Immanuel Kant’s Use of Newtonian Mechanics

by Max Andrews

Newtonian physics treated space and time as absolute inertial reference frames. Space and time was independent of all that it embraced and in that sense, absolute.  Space and time was isomorphic, and together with the particle theory of nature formed a mechanistic universe and static concepts that go along with it. Kant used Newtonian physics of space and time as intuitions.  The sensorium (reference frame) was transferred from space and time itself (or even God) to the mind of the subject.  Thus, the intellect imposes its laws upon nature and not nature upon the intellect.  Kant believed our thought imposes Newtonian concepts on our experiences.  Independent of experience our minds are organized to think about the world in the Newtonian framework.  Scientific knowledge was considered a priori knowledge of synthetic truths.[1]

This is what accounted for deductive methodology—using fixed premises and drawing one’s conclusions from these premises.  Kant believed that one could not know the Ding an Sich by pure reason.  The subject is limited to the fixed categories of the mind and one shapes the apprehensions through these categories.  Kant used these space and time intuitions as necessary. It proved inept for scientists to follow Kant’s use of Newton’s ideas as permanent features of the intellectual landscape having based their philosophy on his model of the universe.[2]

In 1865 James Clerk Maxwell had unified electricity and magnetism by developing his equations of electromagnetism.[3]  It was soon realized that these equations supported wave-like solutions in a region free of electrical charges or currents, otherwise known as vacuums.[4]  Later experiments identified light as having electromagnetic properties and Maxwell’s equations predicted that light waves should propagate at a finite speed c (about 300,000 km/s).  With his Newtonian ideas of absolute space and time firmly entrenched, most physicists thought that this speed was correct only in one special frame, absolute rest, and it was thought that electromagnetic waves were supported by an unseen medium called the ether, which is at rest in this frame.[5] Einstein noticed how the Doppler effect could be applied to electromagnetism.[6]  His rather brief paper on the relation between the energy and the mass of an object gave rise to his famous equation E=mc2.[7]  This meant that mass energy is proportional to mass.  Twice as much mass means twice as much mass energy, and no mass means zero mass energy. The square of the speed of light is called the constant of proportionality.  It does the job of converting from the unit in which mass is expressed to the unit in which energy is expressed.[8]  With this, Einstein’s Special Theory of Relativity was born.

Throughout Einstein’s work, the mechanistic universe proved unsatisfactory.  This was made evident after the discovery of the electromagnetic field and the failure of Newtonian physics to account for it in mechanistic concepts.  Then came the discovery of four-dimensional geometry and with it the realization that the geometrical structures of Newtonian physics could not be detached from changes in space and time with which field theory operated.  Upon the development of relativity theory by Einstein the fixed a priori categories and the intuitions of space and time of the mind were removed from being necessary.

After the First World War, Einstein made contributions to the development of quantum theory, including Bose-Einstein statistics and the basics of stimulated emission of radiation from atoms (which was later used to develop lasers).  He gave the nod of approval that led to the rapid acceptance of Louis de Broglie’s ideas about matter waves but he never came to terms with the Copenhagen interpretation of quantum mechanics.[9] The Copenhagen has become the more popular and standard interpretation, which allowed for and required the indeterminism that led to the inevitable rejection of the mechanistic and deterministic Newtonian system.[10]

According to the Heisenberg Principle, the moment at which a measurement takes place is the moment at which the randomness lying at the heart of quantum reality expresses itself.[11]  Up to that point, everything is fine.  Amplitudes change in a completely predictable, and more importantly, calculable way.  The observer changes the state of what is being observed.  Outcomes can be predicted according to governing probabilities, but the actual outcome cannot be known in advance.[12]

This was something Einstein could not live with.  Einstein, as a determinist, felt that the world is a structured and rigid web where effects follows cause and all things should be predictable, given the right information.  Einstein acknowledged that quantum theory works but he did not like the philosophy behind it.  If whether or not, for example, Niels Bohr, Einstein’s quantum physics counterpart, were to throw a book across the room Einstein would be able to predict the outcome of Bohr’s “choice.” Einstein would of course say that choice is the wrong word to use; rather, the brain is a complex machine with cogs whirring round to produce a predictable action.  The basis of Einstein’s view was a philosophical conviction that the world did not include random events:  an objection summed up in Einstein’s widely quoted saying, “God does not play dice.”[13]  Bohr is reported to have responded to Einstein with the witty reply, “Don’t tell God what to do.”

With this, as previous mentioned, it would be incorrect to suppose Kant was right in treating these intuitions and categories as fixed.  The Kantian intuitions of Newtonian theory and the mechanistic universe proved unsatisfactory.  Rosenberg’s position that science can do better is correct because science has done better.  It’s not wholly inappropriate to extract philosophical truths or axioms from science but it must be done so tentatively and congruently.  Purely philosophical axioms must be in harmony yet independent from scientific discovery.  Following Kant and Hume to Hegel, Gödel, and the logical positivists the idea of reality, describing reality philosophically and mathematically, radically changed. This invigorated the rationalist-empiricist debate, which because of the overthrow of Newtonian theory the philosophy and science continued to change as a result of problems they faced.

[1] Alex Rosenberg, Philosophy of Science (New York: Routeledge, 2012), 12.

[2] This was also challenged by John Locke.  Kant was challenged by the Empiricists.  Why are such ideas necessary? Why these entailments?  For Kantian rationalism it was not so much innate ideas but an innate structure of the mind.

[3] At this time in 1905 Einstein published a series of articles.  These articles included a parallel of Max Planck’s work on black body radiation, his PhD thesis which showed how to calculate the size of molecules and work out the number of molecules in a given mass of material based on their motion, an article on Robert Brown’s motion (1827), his article on relativity replacing Newton’s laws, and his article on the equivalence of mass and energy.  These five works are referred to as Einstein’s annus mirabilis. Jonathan Allday, Quantum Reality: Theory and Philosophy (Boca Raton, FL: CRC Press, 2009), 273.

[4] Vasant Natarajan and Dipitman Sen, “The Special Theory of Relativity,” Resonance (April 2005): 32.

[5] Ibid., 32 -33.

[6]  Depending on the relative direction of the light waves and the frame of the observer (v signifies measured velocity).

 [7] It will be interesting to see how Einstein applies his invariance in his work (which will be discussed in the next section).  His argument developed as follows.  Let an object in a rest frame simultaneously emit two light waves with the same energy E/2 in opposite directions (now having equal but opposite momenta), the object remains at rest, but its energy decreases by E.  By the Doppler effect, in another frame, which is moving at the velocity v in one of those directions, the object will appear to lose energy.  The difference in energy loss as viewed from the two frames must therefore appear as a difference in kinetic energy seen by the second observing frame.  Hence, if v/c is very small, in the second frame (the one in motion) the object loses an amount of kinetic energy.  Since the kinetic energy of an object with mass M moving with speed v is given by (1/2)Mv2 (for v/c≪1), this means that the object has lost an amount of mass given by E/c2.  In other words, a loss of energy of E is equivalent to the loss in mass of E/c2.  This implies equivalence between the mass and energy content of any object.  It turns out that for a particle of mass M, this quantity is equal to M2c2.  After implementing the Lorentz invariant (and if the frame in which the particle has zero momentum), then the equation E=mc2 is recovered.  Ibid., 41-42.

[8] Kenneth William Ford, The Quantum World (Cambridge, MA: Harvard University Press, 2004), 20.

[9] Ford, The Quantum World, 117.

[10] At this time there are at least ten regularly cited interpretations of quantum physics varying in interpretation of wave collapse, determinacy/indeterminacy, superpositions, and Schrödinger’s equations.

[11]  For a given state, the smaller the range of probable x values involved in a position expansion, the larger the range of probable px values involved in a momentum expansion, and vice versa.  The key to the expression is  because it places a limit on how precise the two measurements can be.  The principle is relating and for the same state (signifies change, h-bar, is the Planck constant).  Heisenberg’s target was causality. The Copenhagen interpretation adopted this principle. Jonathan Allday, Quantum Reality: Theory and Philosophy (Boca Raton, FL: CRC Press, 2009), 247-248.

[12] Jonathan Allday, Quantum Reality: Theory and Philosophy (Boca Raton, FL: CRC Press, 2009), 100-101.

[13] Allday, 101.

One Comment to “Immanuel Kant’s Use of Newtonian Mechanics”

  1. Hello, thank you for the post.

    I’m curious why you say that Kant employed a Newtonian conception of space/time as pure forms of intuition? Rather it seems that Kant would say that the pure forms of intuition make a conception like Newton’s or Einstein’s possible. I say this because pure intuition is that through which we can construct concepts a priori, and it is only due to this capacity that the objects of mathematical physics are taken to have an a priori foundation (see Preface of Metaphysical Foundations of Natural Science).

    I have never been satisfied by readings of Kant, such as Russell’s, that seem to overlook the fact that the pure forms of intuition are not grounded in work carried out by any particular mathematical discipline. Russell believed that space in Kant was essentially Euclidean, where Kant would say rather that Euclid’s Geometry has a foundation in our capacity to generate concepts a priori using pure intuition. Claiming that the pure forms of intuition are Newtonian is making a similar error in understanding the priority of pure intuition as Russell made.

    I agree that mathematical thinking has advanced, and has been able to place physics on new foundations. However, the manner in which this has been carried out is entirely in agreement with Kant’s understanding of natural science that we find in the Metaphysical Foundations of Natural Science. Even though Kant’s own grounding of the concept of ‘matter’ in that book was restricted to the mathematics which Kant employed, the heart of this isn’t the particular working out at any time of the basic concepts of a science, but 1) the requirement of mathematics for founding natural science on an a priori basis, and 2) the a priori status of mathematics depending on our capacity to generate concepts of a spacial/temporal nature without first finding them in objects of experience (that is, pure intuition).

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