Some stuff Einstein actually said

These blog posts of mine always turn out much longer than I initially expect. What follows was supposed to be just an introduction, but it became so long that, knowing your attention span (or rather, judging about it based on my attention span when it comes to blog posts), I thought it best to just split it off and give it a separate entry kind of status.

I’d like to talk a bit more about space and time (what are those things anyway?), and about absolutes in the theory of relativity. Yes, not everything is relative.

By the way, Einstein himself has written something like a book (it’s more like a collection of lecture notes) about relativity. It’s called The Meaning of Relativity. Yes. By Einstein himself. If you’re up to the challenge, you can try to understand relativity directly through Einstein’s words. But I wouldn’t recommend that to people who haven’t had at least a basic course on the subject - otherwise the book will be quite anticlimactic.

Actually, I think the book is a bit anticlimactic for anyone, since Einstein is such a deity in science that you expect every word of his to bring you noticeably closer to the true meaning of the Universe.

In fact the book is a normal, at times even boring, exposition of relativity, with a good number of abstruse (also due to their slightly archaic notation) equations. However, he does share some non-mathematical insights, and some of those I just cannot put better than Einstein. Let’s start with time. He writes,

The experiences of an individual appear to us arranged in a series of events; in this series the single events which we remember appear to be ordered according to the criterion of earlier and later, which cannot be analysed further.

While he does not specifically talk about space (the book is really concise), it is straightforward to extend the statement in that direction: our experiences appear to us positionally arranged, so that we can for example say that an object is closer to us than another object. Thus, our concepts for both space and time stem from our experience. Obviously, these are then always associated to a particular individual - the one doing the experiencing - and there is a priori no need for any overlap between various individuals. However, as Einstein writes,

By the aid of speech different individuals can, to a certain extent, compare their experiences. In this way it is shown that certain sense perceptions of different individuals correspond to each other, while for other sense perceptions no such correspondence can be established. We are accustomed to regard as real those sense perceptions which are common to different individuals, and which therefore are, in a measure, impersonal. The natural sciences, and in particular, the most fundamental of them, physics, deal with such sense perceptions.

This is a truly outstanding definition of the object of physics. There seems to be some order in the world in the sense that we all see some things happening in a certain way. Why is that? We don’t really have to, if you think about it, but the fact that we do implies some underlying laws that unite our experiences - and that's what physicists try to analyze. 

Of course, Einstein allows for experiences which are not shared by various observers, but these are not physical. For example, you “totally going all the way with Judy last night” won't be of interest to physicists, especially if it was an experience not even shared by Judy. Now, an obvious question springs up. Does this definition of the physical world as 'shared experiences', well, suck, because it's too anthropocentric? And on a related note, is there space and time beyond the human observation of those? Is there a physical world beyond our perception of it? And how could we ever separate one from the other? 

What is important to realize is that this question is a philosophical and not a physical one. And the philosophers have given it a lot of thought - we have Descartes' cogito ergo sum, which to a first approximation suggests that we can be certain of our existence (through the very act of questioning it), but of nothing beyond that. Descartes also has an evil demon that helps him extend that idea. The modern version of the demon is the brain-in-a-vat, while the ultra-modern Wachowski-siblings version is the backbone to the plot of one of my favorite movies. Which makes me wonder if The Matrix would've been even cooler if it were called The Evil Demon. 

Incidentally, I think therefore I am is a little bit like the E = mc²  of philosophy. Many people know it, but not so many have any idea what the point is. For those, The Matrix is a great starting point to dive in the implications of the cogito ergo sum. On the other hand, it’s not a good starting point to learn any physical laws, as they are consistently broken both in and out of the Matrix... (Still a great movie!). Anyway, coming back to physics, I like Einstein’s stance:

The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy. I am convinced that the philosophers have had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori. For even if it should appear that the universe of ideas cannot be deduced from experience by logical means, but is, in a sense, a creation of the human mind, without which no science is possible, nevertheless this universe of ideas is just as little independent of the nature of our experiences as clothes are of the form of the human body. This is particularly true of our concepts of time and space, which physicists have been obliged by the facts to bring down from the Olympus of the a priori in order to adjust them and put them in a serviceable condition.

As usual, I find it really easy to agree with the great mind.

The main point of this post can then be stated as a summary of everything above. The world in the framework of the theory of relativity is composed of absolute events which are embedded in an observer-dependent space-time. The absolute events are the 'shared experiences' that Einstein talks about. Those are observer-independent in the sense that everyone agrees that they 'happened'. However, when describing the events, everyone has to inevitably refer to their own space-time reference frame, which is by definition observer-dependent. So, in order for different individuals to compare their experiences by the aid of speech, and find that certain sense perceptions of different individuals correspond to each other, a 'common language' is necessary. This provides the means of a translation from one individual's very own, personal space-time to the next. And as I've mentioned before, the theory of relativity is simply a recipe for how to do the translation.

Notice then that the big conceptual leap in the theory is not that everything is relative - in fact it's important that there are absolutes, the shared experiences. Also note that we knew that some things were relative even before Einstein. In particular, we are quite comfortable with the notion that space is relative: if something is two meters away from me, I wouldn’t generally expect it to be two meters away from you - that would only be true in some very particular cases. The main innovation of relativity was actually the fact that time is also relative. We used to think (and still often do) that if something is two minutes away from my 'now', then it's also two minutes away from your 'now'. However, just as with space, this turns out to be true only in some particular cases, which just happen to fully encompass our everyday experiences, which is why it took us so long to figure that out. Better said, it’s not possible to define our 'nows' in a way that they match under all circumstances (in particular when we move fast with respect to one another). Better still, space and time are inseparable and kinda mixed up and only kinda absolute if thought of as a single unit: space-time. However, they are always relative when separated. 

OK, this is getting a bit too technical. But I’ll try to illustrate all these points even further in the next post.