Galilean-Newtonian Relativity

A common view today is that Newtonian Mechanics requires the notion of absolute space, which however cannot be identified, and so is used to motivate a departure into relativistic mechanics in the form of Einstein's Special Theory of Relativity SR without gravitation and General Theory of Relativity GR with gravitation.

But Newtonian Mechanics is already relativistic in the sense that it takes the same form in all Euclidean coordinate systems moving with constant velocity with respect to each other (so called inertial systems) and so it is impossible by experiment to identify a special system to act as absolute space. This is because both Newton's 2nd Law N2 and Newton's Law of Gravitation NG take the same form in all inertial systems. This was well understood already by Galileo. 

We have seen in posts on New View on Gravitation that NG can according to Laplace be formulated as the local assignment

• $\rho (x)=\Delta\phi (x)$ for all $x$       (NG)  

where $\rho (x)$ is mass density and $\phi (x)$ gravitational potential depending on a Euclidean space variable $x$ and $\Delta$ is the Laplacian differential operator. Viewing (NG) as assignment means that somehow matter is endowed with mass through that action of the Laplacian on the gravitational potential.

Since the Laplacian is invariant under both translation and rotation, it follows that so is NG and thus the generation of mass from gravitational potential does not depend on choice of coordinate system, which is a natural requirement. 

On the other hand, N2 is not invariant under rotation since centripetal forces from acceleration arise. It is thus possible to detect rotation by experiment such as Newton's Bucket. 

Conclusion: Newtonian Mechanics is relativistic in the Galilean sense of taking the same form in all inertial systems, and so does not require the notion of absolute space. Thus there does not seem to be any compelling reason to replace Newtonian Mechanics by SR/GR mechanics. Adding propagation of light to the mechanics picture motivates a modification on celestial scales as shown in Many-Minds Relativity. 

Remark:In Newton's Bucket experiment it can be decided that it is the bucket which rotates vs the fixed stars (and not the other way around) by considering the evolution in time from an initial state with the bucket at rest with respect to the fixed stars. With this point of view a Euclidean coordinate system determined by the fixed stars, may serve as an absolute space, but it is also possible to connect coordinate system to the Sun, Earth, or your living room. 

Travel Faster than Light!

Recent posts show that with the 2019 SI Standard, Einstein's Special Theory of Relativity SR no longer is a theory about physics, since the main postulate of SR stating that the speed of light is the same for all observers as a physical fact, which may be true or false, is turned into simply an agreement, which has no truth value. 

This means that SR has no real physical content and so can be dismissed without losing any real physics. In particular the main result of SR that nothing can travel faster light, no longer is supported by theory (nor by observation see PS1).

We are thus back to the end of the 19th century facing the null result of the Michelson-Morley experiment signifying that there is no unique aether for the propagation of electromagnetic waves. Instead of following Einstein claiming that the MM experiment shows that (i) there is no aether at all then leading to SR, we follow the other possibility that (ii) there are many different aethers leading to Many-Minds Relativity MMR.

Let us now see what Newtonian Mechanics NM and MMR have to say about travel faster than light. Let us then consider an $x$-axis with distances marked according to the 2019 SI Standard thus distance in terms of travel time of light with an agreed speed of light equal to 1. Consider a rocket of unit mass traveling through vacuum starting from rest at $x=0$ at time $t=0$ propelled by a rocket engine delivering a thrust $F=1$. 

Newton would say that the rocket velocity $v(t)$ at time $t>0$ is given by $v=t$, thus faster than light for $t>1$.

MMR is different from NM by measuring velocity in terms of Doppler shift, which gives the different rocket velocity $v(t)=\exp(t)-1$, even faster than light for $t>1$.

We conclude that a rocket moving through vacuum subject to a thrust $F=1$ will eventually reach a velocity which is larger than the speed of light. This gives new perspective on the feasibility of human space travel. Maybe it is possible to reach the star closest to Earth (Proxima Centauri) in much less than 4.3 years...if only thrust can be maintained...  

PS1 Recall that there are observations of distant galaxies appearing (from red shift) to recede with a speed more than 10 times the speed of light, in direct contradiction to SR.

PS2 To a mathematician the distinction between definition and theorem is clear. A theorem can (be proven to) be true or false, while trying to prove or disprove a definition would be viewed to be silly. It is also possible to view a theorem as a statement which can be proved to be true, and use the term conjecture as a statement which may be proved to be true or false. But to a physicist educated by Einstein the distinction between theorem/conjecture and definition is muddeled. That the speed of light is the same to all observers, is by Einstein's followers viewed to be both a statement about a physical fact (theorem/conjecture), which can be true or false, and an agreement (definition), which has no value as true or false. By shifting between physical fact/theorem and agreement/definition,  Einstein has confused generations of physicists. It is time to return to use basic principles of mathematical reasoning and make a clear distinction between fact and agreement. Then there is no place for SR after 2019.   

A Contrafactual History of Modern Physics

An early Rangefinder from 1900.

This connects to the recent posts on the 2019 SI unit standard of second and meter.

Suppose the 2019 SI standard had been implemented already say in 1900. This means that from 1900 on length was measured in terms of travel time of light assuming a speed of light of exactly 299792458 meter per second. 

This is how a rangefinder of today works: Send a signal towards an object and measure the time for the reflected signal to come back, assuming a certain speed of light. This would have been possible in 1900. 

Using the SI standard a null result from the Michelson-Morley experiment is to be expected. Each observer "drags along an aether" linked to the observer and defines length from travel time of light under the assumption that light propagates with exactly 299792458 meter per second. 

With an expected MM null result using the SI standard, there would be no reason to invent the new physics of Einstein's Special Relativity SR, because it was motivated by the MM null result seeming to be  inexplicable using the meter sticks/measuring rods envisioned by Einstein. More precisely, what motivated Lorentz to introduce the Lorentz transformation in 1904 (first formulated by Voigt in 1887), was to explain the MM null result as an effect of space contraction in the direction of motion. Einstein picked up the Lorentz transformation in 1905, without reference to Lorentz or Voigt. 

Modern physics as a physics under a SI standard adopted in 1900, would thus be free of SR. Modern physics would thus consist of quantum mechanics added to Newton's mechanics and Maxwell's electromagnetics as a fully compatible combination. This would be a modern physics without the incompatibility of relativity theory and quantum mechanics, as a main trouble behind the present crisis of modern physics.