Quantitative expression of Mach’s principle The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, 2016 Tuomo Suntola An Evening with Ernst Mach Dr. Hayo Siemsen, Ernst Mach’s contribution to natural science Coffee break Dr. Tuomo Suntola: Quantitative expression of Mach’s principle

Mach’s principle The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, In his lectures in the early 1940s, Philipp Frank attributed to Mach himself the following expression of "Mach's principle": "When the subway jerks, it's the fixed stars that throw you down." Main messages of the statement are that -the action of distant masses on the subway-rider's mass is direct and instantaneous -inertia is not affected by the mass of the earth around the subway tunnel -Mach’s principle, when stated in this way, does not fit with Einstein's conception of the retardation of all distant action.

Basic concepts The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, Inertial force – the force resisting a change of the state of motion of a mass object. In contemporary physics, inertia is one of the manifestations of mass (a local property). According to our present picture and understanding, space comprises three spatial dimensions linked to time as the fourth dimension – the spatial extension of space started at point zero in time and has now continued for about 14 billion years. Properties of space-time have been derived from the general theory of relativity (GR) which relies on the equivalence principle equalizing the concepts of inertial mass and gravitational mass. GR explains gravitational interaction as a property of local space-time geometry. According to general relativity, changes in space-time geometry are conveyed at the speed of light – which eliminates the possibility of instant interactions between local and the rest of space. In order to reveal the linkage of local to the rest of space, we need a holistic approach – starting from space as whole.

Towards a holistic approach The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, We may follow Copernicus’s approach to start by outlining the structure of space … The first Chapter of Copernicus’s De Revolutionibus is titled “The Universe is Spherical” : “First of all, we must note that the universe is spherical. The reason is either that, of all forms, the sphere is the most perfect, needing no joint and being a complete whole, which can be neither increased nor diminished; or that it is the most capacious of figures, best suited to enclose and retain all things; … Hence no one will question the attribution of this form to the divine bodies”. Copernicus’s holistic approach to the planetary system made it possible to base the study of celestial interactions on the laws of physics, such as the laws of motion and the conservation of energy.

Gravitational energy Energy of motion time contraction expansion Space as spherically closed energy system Space as the 3-surface of a 4-sphere may only exist as a dynamic system For closing the 3-dimensional space, we need the fourth dimension of metric nature The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, Re Im 0 Re Im 0 Re Im 0

Im v mcmc From time-like to metric fourth dimension The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, time Re Im 0 momentum mcmc Re Im v velocity v t0t0 DU: metric 4th dimension m”c DU: metric 4th dimension SR, GR: time-like 4th dimension mcmc 4D energy4D momentum mvmv momentum in space The frequency of atomic clocks is proportional to the rest energy of the oscillating electrons. tvtv t0t0 Inertial work is the imaginary component of the kinetic energy. It is the work done against gravitational energy arising from all the rest of mass in space. = Mach’s principle

The effect of local gravitation and motion on the rest energy The effect of motion and gravitation on the rest energy The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, Dilated time in GR based Schwarzschild space The effect of motion and gravitation on atomic clocks

The system of nested energy frames hypothetical homogeneous space M1M1 M2M2 M3M3 The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, Hypothetical homogeneous space

Cosmological consequences Gravitationally bound systems in space expand in direct proportion to the expansion of the 4-sphere time The angular sizes of galaxies are observed in Euclidean appearance Gravitational waves – or mass waves – are due to the rotation of the 4D angular momentum of elliptic binary star orbits (due to periastron advance). The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, Supernova observations are explained accurately without dark energy Celestial mechanics shows stable circular orbits down to the critical radius

Gravitational waves The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, General relativity: -Gravitational waves are emitted by rotating gravitational quadrupoles, typically binary star systems -The energy emitted as radiation results in shortening of the orbital period of the binary system. Dynamic Universe: -Gravitational waves (or mass/momentum waves) are emitted by the rotation of the orbital plane of a binary star system due to periastron advance -The energy needed in turning the 4D angular momentum of the orbit results in shortening of the orbital period.

Gravitational waves: The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, GR: Shortening of the period is due to the energy loss resulted by the emission of gravitational waves due to the rotating quadrupole moment of the mass system: GR DU (Taylor ) DU: Shortening of the period is due to the energy rotating the 4D angular momentum of the orbit. The energy of rotation of the 4D orbital angular momentum is not cumulated in the angular momentum but radiated to the surrounding space. binary pulsar B z 0d (Im 0d ) x0dx0d r (2)0d r (1)0d  L orbit dL orbit 

Gravitational waves The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, General relativity: Gravitational waves are emitted by binary mass systems with circular orbits Dynamic Universe: Gravitational waves (or mass/momentum waves) are not emitted by binary mass systems with circular orbits

Mach’s principle The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, A quantitative expression of Mach’s principle requires linkage between local and the whole. Such a linkage is obtained in space spherically closed through the fourth dimension of metric nature. -Spherically closed space allows “gestalting” of the structure and dynamics of space; -it shows relativistic effects (like clock frequencies) as direct consequences of the zero- energy balance in space, and -the inertial work as the work against the global gravitation arisen from all the mass in space. Any motion in space is linked to the motion of space in the fourth dimension – and any local gravitational interaction is linked to the gravitational interaction with the rest of space. Gravitational interaction is immediate – a mass object senses the local gravitational potential as gravitational energy, and the gradient of the local gravitational potential as gravitational force. Gravitational potential, the scalar field arising from any mass in space follow the motions of its source immediately.

Gravitational potential and gravitational waves The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, GR: Rotating double stars emit gravitational radiation DU: Instant gravitational potential follows the motion of its source (no radiation) DU: Rotating orbit plane emits radiation (related to the rotating orbital 4D angular momentum) This is the way gravitational interaction is calculated in celestial mechanics

Thank you for your attention The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9,