofar they express propagation of light with the same constant speed in all inertial systems, but not concerning initial conditions and the connection between electric and magnetic fields, as made clear in Chapters 5 and 17 of Many-Minds Relativity.

PS2 The starting point for Einstein in 1905 was that it is impossible to determine the speed of a train traveling in rectilinear motion with constant velocity (inertial motion) from an experiment made inside the train, if there is no possibility to look out into the environment. This is the same in Newtonian mechanics under Galilean invariance. Similarly it showed to be impossible (the null result in the Michelson-Morley experiment) to determine motion of the Earth vs a (stationary) aether medium carrying electromagnetic waves. Without an environment or aether as (stationery) reference,  inertial motion is impossible to detect; only relative inertial motion is possible to detect. But that does not hold for non-inertial motion, like rotation; an ice skating princess with closed eyes can certainly feel if she is spinning or not.

In any case the Michelson-Morley null experiment made Einstein claim that there is no aether at all, and postulated that therefore all observers independent of inertial motion must record the same (unit) speed of light, independent of any physics of propagation of light. This was not an assumption about physics,  but simply a human standard or recipe about how to measure time and space so that the speed of light comes out to be 1, independent of any physics. This made special relativity to a theory without physical content and as such without scientific meaning.

PS3 Many-Minds Relativity proposes a different way to explain the MM null result based on the following assumption with clear physics content: All observers share a common time (have identical clocks), travel with respect to each other with constant velocity and make observations in a Euclidean space coordinate system in which they are stationary. Different observers thus use different inertial systems or aethers, and there are thus as many aethers as inertial coordinate systems (in the spirit of Ebenezer Cunningham). Each observer assumes the validity of a wave equation in the observer's coordinate system which says that light propagates with unit speed in the observer's coordinate system and which effectively determines how to measure length (in light seconds). This is an assumption about physics which is consistent with the MM null result. The key question of focus in Many-Minds Relativity is then to what degree different observers will agree on lengths and motion in space.

Many-Minds Relativity is different from special relativity in that all observers use the same type of clock (with operation independent of inertial motion such as a pendulum) and thus can share a common time without time dilation by some suitable synchronisation, while all observers are tied to their own inertial system. The conundrum of special relativity of one observer making observations in two different inertial systems, then is not an issue at all and the paradoxes of special relativity all collapse to null.

To modern physicists special relativity and Lorentz invariance is viewed as such a holy cow that it cannot be subject to a critical analysis and only be swallowed without any questioning, despite all its paradoxes. My experience is that it is very difficult to find a physicist willing to enter into a discussion about special relativity and its role as pillar of modern physics.          

  

Special Relativity: Unphysical Event Theory

A great physics event: Einstein's Nobel Prize reception speech about his special theory of relativity presented to a stunned  King Gustav V in middle front row at the Gothenburg Words Fair in 1923.  Notable is that Einstein did not speak about the law of the photoelectric effect, for which he was awarded the Prize, along with the remark by the Nobel Committee that Einstein did not get the prize because of his special theory of relativity but despite of it!  Here x = Gothenburg and t = 1923 with the space-time coordinates (x,t) telling nothing about the physics of the event.

It was Einstein who introduced the concept of event to physics in his 1905 article presenting his new revolutionary theory of special relativity as follows:

• We have to take into account that all our judgements in which time plays a part are always judgements of simultaneous events. If, for instance, I say: "That train arrives here at 7 o'clock" I mean something like this: "The pointing of the small hand of my watch and the arrival of the train are simultaneous events". 

We here meet both the concept of event and the qualification of simultaneous events. We learn that the time of an event is something which can be recorded by the hand of a watch while the event itself can be just anything. The time of an event is thus identified with measurement while the physical nature of the event appears to be irrelevant. It can be a train arriving at station or anything. In previous posts we have also noted that an event according to Einstein has no extension in space and thus can be recorded with a single space coordinate and reading of a clock. 

Altogether, we find evidence that the notion of event used by Einstein has no real physical meaning, which suggests that his special relativity about events is not a theory about physical reality, only an empty play with definitions. Einstein's mastery was that he could turn this emptiness into shining physics blinding the world of both professional physicists and media, if not ordinary people who simply where confused.

Einstein's mastery is exercised through a double play between reality and  illusion as revealed in Physik Zeitschrift 12, p 509, 1911:

• The question whether the Lorentz contraction does or does not exist is confusing. It does not really exist in so far as it does not exist for an observer who moves (with the rod); it really exists, however, in the sense that it can as a matter of principle be demonstrated by a resting observer.

We read that Einstein considers the Lorentz transformation with its built-in Lorentz contraction to be a matter of principle,  in other words is a tautology true by definition, something which does not really exist and thus is empty of physical meaning and thus is unphysical. It is a complete mystery that modern physicists have been so overwhelmed by Einstein's form of jokery that all rational thought has evaporated. 

Coexistence vs Special Theory of Relativity

Two cars sharing time before collision

This is a continuation of the previous post on the special theory of relativity based on the concept of event which is something which can recorded by a space coordinate $x$ and time coordinate $t$ into a space-time coordinate $(x,t)$. This is also the basic element of Minkowski space-time physics closely connected to theory of relativity, where the distinction between space and time of such fundamental importance in classical physics, is given up and space coordinates are mixed into time coordinates as in the Lorentz transformation of special relativity.

An event is thus something without extension in space which takes place (exists) at a specific point in space $x$ and time $t$. But is existence without extension in space possible? Of course not, but a modern physicist would probably say that an event recorded by $(x,t)$ is an idealisation of the position $x$ in space at time $t$ of a physical phenomenon of such small dimension in space that one space coordinate $x$ is enough to describe its position in space.

But in both mathematics and physics it can be misleading to stretch an idealisation into a singularity such as that connected with the concept of a physical phenomenon without extension in space, that is introducing the concept of particle as the basic element of modern particle physics.  Singularities are tricky because they hide their true nature and thus can be misunderstood.

Real physical phenomena like a physical body has extension in space and as such represents coexistence in the sense that the different parts of the body all exist a the same common instant of time and thus can be viewed to share the same time coordinate. The Lorentz transformation has no role for bodies with extension in space because it mixes space into time an upsets coexistence with shared time.

As an illustration consider two objects moving with constant velocity with respect to each other and connect to each body a Euclidean space coordinate system attached to the body with the body at the origin. This gives us two inertial systems $(x,t)$ and $(x^\prime ,t^\prime )$ and we now ask if it is possible that they can be connected by the Lorentz transformation supposed to connect space-time coordinates of inertial systems without common time.

Assume now that the bodies approach each other and collide. In special relativity a collision is viewed as an event without extension in space and as such can be recorded in different inertial systems connected by the Lorentz transformation without common time. But a collision is not an event without extension in space, because it is the end of a process where the two bodies approach each other and thus form a two-body system with extension in space with necessarily coexistence of the two bodies with necessarily shared common time prior to collision.

Collision without shared time is impossible. You cannot decide to meet a good friend at a cafe without sharing time. When meeting you share time. Without shared time there can be no meeting.

We conclude that the theory of special relativity concerned with events without extension in space  misses the physics of real phenomena, which all have extension in space. Even the physics of collision between two particles (even without extension in space), which in special relativity is viewed as an event without extension in space,  in fact is a phenomenon with extension in space because the particles prior to collision approach each other and thus form a system with extension in space, coexistence and shared time.

In order for two particles about to collide they must coexist and corresponding inertial systems then cannot be connected by Lorentz transformation without common shared time.  In order words, special relativity is not a theory about real physics, and as such of no interest from scientific point of view. Special relativity is a fantasy identical to a Lorentz transformation without physical meaning.

How to Understand that the Special Theory of Relativity is Unphysical

Two space traveling Lorentz invariant twins both one year older than the other: Deep but unphysical. 

Einstein's special theory of relativity is loaded with paradoxes, such as the twin paradox, ladder paradox, cooling paradox and Ehrenfest's paradox, expressing effects of time dilation and space contraction. In classical physics one paradox would be enough to kill a physics theory, but not so in modern physics with the special theory of relativity as corner stone, where the presence of paradoxes instead is taken as evidence that the theory is deep.

The paradoxes of special relativity express physical paradoxes such as traveling twins both ageing more slowly than the other. So even if special relativity is deep it cannot be a theory about true physics if it contains paradoxes, because true physics cannot be paradoxical that is contradictory.
Two twins cannot both physically age more slowly than the other.

The quickest way to understand that special relativity is unphysical, and as such can carry seemingly physical (but unphysical) paradoxes, is to recall Einstein's starting point as a description of so-called events recorded by space-time coordinates $(x,t)$ with $x$ a space coordinate and $t$ time coordinate. Einstein thus consider events to have no extension in space so that one single space coordinate $x$ is enough to describe its location in space.

Einstein's special theory concerns the description of events in two different (Euclidean) coordinate systems assumed to move with respect to each other with a certain constant velocity, so-called inertial systems.

In classical physics the connection between such systems is given by a Galilean coordinate transformation where space coordinates are transformed to match the difference in motion between the two coordinate systems while time coordinates remain the same.

In special relativity the connection is instead given by the Lorentz transformation where also time coordinates are transformed by mixing space into time. Special relativity thus boils down to the Lorentz transformation and all the paradoxes from physical point of view such as time dilation and space contraction, are consequences of the Lorentz transformation mixing space into time.

Einstein's catch is that Maxwell's equations for electromagnetics, like any wave equation, has the same analytical expression in all inertial systems under the Lorentz transformation (but not under the Galilean transformation).

Einstein then postulates that physical laws are laws which take the same form in all inertial systems connected by the Lorentz transformation, and thus declares that Maxwell's equations express a physical law.   In circular reasoning Einstein then argues that because a physical law expresses physics the Lorentz transformation expresses physics and therefore special relativity is a physical theory as a mathematical theory about physics.

Einstein's great contribution to modern physics is viewed to be his postulate that physical laws (must) have the same analytical expression in all inertial systems connected by Lorentz transformation, in other words must be Lorentz invariant.

Einstein's basic idea is thus that (true) physical laws (must) be Lorentz invariant. What we now first must understand is that this whole idea is absurd: Of course physical laws in their physical meaning must be independent of choice of coordinate system, but it is absurd to ask that they would literally have the same analytical expression. It is like claiming that a statement translated to different languages would not only have the same meaning but also the same notational expression letter by letter. This would mean that there was only one language, which is absurd. What is not absurd but rational is to expect that the same physical law will have different analytical expressions in different coordinate systems.

Next, we return to Einstein's starting point as a study of events without spatial extension, which we will see is the very reason Einstein can make the absurd claim that Maxwell's equations are Lorentz invariant. Now, solutions to Maxwell's equations represent physical waves and waves have extension in space. And now comes the catch: Maxwell's equations come along with initial conditions, which describe the initial configuration of a wave with extension in space at a certain initial time. And initial conditions are not Lorentz invariant because they mix space into time. Only Einsteinian events without extension in space can be claimed to be Lorentz invariant. A detailed account of the mathematics by  physics is given in Chapter 5 and 11 of Many-Minds Relativity.

Einstein's insistence on Lorentz invariance thus builds on the misconception that initial conditions with extension in space as physics, can be reduced to events without extension in space as unphysics. This is absurd and is the root to all the paradoxes of special relativity resulting from mixing space into time by Lorentz transformations without physics.

Einstein insisted on Lorentz invariance forgetting that wave equations have initial conditions with extension in space.  The result is a lot of modern physics formed to be Lorentz invariant which cannot be physics.

The basic trouble with modern physic preventing progress is generally viewed to be that quantum mechanics is incompatible with relativity theory in that Schrödinger's equations are not Lorentz invariant. The above analysis indicates that this is a ghost problem which should not be allowed to prevent progress. Asking for Lorentz invariance is unphysical. There is no incompatibility. There can be no incompatibility between physical theories because physics cannot be incompatible with itself. Twins cannot be incompatible.

Einstein confessed at several occasions that his knowledge of mathematics was superficial:

• I neglected mathematics...because my intuition was not strong enough to differentiate the fundamentally important from the dispensable erudition.

It is therefore not so strange that Einstein could be misled to give the Lorentz transformation a meaning which lacked physical reason. What is strange is that his delusion has come to represent the highest level of understanding of a modern physicist even that of Ed Witten as the smartest living physicist, by many viewed to be smarter than Einstein with an extraordinary deep understanding of mathematics...

PS The reason Einstein's unphysical events without extension in space and the associated Lorentz transformation have come to serve as a corners stone of modern physics, is that it fits with the modern physics core concept of elementary particle as an object without extension in space. But this concept is loaded with poison in the form of infinities and divergent integrals and more, and so modern physicists have been driven into a despair of string theory, in 11 space dimensions on a spatial scale 15 orders of magnitude smaller than estimated scale of a proton, all way beyond any scientific reason.

A better way out is to accept that there are no particles without extension in space, only waves with extension in 3d space, all according to Schrödinger, the inventor of quantum mechanics. Without particles the special theory of relativity has no physical meaning and scientific relevance. What has  Ed Witten to say about this revelation?

Was Einstein a Swindler?

What is the most compelling argument showing that Einstein's special theory of relativity as based on the Lorentz transformation connecting observations by different observers in different coordinate systems (inertial systems) moving with constant velocity with respect to each other, is unphysical and thus void of scientific content?

You find this argument in a previous post showing that although Maxwell's equations, as a form of wave equation, describing the propagation of electromagnetic waves including light, which is the central object of study in the special theory of relativity, takes the same mathematical form in different inertial systems, and thus appears to be invariant as requested by the special theory of relativity, initial conditions are not invariant and thus the whole point of relativity theory evaporates. We recall that an initial condition represents a configuration of an object extended in space, like a wave form, at a special instant of time.

The fact that this is not seen in presentations of relativity is a result of Einstein's restriction to consider events in space-time as isolated flashes at specific coordinates in space $x$ at specific instances of time $t$ described by space-time coordinates $(x,t)$. The unphysical aspect of such isolated flash-like events, is that they have no spatial extension and thus do not appear in the form of initial conditions for a wave equation. By restricting events to concern objects of no spatial extension, the non-invariance of initial conditions for a wave equations with a collapse of the basic idea of special relativity, can be hidden and success can be declared. This is what Einstein did, and the world was stunned!

But real objects/waves have extension in space, even flashes, and so their physics cannot be described by the special theory of relativity. The special theory of relativity is thus unphysical and as such is loaded with physical paradoxes, including the Ladder Paradox arising because a ladder has spatial extension.

Are you convinced by this argument? That the special theory is unphysical because it concerns physics without extension in space. If you are convinced, what is then your conclusion about the status of modern physics with the special theory of relativity declared as a corner stone? If the corner stone is unphysical, what about the building erected on the corner stone? So was Einstein correct when he described himself as a swindler? For more evidence see Many-Minds Relativity, in particular section 5.9 and Dr Faustus of Modern Physics. Or maybe you say that we must leave physics to physicists even if they are misled by a swindler?

PS1 The above argument shows that the idea of Lorentz invariance of Maxwell's equations is misconceived. The logical conclusion made in Many-Minds Relativity following an idea of Ebenezer Cunningham, is that formulation of Maxwell's equations requires specification of a Euclidean spatial coordinate system with the observer in normal case tied to its origin. Such a coordinate system acts like an aether for propagation of electromagnetic waves, and there are thus as many aethers as Euclidean coordinate systems. Einstein said that there is no aether, and then there can be no Maxwell equations and no electromagnetic waves and no light...

PS2 The logical conclusion from the Michelsen-Morley null result is that there are many aethers, as many as there are Euclidean coordinate systems and that physical laws in general take different forms in different coordinate systems, while expressing the same physical reality. Einstein's idea that true physical laws take the same formal mathematical form in all (inertial) coordinate systems represents a fundamental misconception of the meaning of a physical law. It is like claiming that a statement about a physical fact necessarily must have the same form in all languages, while it is clear to everyone with a rational mind that different languages express the same thing in different ways and not with the same words. Yes, Einstein was a swindler and led modern physics into a quagmire, but this is something modern physicists are unable to fathom. If you think this analysis does not capture reality ask your favourite physicist about the physics of special relativity and notice that you get no meaningful response.

$E=mc^2$: Definition or Physical Fact?

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta (photons)?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)

We continue exploring the meaning of the most famous equation of physics $E=mc^2$, which Einstein suggested in 1905 to be a consequence of his special theory of relativity and struggled through all his life to justify theoretically, however without success.

The equation $E=mc^2$ carries the same ambiguity as the basic postulate of Einstein's special theory of relativity, the constancy of the speed $c$ of light, for which it is never clear if it is only a definition true by logic, or a law of physics which may be true or false.

Is then $E=mc^2$ a definition or a physical law as a statement about a physical fact, which may be false?

We start with the following natural question: From where does the factor $c^2$ come, which attributes the energy $mc^2$ to mass of size $m$?

This question can be given an answer for a photon of frequency $\nu$, which can be observed e.g. through the photoelectric effect, to have the energy

• $E=h\nu$,      

with a properly specified Planck's constant $h$. We can now, if we want, attribute the mass $m=\frac{h\nu}{c^2}$ to a photon, to get 

• $E=h\nu =mc^2$

simply by definition.  We can do this because the physics of a photon is unclear.  We can supplement by naturally attributing the momentum $p=mc$ to a photon of mass $m$ and speed $c$ and so obtain $E=pc$ as an equivalent form of $E=mc^2$ (also discussed in the previous post).  

In short, we can argue that for the fictitious concept of a photon (compare with the Einstein quote above), energy and mass indeed can be viewed to be, in the words of Einstein,  different manifestations of the same thing (namely energy). 

By claiming that a radiating body loses the mass attributed to emitted photons (although the loss is too small to be measured), we can then give the relation $E=mc^2$ a general meaning beyond photons, still however essentially by definition with eventual physical meaning remaining to be explained.

That mass indeed can be converted to energy in nuclear fission and fusion processes, was a surprise to Einstein and cannot be seen as a consequence of his special theory of relativity, because it has no connection to nuclear physics. The  first quantum field theory Standard Model proof (with quarks and gluons) of $E=mc^2$ was presented only in 2008.

The general idea of a connection between mass and energy is as old as physics, with in particular the kinetic energy of a body of mass $m$ moving with speed $v$ being equal to $\frac{1}{2}mv^2$. Moreover, the factor $c^2$ was suggested prior to Einstein by Poincare and Hasenörhl preceded by Heaviside and Wien, among others. But it was Einstein who got the Prize.

Recall that in Maxwell's equations for electromagnetic waves in vacuum, with the electric field $\hat E$ (in Gaussian units) satisfying an equation of the form

• $\frac{1}{c^2}\frac{\partial^2\hat E}{\partial t^2}-\nabla^2\hat E=0$,

with the factor $\frac{1}{c^2}$ serving the same role as mass $m$ in a mechanical wave equation with connection to energy, thus supporting a relation of the form $m=\frac{E}{c^2}$, which was the original form suggested by Einstein, among others, as an expression for (fictitious) mass rather than (real) energy.     

Recall that with the new meter standard as a certain fraction of a light second, the speed of light is by definition equal to exactly 1 (light second per second). For perspective see Many-Minds Relativity. So today, the constancy of the speed of light is a matter of definition. To Einstein in 1905 it was both a definition and a physical fact with truth secured by pure logic as the unique nature of Einstein's physics, which so impressed the world, although there has been many critical views from start which however have been muted since they did not fit the success story of modern physics.

Is it then true that a radiating body loses mass, even if the emitted energy comes from a source of internal heat energy as a form of kinetic vibrational energy measured by temperature (and not mass) according to a new analysis of blackbody radiation? I will seek to return with an answer.

To start with let us recall that the concept of mass $m$ connects to force $f$ and motion/acceleration $\frac{dv}{dt}$ with $v$ velocity through Newton's 2nd law $\, m\frac{dv}{dt}=f$, which can be used to define mass in terms of force and motion, as well as momentum $mv$ as the integral of force, and kinetic energy $m\frac{v^2}{2}$ as the integral of $fv$ as work. Force can be measured by a spring and motion by a meter stick and time, which defines mass threefold in terms of Newton's law, momentum and kinetic energy. The basic relation is Newton's 2nd law, while the integrals of $f$ and $fv$ are computed/collected in physical form as momentum and kinetic energy. Newton's 2nd law is Galilean invariant, while momentum and kinetic energy as integrals depend on initial velocity. Momentum and kinetic energy thus carries information about mass modulo initial velocity: If you travel at the same velocity as a cannon ball, its mass is hidden and you cannot detect it by being hit.

Defining mass by Newton's 2nd law in terms of force and motion/acceleration makes mass = inertial mass, from which equality of inertial mass and gravitational mass follows by definition, since gravitation appears as force. Einstein's Equivalence Principle as the basic assumption of the general theory of relativity is thus empty of physical content,  as the general nature of Einstein's physics jumping freely between definition and physical fact, as exposed in detail  Many-Minds Relativity. Take a look and get enlightened by understanding the confusion between definition and fact, which has corrupted modern physics into a mess of subjective epistemology instead of a science of objective ontology in the spirit of Enlightenment. This was understood by Einstein but he only gave cryptic evidence to this insight like in the above quote and

• If I would be a young man again and had to decide how to make my living, I would not try to become a scientist or scholar or teacher. I would rather choose to be a plumber or a peddler...