The fabric of the Universe

Brian Greene wrote an excellent book with a similar title (The Fabric of the Cosmos) which I briefly touched on here. Basically, it’s space and time, and the discipline of physics can’t avoid it. In fact, if you add mass and charge, you’ve got the whole gamut that we’re aware of. I know there’s the standard model along with dark energy and dark matter, but as someone said, if you throw everything into a black hole, the only thing you know about it is its mass, charge and angular momentum. Which is why they say, ‘a black hole has no hair.’ That was before Stephen Hawking applied the laws of thermodynamics and quantum mechanics and came up with Hawking radiation, but I’ve gone off-track, so I’ll come back to the topic-at-hand.
 
I like to tell people that I read a lot of books by people a lot smarter than me, and one of those books that I keep returning to is The Constants of Nature by John D Barrow. He makes a very compelling case that the only Universe that could be both stable and predictable enough to support complex life would be one with 3 dimensions of space and 1 of time. A 2-dimensional universe means that any animal with a digestive tract (from mouth to anus) would fall apart. Only a 3-dimensional universe allows planets to maintain orbits for millions of years. As Barrow points out in his aforementioned tome, Einstein’s friend, Paul Ehrenfest (1890-1933) was able to demonstrate this mathematically. It’s the inverse square law of gravity that keeps planets in orbit and that’s a direct consequence of everything happening in 3 dimensions. Interestingly, Kant thought it was the other way around – that 3 dimensions were a consequence of Newton’s universal law of gravity being an inverse square law. Mind you, Kant thought that both space and time were a priori concepts that only exist in the mind:
 
But this space and this time, and with them all appearances, are not in themselves things; they are nothing but representations and cannot exist outside our minds.
 
And this gets to the nub of the topic alluded to in the title of this post: are space and time ‘things’ that are fundamental to everything else we observe?
 
I’ll start with space, because, believe it or not, there is an argument among physicists that space is not an entity per se, but just dimensions between bodies that we measure. I’m going to leave aside, for the time being, that said ‘measurements’ can vary from observer to observer, as per Einstein’s special theory of relativity (SR).
 
This argument arises because we know that the Universe is expanding (by measuring the Doppler-shift of stars); but does space itself expand or is it just objects moving apart? In another post, I referenced a paper by Tamara M. Davis and Charles H. Lineweaver from UNSW (Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe), which I think puts an end to this argument, when they explain the difference between an SR and GR Doppler shift interpretation of an expanding universe.
 
The general relativistic interpretation of the expansion interprets cosmological redshifts as an indication of velocity since the proper distance between comoving objects increases. However, the velocity is due to the rate of expansion of space, not movement through space, and therefore cannot be calculated with the special relativistic Doppler shift formula. (My emphasis)
 
I’m now going to use a sleight-of-hand and attempt a description of GR (general theory of relativity) without gravity, based on my conclusion from their exposition.
 
The Universe has a horizon that’s directly analogous to the horizon one observes at sea, because it ‘moves’ as the observer moves. In other words, other hypothetical ‘observers’ in other parts of the Universe would observe a different horizon to us, including hypothetical observers who are ‘over-the-horizon’ relative to us.
 
But the horizon of the Universe is a direct consequence of bodies (or space) moving faster-than-light (FTL) over the horizon, as expounded upon in detail in Davis’s and Lineweaver’s paper. But here’s the thing: if you were an observer on one of these bodies moving FTL relative to Earth, the speed of light would still be c. How is that possible? My answer is that the light travels at c relative to the ‘space’* (in which it’s observed), but the space itself can travel faster than light.
 
There are, of course, other horizons in the Universe, which are event horizons of black holes. Now, you have the same dilemma at these horizons as you do at the Universe’s horizon. According to an external observer, time appears to ‘stop’ at the event horizon, because the light emitted by an object can’t reach us. However, for an observer at the event horizon, the speed of light is still c, and if the black hole is big enough, it’s believed (obviously no one can know) that someone could cross the event horizon without knowing they had. But what if it’s spacetime that crosses the event horizon? Then both the external observer’s perception and the comoving observer’s perception would be no different if the latter was at the horizon of the entire universe.
 
But what happens to time? Well, if you measure time by the frequency of light being emitted from an object at any of these horizons, it gets Doppler-shifted to zero, so time ‘stops’ for the ‘local’ observer (on Earth) but not for the observer at the horizon.
 
So far, I’ve avoided talking about quantum mechanics (QM), but something curious happens when you apply QM to cosmology: time disappears. According to Paul Davies in The Goldilocks Enigma: ‘…vanishing of time for the entire universe becomes very explicit in quantum cosmology, where the time variable simply drops out of the quantum description.’ This is consistent with Freeman Dyson’s argument that QM can only describe the future. Thus, if you apply a description of the future to the entire cosmos, there would be no time.
 
 
* Note: you can still apply SR within that ‘space’.

 

Addendum: I've since learned that in 1958, David Finkelstein (a postdoc with the Stevens Institute of Technology in Hoboken, New Jersey) wrote an article in Physical Review that gave the same explanation for how time appears different to different observers of a black hole, as I do above. It immediately grabbed the attention (and approval) of Oppenheimer, Wheeler and Penrose (among others), who had struggled to resolve this paradox. (Ref. Black Holes And Time Warps; Einstein's Outrageous Legacy, Kip S. Thorne, 1994)