The universe is quantised!

I just read a post on Don’s Hotel Room Nudes regarding “What comes after digital technology?” This is a discussion about where digital can go and why is cannot compete with film given its inherent digital restrictions and why analog is better than digital.

Don has challenged me to back up my statement that the universe is inherently digital.

This prompted me to consider a reply based on my experience in the field of physics. So here it goes.

At the smallest scale of the universe everything is quantised, that is it consists of finite steps in value. There is not a continuous set of states between any two values of energy; you must jump from one energy value to another in finite steps. This step size is known as Planck’s constant (h) and it has a value of 6.62x10^-34Js which is pretty darn small.

Now lets consider how this quanta effects photography.

Light is energy, so light is also quantised and if we were to measure the frequency of the light reflected from a surface we could assign an energy value to it.

Visible light has a frequency range from 4x10¹⁴Hz to 7.5x10¹⁴Hz

Now you can specify exactly the energy of light from the equation e=hf, So this gives an energy range of 4.2x10^-20 to 7.9x10^-20 or a range of 3.7x10^-20.

The number of discreet energy values that are needed to describe every possible frequency of light in that visible range is 3.7x10^-20/6.62x10^-34=3.5x10¹⁴ states. So the whole visible spectrum has roughly 350000000000000 separate states in it.

So if we have a digital system that can measure with quantum accuracy, how many bits of data do we need to represent this with no data loss. The number of states in a binary number is represented 2^n, and a little bit of playing with my calculator shows 2⁴⁸=3x10¹⁴. So if we have a 48 bit sensor we can accurately record every single part of the visible spectrum with quantum accuracy.

Now a digital camera and colour film work by measuring the energy of the photons in the red, green and blue portion of the spectrum and summing them over time. This gives a measure of the colour but not a complete measurement of it. Each of the photons delivers energy to the sensor or crystal and determines its numeric value or exposure level.

The actual value in the sensor or change in the crystal is quantised and therefore can be measured, in theory, with a digital system that has sufficient accuracy.

Let’s consider distance. The closest you can place any two subatomic particles is also controlled by the Planck constant. This is the most accurate measurement you could make. You could convert all distances to a multiple of the Planck constant, so distance is also quantised.

Now Don brought up the factor of Pi and that the fact that you cannot represent it using a digital system. This is correct, but Pi is not a physical constant. Pi is a ratio that measures the curvature of space time at a specific location. If you were able to tie a tape measure to the centre of the sun and use it to measure radius, and then measure the circumference outside the sun, Pi would not be exactly the same as on earth because the curvature of space due to the mass of the sun would distort the measurements. Thus Pi is a simple ratio, not a physical constant. The circumference is quantised and can be measured, the radius is quantised and can be measured but the ratio cannot.

However, this is not a failing of the digital system or the quantum nature of reality, because the universe doesn’t measure Pi, Pi is a mathematical construct.

Thus I believe that having discussed the quantum nature of light and distance and the lack of relevance of a pure ratio, my statement that the universe is inherently digital holds true.

Now, after all that I really think you need reward, so here is the lovely Kate not thinking about physics at all.