This post will pretty much sum up various thoughts which popped into my head during the last week of the Physics and Reality course I’m currently on, specifically my impressions from the lecture and thoughts I had during the seminar.
In advance, I apologise for the confusion with terms relating to time – the english language is simply not set up for explaining such things well. I would put markers in where problems exist, but they’re probably pretty self-evident anyhow.
Why I don’t like Leibniz time (and why I possibly do, too)
During the lecture, Dr. Barlow introduced the two viewpoints of time held in the 17th century – one by Newton, one by Leibniz. (This relates to the whole Leibniz/Clarke correspondance thing from earlier in the course).
Newton’s time is something that is continuous – think of how we tend to view space, as something that can be split up into infinitesimal pieces, and you can just keep on splitting it up. It acts as a background to everything that goes on in the universe.
Leibniz’s time, on the other hand, is far from continuous – it consists of a series of events, which follow on from previous events in a certain order. There’s no specified interval between each event, no metric. The example given in the lecture was that of a chess game – the actual playing of the game is Newtonian time (on the surface – more about that later), while the list of moves is Leibniz time.
So, why don’t I like Leibniz time? Let’s look at space briefly. It’s generally considered to be continuous, infinitely divisible (again, see later). On top of this, we typically introduce some coordinate system. Let’s stick with cartesian coordinates, and restrict our thinking to one dimension. So we have x = 0, 1, 2, 3, … . You can equally well look at the case when x = 0, 0.25, 1.34, 1.35, … – i.e. remove the metric from the problem. I would consider this to be Leibniz time. My point is that it’s possible to start with a Newtonian time, and reduce it to Leibniz time – so Leibniz time is just a reduced form of Newtonian time, with some information lost.
The problem comes when you look at time on the smallest units possible. I don’t know whether on this kind of scale it becomes quantized or not – Planck timescales would seem to indicate that it does, but they’re just a mathematical argument not a scientific proof. Heisenberg’s uncertainty principle, dEdt <= h-bar, probably has something to say before we get to those scales, anyhow. But for the sake of this argument, let's say that time is somehow quantized. Wouldn't this be Leibniz time? There would be no way to identify whether or not there's any sort of metric involved here. So what I considered to be Newtonian time above would in fact reduce to Leibniz time.
That pretty much sums up what I was discussing with Kei on the way back from the lecture. I guess it’s a fairly circular argument, with no clear winner, but I generally come down on the side of Newtonian time – at least, while I’m lacking evidence to the contrary.I want to go on to discuss something related (i.e., it’s about time), but which came later in my thinking – it was sort of brought up in the seminar, but I hope to show the divide more clearly here than then.
Two viewpoints on time
There’s two different viewpoints from which you can view time. These represent something much more fundamental in the world, which should become obvious shortly.
The first is the physics viewpoint. This is the standard, accepted one by pretty much any scientist out there. It says that time, and space, are something through which we are passing – it has existence separate to humans, existed before humans, and will continue existing well after humans have become extinct. I guess this’s related to the Newtonian viewpoint of time above.
The second is the personal viewpoint. This is probably the more natural, less abstracted viewpoint – but very much more paranoid, I guess. I would state this as: I was born 21 years ago. I have no proof that the universe before I was born defiantly existed. For all I know, it might all be a big con set up by some god on me, to fool me into thinking that I’m just part of something larger. So the universe, as I see it, came into existence when I was born, and will end its existence when I die.
(In the seminar, this was brought up slightly differently – it was discussed whether time existed before humanity, not before the individual person. I prefer my approach, as it’s much more personal and easily applicable).
The second viewpoint is very much an egotistical viewpoint of the universe – but try to prove that it isn’t the case. Personally, as an aspiring scientist I naturally subscribe to the former, but my mind keeps bringing up the latter. Either way, they’re both just theories – and both are fundamentally unprovable, as the majority of philosophy is. I guess I’ll either find out when I die (read: pass on from this reality), or I’ll never find out. For now, I’ll just stick with theorizing – at the very least, it’s interesting.
The last paragraph would be a really nice place to end this post, but I still have one more point I want to make. I tried to explain this in the seminar, but it didn’t go down well. While this is possibly for good reason, I didn’t hear a good explanation why it is wrong – the lecturer just pointed out the english problems, and left it at that.The question was brought up – if space is expanding (i.e. the expansion of the universe), then is time also expanding? My approach to answering this was that it’s two sides of the same coin. Either space is expanding, while time remains “constant” (this is where the english problems really kick in), or equally well you can say that space is constant while time is “expanding”.This is probably an odd way to look at the problem. If space is remaining constant, then that implies that the various scales are also remaining constant – so for example, atomic scales are constant, but the time they exist in is expanding. What does this do for quantum mechanics? I’m not sure it’s in a good position to answer, but hopefully I’ll find the answer someday.Addendum: another idea which I mentioned in the seminar, but didn’t go anywhere, was Wheeler’s view of electrons and positrons – basically, as positrons can be viewed as electrons going backwards in time, all electrons and positrons can be viewed as a single electron constantly going backwards and forwards in time. If I’d have thought about this a bit longer, I’d have presented it differently. I’d probably have pointed out that antiparticles can be viewed as going backwards in time – so could the fact that the universe is dominated by matter rather than antimatter be the reason why we only travel forward in time? If the universe was made of antiparticles, then we’d only be going backwards in time. As a universe with a mix of particles and antiparticles would be unstable, there can be no long-lived universe where both forwards- and backwards-time travel is possible.