PLANCK ERA

Our understanding of the Planck era is poor at this time. To make progress a theory which encompasses both quantum mechanics and gravity must be developed. This is a difficult proposition and has defied many attempts over the years. To see why we may need to marry these two great theories, consider the following.
Compton Wavelength

Quantum mechanics is a strange and wonderful theory which describes the atomic and sub-atomic world. It offers a different way in which to view the world and makes many strange predictions which experiments have never failed to confirm. For now, let me concentrate on one aspect of the theory, the Heisenberg Uncertainty Principle:

When you measure the position and momentum of a particle, you cannot measure both quantities with infinite precision. The product of the uncertainties in your measurements must always be greater than some constant nonzero number (roughly Planck's constant, named in honor of a man who performed pioneering work in the field).

The uncomfortable notion is that the more precisely you measure the momentum, in order to keep the product of the measurement errors larger than some minimum value means that the uncertainty in the position must be large. An upshot of this is that in Quantum Mechanics, one can only calculate the probability of where particles will be found. This is annoying.

Roughly speaking, this spread in location is small and virtually undetectable in our world, but it does have consequeneces. We define something known as the Compton wavelength as a measure of the spread.

You cannot localize a particle any better than its Compton wavelength.
Black Holes

Recall that a black hole has a singularity at its center which is cloaked by its event horizon. The radius of the event horizon is the

Schwarschild Radius ===> R(Sch) = 3 km [Mass/M(Sun)].

In general, it is good that singularities are hidden from our Universe by event horizons because interesting (and odd) things can happen in the vicinity of singularities. For example, causality can be disrupted near a singularity. This is bad. The problems are so severe that people have proposed something known as the Cosmic Censorship Theorem, which states that singularities must always be cloaked by event horizons.

Quantum Mechanics meets General Relativity

Ask the question, What happens if you merge the ideas of Quantum Mechanics with the ideas of Einstein (General Theory of Relativity)? Well, suppose that the Compton Wavelength and the Schwarzschild radius of an object are roughly the same. This can happen for objects with small masses. In this case, the uncertainty in the position of the singularity is comparable to the radius of the event horizon. This uncloaks the singularity!! On this scale, the structure of space-time becomes poorly defined and General Relativity (as formulated) breaks down.

Planck Scale

The breakdown occurs for tiny masses in the early Universe. This tiny mass is referred to as the Planck mass -- Planck mass = 5.5 x 10^-8 kil0grams. The Sun has a mass of 2 x 10³⁰ kilograms.

The Compton wavelength and Schwarzschild radius which correspond to the Planck mass are 4 x 10^-33 cm. This length is known as the Planck length and the light travel time across this distance is known as the Planck time. The Planck time is 10^-43 seconds !!!

What this means is that the General Theory of Relativity breaks down for times less than 10^-43 seconds, the Planck time. As a result, if we want to try and understand the earliest phases of the Universe we need to develop a theory which merges Quantum Mechanics and General Relativity.

For further reading: Stephen Hawking and Roger Penrose, two noted relativists, make some interesting comments on this issue and other equally interesting issues in this piece taken from Scientific American