, ladies and gentlemen, was tough. My essay on this subject is due in at 9 am today, or in about 2.5 hours time. I've just spent all night typing it up because instead of doing it over the weekend like I should've I've been doing a series of nodes on the subject. You bastards.
, 18 September 2000
I've got the essay back now, an A- was my grade, and I've included all the marker's comments in italics in the body of my essay below.
Observer Independence of General Relativity
By Leith McLean - italicised text transcribed
from marker comments by Philip Catton, University of Canterbury New Zealand
Though Einstein contributed to both quantum physics and relativity, this essay will not concern itself with the seminal work he did relating the wave-like and particle-like aspects of light. Although this wave/particle duality was to become a cornerstone of quantum physics, which, under the Copenhagen interpretation (which Einstein famously disagreed with) places central import on the observer as the act of observation itself collapses the wave function of a particle, to use Einstein’s contribution to quantum theory in claiming that he himself brought the observer into the laws of physics would be no more accurate than to say that Euclid stated the principle of universal gravitation. Rather, it is his theories of relativity, special and general, that are the most Important reflections of his thinking and that represent a body of work that many people consider to have placed the observer squarely at the centre of the laws of physics and it is with this theory that I am here concerned. Whether Einstein indeed brought the observer into the laws of physics depends in part on what is meant by this ‘bringing in’ and exactly what it is brought into. It is to this that I now turn my attention.
Science is concerned with accurately and systematically describing the reality in which we find ourselves. By unbiased experiment and colligation of data, scientists hope to uncover the principles that govern it. Now the ‘laws’ of physics may be taken to be either the actual principles that govern the interaction of matter, or the scientists’ formulation of them. If we take the prior case, there is precious little Einstein can do to bring the observer into them, unless our theories of the universe actually affect its functioning (and if this were the case it is unclear how he could bring the observer any further into the laws of physics. To ‘bring’ the observer ‘into’ the laws of physics, then, is to formulate our theory of reality in such a way as it (in the weak sense) accounts for the observer and their actions, or (in the strong sense) to make the theoretical conception of reality dependent on the observer in some way. I shall examine the question in light of this.
I like your thoughtful discussion here, but I suppose I should mention that the distinction about laws - between those "out there" and those "in our theories or heads" would seem naive to some philosophers.
Einstein’s ideas on relativity were hardly a static entity. In 1905 he published his theory of special relativity (so-called because it deals only with a special case of the possible relations of two frames of reference – that in which they are in inertial motion relative to one another), which was a systematisation of certain phenomena, but following Minkowski’s geometrical treatment of this theory he was able to produce general relativity (so-called because it was applicable to the general case of relations of motion between two frames of reference – both inertial and non-inertial). I will argue that in the theory of special relativity Einstein brought the observer into the laws of physics in the strong sense, but as his ideas developed he was able to remove the emphasis on the observer and in general relativity he brought the observer into the laws only in the weak sense, by allowing them to be used to represent things from many different frames of reference.
In the creation of special relativity, Einstein was guided by the desire to create a theory that could apply to observers in all states of inertial motion, and also explain the recent null-results of experimenters trying to detect the motion of Earth through the luminiferous ether.
Einstein was not motivated by the null results, but did find a way to exploit them for the purpose of pointing to a better theory.
Einstein was seeking to overcome a "deep-going opposition" in physics betweeb (in effect) particle and field. The work he did towards SR was directed towards achieving a more unified physics. The relativity principle was a deep-lying feature of the general description of particles. Einstein was seeking some way to reconcile it with (or within) the general description of fields. The null results you mention were grist to his mill but were not any part of the inspiration for his work.
With the theory of special relativity, Einstein systematised the phenomena of time dilation etc and gave a mathematical apparatus for predicting them, and as he did so in absence of an explanation for the phenomena (i.e. in an operational way) he introduced the observer as the centre of his theoretical model. The equations he generated for length contraction, time dilation, and mass increase all featured the variable sqrt(1 - v2/c2) and were expressed in terms of rest time/length/mass (or the value in the observer’s frame of reference) and apparent length/time/mass (or the value observed in a ‘moving’ frame). v is also a quantity, which is relative to the observer, and so it can be seen that in this formulation the observer is indeed vital to the theoretical representation of reality. By simply creating operational definitions of the concepts involved, the observer is placed at the centre of the laws right from the beginning. Special relativity, however, did not explain why the phenomena were as they were. It merely provided certain predictive formulae that fitted how they were.
By no means was special relativity the end of the story. Following Minkowski’s geometrical formulation of the theory, Einstein was able to come back and use it to revolutionise the way space and time, mass and energy are thought of, as well as providing an explanation of the phenomena systematised under special relativity in such a way as to remove the emphasis on the observer.
Minkowskian geometry allowed this by providing a co-ordinate systemfor Einstein to place his many frames of reference in.
Rather, the intrinsic geometry of Minkowski space-time leads us to appreciate why various coordinate systems - each adapted to its own reference frame - relate to one another as Einstein's theory of SR says they do.
Under special relativity all that could be described was how frames of reference appeared to each other, but under general relativity the frames were related to each other in a geometrical way within a co-ordinate system that was independent of either of them.
This seems to imply that Minkowski's geometrical formulation gives us general relativity theory. On the contrary, the Minkowski geometry is a way to formulate special relativity. The geometry of general relativistic spacetime differs from Minkowski Geometry by being inhomogeneous and not even semi-Euclidean.
With a co-ordinate system that allowed this, it was possible for Einstein to explain how an independent reality can exist and yet appear to change so radically through simple relative motion. The co-ordinate system used is spatio-temporal, that is, featuring both space and time in equivalent units (essential for a co-ordinate system) and so suggests a reality that is 4-dimensional – 3 spatial plus one temporal – in which space and time are actually just perceived aspects of space-time and what we observe as space-like and time-like changes depending on our movement relative to the observed. While special relativity, giving no explanation of the phenomena it deals with but merely giving an operational apparatus to quantify them, hinted at an important role for the observer in determining the nature of reality, general relativity revealed the independent reality underlying the perceived changes and showed that the role of the observer had no more effect on the nature of reality than in 3 dimensions when observing objects from different angles.
In conclusion, then, the answer to the question “Did Einstein bring the observer into the very laws of physics?” can be seen to be, trivially, “Yes”, but with the important qualification that this was simply a step on the way to developing a theory which was independent of the observer. After all, if special relativity had never been formulated Minkowski could never have generated his space-time geometry and Einstein could not have created general relativity. It remains to be said that general relativity is the cosmology of Einstein, and as such should be taken as superseding the operationalism of special relativity as it explains the framework underlying the phenomena of special relativity. Perhaps the most succinct way of answering the question would be “Yes, but then he took it back out again”.
Mighty fuck that night pains me like wolverines chewing my nipples. I'm gonna go drink Tang 'til i forget it all. Oh, this isn't my essay any more, btw.