General relativity v Quantum theory

The two branches of modern theory are incompatible. While there are many negative aspects of modern theory, detailed on this site, this incompatibility is one that physicists are inclined to emphasise rather than obfuscate, not least because it is a major part of the drive for funding.

An entire branch of theoretical physics is devoted to tackling this incompatibility, and that includes not only string theory, but also mathematical extensions of this very mathematical theory, together with many flavour-of-the-month endeavours such as ‘loop quantum gravity’ and ‘doubly special relativity’.

On this page, we will spell out the ways in which these two core theories differ, explain why this divergence has proved so intractable, and say what this tells us about the theories themselves.

## Mathematics

Modern physics is highly mathematical, and it is even said – with some justification – that the mathematics is the physics. This implicitly agrees with the conclusion of this site, that none of the verbal explanations in these theories work.

Yet there are also problems with the mathematics, and these problems are different for the different theories.

The Lorentz transformation in special relativity is validated by a range of observations, but only in situations that are profoundly non-‘relativistic’. This is detailed here.

The Schrödinger equation of quantum mechanics is considered to be profoundly resistant to physical interpretation, but this is far from the case, and this has been known since 1927. The Schrödinger equation is considered here.

The Schwarzschild metric of general relativity contains a single simple calculation, which is all that is needed to generate all of the ‘key predictions’ of modern gravitational theory. The Schwarzschild metric and its use are detailed here.

The question of whether a metric approach to the motion (or ‘geometrodynamics’) of both light and matter is valid is considered here.

The Einstein equation of general relativity has no validating observations and appears to be part of the mathematical smokescreen of failed science in modern physics. It is discussed here.

## Differences

It is far too early in our considerations to attempt to make a choice between general relativity and quantum theory, and it is not yet certain that this is what we must ultimately do. We can instead highlight the accepted points of difference and dispute between them, as a way of guiding our further examination. The divergences between the two theories may not be exactly what you expect.

What seems at first a trivial disagreement is in relation to the role of the observer.

Relativity theories have an inbuilt status for the position, and more importantly the state of motion, of the observer. This is inherent in the original principle, and the consequent recognition that you and I might see my timing and mensuration differently. Even though the principle has its problems, especially within the general theory, the emphasis on taking meticulous care over this feature remains, despite this being honoured mainly in the breach.

Quantum mechanics declines to get hung up on this aspect. Instead, it insists that each photon we see with is a particle, and that each emission or collision with other particles en route will have altered the position that we think we have observed. Every observer retrospectively affects each and every observation.

That each theory does not share the other’s preoccupation suggests that there is some essential difference between them, if we could only be certain what that is.

A second crucial difference is in their view of time. Special relativity required a metric and that metric had to include effects on time as well as distance, with the consequence that both relativity theories insist on grouping the two very different forms of measurement together. Quantum mechanics, on the other hand, has no strong feelings about this either way.

Neither the Heisenberg nor the Schrödinger formulation treats time as another length dimension, but instead in the conventional way as a constant background feature. The latter is the most commonly used equation in quantum mechanics, and is not considered to be disadvantaged by this. The Dirac equation does incorporate the Lorentz transformation, so as to be accurate in its treatment of fast moving particles, but it is not otherwise considered superior to the other versions.

‘The basic fact is that conventional quantum theory presupposes an external time whose ontological status is the same as it possesses in classical Newtonian physics.’^{i}

It is often said that general relativity takes the view that spacetime is continuous while quantum theory requires it to be discrete, composed entirely of separate elements, but this is not clearly the case. Although quantum theory, through its name and rhetoric, insists that everything – light, matter and force – are discrete particles, these are not found naturally in the mathematics. Indeed, the Schrödinger equation is commonly called a ‘wave equation’ (though we will have more to say on this here). On the other side, those who propose quantum gravity do not see gravitation as continuous.

It has also been claimed that quantum mechanics has abandoned cause and effect reasoning, while general relativity has retained it, but I cannot see that even this is true. Quantum theorists routinely use determinist logic when they can – though this is naturally piecemeal – and there are aspects of general relativity, for example the flirtation with time travel, and most especially in relativistic cosmology, where causal thinking appears to hold no attraction whatever. ‘Matter tells space how to curve, while space tells matter how to move’ is the mantra of the gravitational relativist, but there is no attempt to ask ‘how?’

The real difference, it seems to me, is in the way the mathematics of each is formulated, and we can be certain that this is not simply stylistic, since quantum mechanics has had three very different goes at its equations, and yet the best mathematical physicists have been unable to find formulations that are compatible across the divide. We will look at this here, where we pick over the mathematics of each discipline.

Return to top of page

i. Chris Isham, of Imperial College, London, quoted by Gary K. Au of the University of Melbourne: http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9506/9506001.pdf