# What is Newtonian time

LECTURE: Time - From primeval times to computer time
Author: Klaus Mainzer

Glanznig Michael 7.C 2000/2001

II. Time in the world view of classical physics

In classical physics, time becomes a measurable and calculable quantity. There is the possibility of building more accurate chronometers. Mathematics allows the determination of arbitrarily precise points in time using real numbers.

In the formalism, time is a real coordinate in equations of motion. This also applies to transformations in the reverse time direction. Time invariance is the basic requirement for the physical conception of time (e.g .: relativity and quantum theory)

Furthermore, time becomes a consciousness reform examined.

1. Newton's absolute time:

The Departure to the modern worldview is called Copernican turn designated (geocentric worldview -> heliocentric worldview).

Nicolaus Copernicus (1473 - 1543) was convinced of a planetary motion ("They move uniformly out of spheres")

Johannes Kepler (1571 - 1630) had better observation possibilities and found that planets move on ellipses. He established three laws (e.g .: the radius of the sun - planet sweeps over the same areas at the same time).

Kepler also introduced time as the measure of movement. Time and movement are basic concepts for the first definition of Galileo Galilei (1564 - 1642): Speed ​​is a quantity with which changes in the location of a body over time are determined. This is the first time there is talk of a uniform acceleration (free fall), which is proven on the inclined plane. Acceleration is defined as the change in speed over a period of time. Gravity is therefore the change in speed over time due to forces. Because the time intervals are getting shorter and shorter, there is a better approximation of the current speed.

In differential calculus, the instantaneous speed is the limit value of a sequence of average speed. This means: the duration is approaching zero. The instantaneous speed is the first derivative of the spatial coordinate x (t) with respect to the time t and shifts the differential quotient dx / dt in Newton's notation x and Leibniz's notation. Acceleration and speed changes are the same as the temporal change of the place: This is also the second derivative. A new method of timekeeping is emerging. Galileo suggested counting the oscillations of a pendulum clock.

Implementer of this idea was Christian Huygens (1629 - 1695). Nicolo Oresme then introduces a time coordinate.

Isaac Barrow, Newton's teacher, said: "Time is the universal, absolute basic quantity of nature, independent of observation and measurement methods." He also differentiates between absolute time and relative time.
Isaac Newton
claims that there is no such thing as uniform motion. According to him, all movements must be accelerated or decelerated as there is no accurate time measurement. He introduces absolute time as a theoretical quantity, although he had no direct experience. He also claims that nature is universal time. The topological structure (= chronological order of events) and the metric structure (= the measure of time) are fixed.

The time measurement procedure is continuously being improved. The concepts of absolute time are independent and have fundamental physical consequences. This can be seen in mathematical precision. For two events it is of the utmost importance whether they take place at the same time and in the same place.

Causal structure or the interdependence of the Newtonian world, for which applies: If you shoot balls with different speeds from world point 0 in all directions, only world points that are later than 0 will reach world points. Events that take place in 0 only affect the future, not the past. Accordingly, there is an arbitrarily fast time transfer through the common point 0, which is located in the present, which takes place between the past and the future.

Example:

Think of a pole as a connection between two points, A and B. If you give point A a jolt, this is transferred directly to point B. There is a psychological reason to believe in such phenomena: In the everyday world, perceptions are the focus. An important assumption is the "belief in the absolute resting point"!

2. Leibniz relational time:

G. Leibniz (1646 - 1716) accepted the causal structure of Newtonian space-time, but questioned absolute rest and movement. Speculations in his empirical science program ("Hypotheses non figo") were imputed to him. Leibniz maintained that space is a system of relations between bodies that has no metaphysical or ontological existence. According to Leibniz, the positional relationship of two points is sufficient to define space. Leibniz only considers relative spaces or reference systems.

He justified the relativity of all space and time by the principle of sufficient reason.

Quote: "Nothing in the world happens without a good reason."

From this point on there is a new space-time symmetry. The concept of absolute rest and movement (rotation) must be dropped. The concept of simultaneity remains unchanged, however, since Leibniz's space-time has the same causal structure as Newton's. The kinematic (= moving) question, however, was that Leibniz's time exactly described the space-time of classical physics. Leibniz specifies the kinematic principle of relativity. He could not explain dynamic effects such as the occurrence of centrifugal forces in a circular motion. Huygens, Leibniz's physics teacher, was able to explain the centrifugal forces on the basis of a rotating disk through the relative movement of various particles that were on the disk.

The movement of this could, however, be transformed away if the system selected as the reference system has the same origin and the same angular velocity as the rotating disk. The result: the particles in the disk would be "at rest" because the pressure exerted by the centrifugal forces is not removed!

3. Time in classical mechanics:

Newton and Leibniz were both right.

Newton's fiction of an absolute calm pole in the universe cannot be proven by any observation or experiment. So its space-time has too much structure. Leibniz 'space-time has too little structure, since Newton's excellent absolute rotational movement needs a dynamic explanation.

Now the question arises whether the assumption of absolute space is necessary at all? Leonardo Euler said that it would be impossible to formulate a law of inertia without Newton's absolute space. A body moves after it, as long as no external force acts on it, with uniform speed and in a straight line. Absolute space turns out to be superfluous after Ludwig Lang introduced the inertial and inertial systems in 1885. In his opinion, his law of inertia retains its physical meaning even without the assumption of an absolute space.

The inertial system is a coordinate system in which Newton's law of inertia is valid. In contrast to absolute space, however, in classical mechanics there is a uniform and therefore absolute time for all inertial systems. This assumption makes it possible in classical physics to speak of a universal simultaneity that is independent of the respective inertial system. A certain point in time t = t (0) separates past and future in a way that is uniform for all observers. In mathematics, the assumption of absolute time is expressed in the Galileo transformation. It is stated that the Galileo invariance is evidently more special than Leibniz's space-time, but Leibniz does not need absolute rest for his theory.

The time symmetry of classical mechanics is central. Newton's axiom for mechanical laws of motion determines acceleration as the 2nd derivative of the position of a body with respect to time. His law remains unchanged if one replaces the positive time with a negative one. Therefore, in classical mechanics, it is not possible to differentiate between the two time directions. Mechanics laws are reversible. According to the laws of the planets, they could move around the sun in a different direction. In fact, however, they run in one direction. The reversal of many processes has never been observed (e.g. breaking glass, humans are born and die, trees grow). Mechanics cannot explain irreversible processes. That a broken glass will reassemble is quite unlikely, but in principle possible.

4. Time in epistemology according to Kant:

The philosopher Kant does not see time as an empirical reality, but as a form of our consciousness before every experience (a priori). Human knowledge arises through cooperation between sensuality and intellect.

Our sensory organs only supply the material of stimulus and sensation signals (light, color, tones, pressure), which are ordered as spatial juxtaposition and temporal succession in the perception. According to Kant, concrete empirical clocks presuppose time as a priori form of perception. For Kant, time is an objective (transcendental) form of perception, which makes the material sense of time possible in the first place. Conceptual and judgment forms of the mind must be distinguished. We take beliefs and then judge them.

Our perceptions are based on time as a continuum, which can become stronger and weaker over time. It is the task of each individual to determine his laws of experience.

This is how physics determines its experiments and measurement methods. According to Kant, time is a categorical framework, which must be assumed for all observations, measurements and the formation of physical laws and theories. The definition of empirical time units such as year, day, hour, ... is chosen arbitrarily.

Regardless of which units it is, which assignment definition it is, it is a question of expediency and not true knowledge.

Created by Glanznig Michael 7.C-2000/2001