Can we definitively know the global structure of spacetime? This is a good question. It is one that is actively discussed in the area of the philosophy of modern physics.1,2
However it is a question that highlights the fundamental weakness of cosmology and hence of cosmogony. (Cosmology is the study of the structure of the cosmos whereas cosmogony is the study of the origin of the universe.) That weakness is the inherent inability to accurately construct any global cosmological model, i.e. a model that accurately represents the structure of the universe at all times and locations. The reason for this is underdetermination.3
“There seems to be a robust sense in which the global structure of every cosmological model is underdetermined.”1
In the philosophy of science, underdetermination means that the available evidence is insufficient to be able to determine which belief one should hold about that evidence. That means that no matter what cosmological model one might conceive of, in an attempt to describe the structure of the universe, every model will be underdetermined. Or said another way, no matter what amount of observational data one might ever (even in principle) gather, the cosmological evidence does not force one particular model upon us. And this underdetermination has been rigorously proven.1 Continue reading
The imaginary time axis is drawn orthogonal to the real time axis. Credit: Wikimedia commons
Update 14/03/2018 Professor Stephen Hawking died today. See his obituary here. From all I have read he remained an ardent atheist his whole life. And he never really understood the worldview issue in cosmology and the origin of the universe. This proves that even very smart people can get it wrong. Nevertheless he gave us much to ponder, debate and learn.
What is imaginary time? I don’t mean the time you spend day-dreaming but the concept in physics, promoted by theoretical physicist Stephen Hawking. It is used in some quantum mechanics and special relativity theory. Imaginary time is where the usual time dimension undergoes a Wick rotation (a phase rotation)1 so that its coordinates are multiplied by the imaginary number the square root of -1, represented by the symbol i. In such a situation time theoretically behaves like a spatial dimension.
Stephen Hawking Credit: Wikipedia
“One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?” (emphasis added)
Positivism is the philosophy that we cannot determine what is real, but we can only propose hypotheses and test those against what we observe. Hawking is an atheist—an anti-theist—and has spent some time attempting to show that the Creator is unneeded in the universe.
Hawking claims that imaginary time is as real as real time, only that it is travelling in a different direction.3 He claims that ‘before’ the big bang time was imaginary and thus there was no time. Imaginary time may have “always existed” he said, but because we have no idea of what the laws of physics were ‘before’ the big bang, and there is no way to measure what happened ‘before’ the big bang, hence there is no point including time back then in a discussion of our universe. Continue reading
I have previously made the argument that the cosmic microwave background (CMB) radiation, ‘light’ allegedly from the big bang fireball, casts no shadows in the foreground of galaxy clusters.1 If the big bang were true, the light from the fireball should cast a shadow in the foreground of all galaxy clusters. This is because the source of the CMB radiation, in standard big bang cosmology, is what is known as the “last scattering surface“.
The last scattering surface is the stage of the big bang fireball that describes the situation when big bang photons cooled to about 1100 K. At that stage of the story those photons separated from the plasma that had previously kept them bound. Then expansion of the universe is alleged to have further cooled those photons to about 3 K, which brings them into the microwave band. Thus if these CMB photons cast no shadows in front of all galaxy clusters it spells bad news for the big bang hypothesis.
Fig 1: Schematic of the Sunyaev-Zel’dovich effect that results in an increase in higher energy (or blue shifted) photons of the CMB when seen through the hot gas present in cluster of galaxies. Credit: astro.uchicago.edu/sza/primer.html
The CMB radiation shadowing effect, or more precisely the cooling effect, by galaxy clusters is understood in terms of the Sunyaev–Zel’dovich Effect (SZE). This is where microwave photons are isotropically scattered by electrons in the hot inter-cluster medium (ICM) (see Fig. 1) via an inverse Compton process leaving a net decrement (or cooling) in the foreground towards the observer in the solar system. Of those CMB photons coming from behind the galaxy cluster less emerge with the same trajectory due to the scattering. Even though the scattered photons pick up energy from the ICM the number of more energetic CMB photons is reduced. After modelling what this new CMB photon energy (hence temperature) should be, a decrement can, in principle, be detected.
Starting around 2003 some published investigations, using this SZE, looked for the expected shadowing/cooling effect in galaxy clusters. No significant cooling effect was found, by multiple studies, including the WMAP satellite data.2 This was considered to be very anomalous, significantly different from what was expected if the CMB radiation was from the big bang fireball. The anomaly was even confirmed by the early Planck satellite survey data in 2011.3