..Because states are quantized, it seems the most obvious thing to many people who don't think deeply to state that the universe must be digital. What they forget is three things:
1. The quantized states have the same values only for the same type of atom; atoms of different composition have different available states, and there is no restriction on the possible values these states can take on.
2. More importantly, these states can be "smeared" across a continuum of possible values, either (as you are no doubt familiar with) within a semiconductor crystal lattice, forming the "conduction band" and the other bands of energy states, which please note are not single values but collections of values all very close to one another but necessarily not the same due to Pauli exclusion, or by the action of a magnetic field on the orbits and therefore on the energy levels of the atoms.
3. Most importantly of all, once created, the photons can be continuously varied in energy level by relative motion of an observer, or by the presence of a gravity field or an acceleration on the part of either the source or the observer.
Reality is not digital. It is analog. These three examples prove it conclusively.
This post by you was not addressed to me. I had been away from the forum a few days when you posted this. I wonder now if this is what you expected for me to address.
If so, here is my response per each of your points:
1. The fine structure constant, as a result of theory corroborated with experiment is known to the precision of better than 10^10. The success of QED is extraordinary. Measurement of fine-structure is to a resolution of about 1KHz out of 300THz. Let’s see: from K, M,G,T,x100 is about 10^11, right? That’s the best we’ve done with theory corroborated by experiment. I’ve read that there are some physical properties measured to the precision of 1 part in 10^20!! But all that is gross in comparison to the level of discretization of space-time it makes sense to consider plausible. It seems to me you may be thinking of discretization at much larger scales than planck scales because maybe you expect to be able to detect it directly?
2. To talk about potential values of the quantum state is also not something that can be observed. This is an ideal construct. To say it is “smeared” is like my saying that real numbers are “smeared” between 0 and 1. ...Surely, in our imaginations. But what reality does the mathematical continuum actually possess? None! Potential quantum values are a mathematical construction that can be represented as taking on all real (or imaginary) values. But potential quantum values become realized as actual values upon measurement. So I am confused as to how you might expect the potential values that can't be measured to be evidence of continuum.
3. This third statement presumes continuum and then concludes in a circular fashion. Notice that the observer’s or source’s velocities are assumed to be continuous, which is used to conclude therefore that the photon’s energy can be varied continuously due to relativistic effects. Can you see how this is obviously a circular argument?
These three points you made all say the same thing to me. Something like “direct measurement reveals a universe that, if space-time is discrete, is so at a level that is much tinier than we can observe. Therefore, if they are so tiny we can't observe them, they must be infinitesimal."
My contention with this is that
direct measurement may not be a source of evidence one way or the other – ever. I think the evidence will be found by starting with the proper interpretation of many things we already know. Subsequently that should lead to enough of the right mindset in theoretical formulation so that more evidence will come from new models that predict things for which we previously had no explanation.
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but take all the time you need.