Tuesday, September 01, 2020

Theory and Experimentation in Physics: An Analysis on Examples from the Past

 

1.          Introduction

            Every branch of Science is categorized into theoretical and experimental parts. However, in the areas of Physics and Chemistry the distinction between the two becomes prominent. In this essay, I would like to discuss these two different aspects in Physics and their significance by isolating examples from historical discoveries.

            We have no knowledge about the exact origin of Science. One can say it originated through a series of simple experiments (both practical and theoretical) conducted by people when they started observing nature; through astronomical observations made by the Babylonians and the mathematical discoveries of Euclidean Geometry; through Archimedes Principle and the Pythagorean Theorem. There were advances in experimental as well as mathematical and theoretical sides of Science. At that stage, the concepts were too tender and could not be broken down into simpler statements. Almost all of them were empirical. Why the Pythagorean Theorem holds? – Nobody knows, of course one can derive it but those derivations themselves involved some fundamental axioms[1]. But philosophers and scientists of that time used these fundamental theorems to construct models which described reality along with some predictions. These predictions in turn could be verified by experiments, which transform them into “a law”. Prior to that, it is simply regarded as a theory. No matter how beautiful, elegant or intuitive it is, there exists no obligation to accept it as a law. With simple mathematical tools, philosophers of the past determined the radius and circumference of Earth, without even traversing the entire Earth. Their predictions were later verified through experiments. However, as time went by, there were significant developments both in theory and experiments. It was realized that Physics could be split into its theoretical and experimental parts. Thus arose two branches of Physics: Theoretical Physics and Experimental Physics. In the present day, people choose to specialize in one or the other. Despite, the distinction these two branches overlap inevitably and according to my belief the experimental part shall continue to hold an upper hand. After all, experiments distinguish reality from fantasy. The act of observation is what completes Physics as well as Science. Nevertheless, one should not deny the importance and potential possessed by Theoretical Physics. In the history of Physics, there are two great examples in which a discovery was made in one of the branches and later extended into the other. These examples are the two main pillars of Modern Physics : 1.) Einstein’s Theory of Relativity and 2.) Quantum Physics.

 

2.) Special and General Theory of Relativity

            Einstein’s Theory of relativity was a special modification of Galileo’s Theory of Relativity. In the early 20th century, a series of experiments showed that electromagnetic radiations travelled through space at a constant velocity. These experiments also ruled out the concept of hypothetical luminiferous aether as a medium for the propagation of electromagnetic radiations[2]. Physicists were baffled when this constancy of velocity was not maintained in Galilean Relativity. Since, the existence of ether was disproved and repeated experiments confirmed the velocity of electromagnetic radiations to be unchanged, there was no option left but to reject or modify Galilean Relativity to accommodate the experimental observations. In the year 1905, which was also called as Annus mirabilis (miracle year) for Albert Einstein, he published four papers in the Annalen Der Physik scientific journal. The third paper titled – “On the Electrodynamics of Moving Bodies”[3] carried the idea of Special Theory of Relativity. The paper suggested brilliant modifications of the equations of Galilean Relativity so that the constancy of the velocity of electromagnetic radiations can be preserved. Even though, Albert Einstein was accredited for this genius theory. The equations involved in it are called as – “Lorentz Transformation Equations”, named after a Dutch physicist – Hendrik Lorentz, who originally derived those equations. But, Lorentz chose to adhere with the previous idea of hypothetical aether and interpreted his theory accordingly[4]. The genius of Einstein was to use these results by Lorentz to explain the constant velocity of light. This clearly points out the fact that even though Lorentz’s theory was correct, the way he interpreted it made a lot of difference about the perception of reality. The Special Theory of Relativity was for inertial frame of references (objects moving with constant velocity with respect to another object). A much more general theory was required for non-inertial (accelerating) reference frames. It took Einstein nearly ten years and a number of failed attempts to come up with a General Theory of Relativity. He borrowed the mathematics from Differential Geometry and Tensor Calculus to demonstrate how space and time is curved by mass and energy giving rise to Gravity. It is believed that when Einstein was working for a General Theory of Relativity. There was yet another German mathematician named David Hilbert who was also simultaneously working for it. He was thought to be closer to discovering it, but Einstein won the race[5]. General Relativity was later confirmed by a number of experiments and observations. In 1915, Einstein predicted the existence of Gravitational Waves using his theory – these are ripples in the fabric of spacetime. He believed that it would be impossible to detect these waves. However, nearly a century after its prediction, the LIGO (Laser Interferometer Gravitational – Wave Observatory) observed these waves and confirmed its existence. General Relativity also predicted the existence of Black Holes. In April 2017, the first image of a Black Hole was captured using the Event Horizon Telescope and Einstein’s Theory of Relativity passed another test.

            This long tale of the Theory of Relativity is a supreme example of how powerful a theory can be. If forged properly by considering all pre-existing laws, it can be a vital tool for understanding reality and even yielding testable predictions. The sheer power of mathematics and imagination allowed Physicists to predict something which had never been observed before. Yet, they were so precise that those assertions were verified in the same form as predicted, almost a century later.

 

3.) Quantum Physics

            On the contrary, there is another contender on the stage. A theory which arose from a set of observations conducted in the early and mid twentieth century – Quantum Physics. It is known for its unintuitive and chaotic character. Quantum Mechanics was discovered when Physicists started conducting experiments with small scale objects and the nature of radiations. They observed the laws of classical mechanics failed to explain the behavior of these objects and a new theory was necessary. The subject introduces an unavoidable element of uncertainty and randomness into the quantum realm. Unlike the Theory of Relativity, Quantum Physics is not theoretically rigid. It is associated with a number of different theories or “interpretations” for the same experimental observations. The most orthodox explanation is the – Statistical Interpretation[6] or the Copenhagen Interpretation because it was mostly formulated by Niels Bohr and Werner Heisenberg in Copenhagen, Denmark. Another well known interpretation was formulated by Louis De-Broglie and later used by David Bohm to present the Pilot Wave Theory or Bohmian Mechanics[7]. Of course, there are other interpretations like Hugh Everett’s Many Worlds Interpretation[8] or the Spontaneous Collapse Theories. All these different theoretical formulations of Quantum Physics debate on whether reality is deterministic or stochastic. Inspite of this, one should not forget that the core of these theories is the fundamental observations made through experiments. These interpretations are nothing but different models of the same reality and till date one has no reason to believe in one and disregard the other.

 

4.) Conclusions

            Why are there different theories associated with Quantum Physics but not with Relativity? I believe it boils down to the sequential manner of theory and experiment. Special and General Relativity was first predicted theoretically through a series of “thought experiments”. Hence, when actual experiments were conducted later, there was no ambiguity in the conclusions because they were conducted with the purpose of testifying Relativity. On the other hand, Quantum Physics was first hinted from experiments conducted with small scale objects. Owing to this, physicists had the experimental results in hand but the task of formulating a theoretical model for them got tedious. Each model had the potential to describe these results in their own manner whilst having their own imperfections. Had relativity not been discovered by Albert Einstein, then we would have certainly obtained hints of it. Perhaps from the errors in Global Positioning System satellites; and from the precession of perihelion of planet Mercury; and from the Gravitational Lensing observed near a galaxy or a black hole. However, the chances of formulating the Theory of Relativity in its exact form as we have today from these observations would have been less. The Theory of Relativity would then have been one amongst many other seemingly possible interpretations of those observations. This might demonstrate how sometimes psychological aspects decide how we view reality. To conclude, both theory and experiments are paramount in Physics. Although, practical experiments should be viewed as keys to unlocking the secrets of Universe, for they are depict reality. Our theories are merely viewpoints on this Universe and are doomed to change with time. With each experiment conducted with increasing precision, these theories would be discarded or refined to fit into reality. The inverse of this cannot be true.


5.) References

 

[1] C.G. Hempel, “Geometry and Empirical Science”, The American Mathematical Monthly, 2018, 52:7-17

 

[2] R.S. Shankland, “Michelson-Morley Experiment”, American Journal of Physics, 1964,32:16

 

[3] A. Einstein, “On the Electrodynamics of Moving Bodies”, Annalen Der Physik, 1905

 

[4] H.A. Lorentz, “Simplified Theory of Electrical and Optical Phenomena in Moving Systems”, Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings, 1:427-442

 

[5]  Einstein and Hilbert's Race to Generalize Relativity

 

[6] M. Born, “Statistical Interpretation of Quantum Mechanics”, Science, 122:675-679

 

[7] D. Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables.I”, Physical Review,85:166

 

[8] H. Everett, “Relative State Formulation of Quantum Mechanics”, Reviews of Modern Physics, 29:454