transition said:
https://en.wikipedia.org/wiki/No-hiding_theorem
just read that^, damaged my neuron the effort did, being early after a late night, well I was up for a while which makes it feel early
Reading that now. I see that I was wrong. The act of observation does not collapse the probability function, contrary to the Copenhagen interpretation of QM.
Rather, the act of observation scatters the information from the observed entity into the entities that carry out the observation, in such a way that this information can be reconstructed externally. This is news to me.
In following up on this I’m finding heaps of false information on the web.
Fiction 1. Information is not lost in QM but is lost in GR at black hole boundaries.
Fact. To outside observers it takes an infinite amount of time for a particle to reach the black hole horizon, so in GR the information remains still available for all future time. Or to put it another way, Susskind’s solution to the so-called black hole information paradox is correct. To co-moving observers there’s no loss of information at the black hole event horizon either.
Fiction 2. General relativity has an arrow of time. QM has no arrow of time.
Fact. GR has no arrow of time either, the equations in GR are completely symmetrical with time, too.
Fiction 3. General relativity cannot be probabilistic. QM is probabilistic.
Fact. It’s just as easy to create probability density function in GR as it is in QM.
Fiction 4. In General relativity everything exists to infinite future, but not in QM.
Fact. In QM, in order to calculate even the simplest things such as the results of the double split experiment, we need to precisely integrate both back to the infinite past and into the infinite future and out to infinite space. So predetermined infinite future is a common factor of both QM and GR.
Fiction 5. There is a factor of 10^120 difference between GR predictions and QM predictions.
Fact. This was a joke, damnit. But it entered popular literature and has been re-quoted hundreds of thousands of times since. It’s not true.
So, where does that leave us in the question of QM vs GR?
Well, physicists use both QM and GR, together.
QM on the small scale gives us confidence in classical mechanics on the large scale.
Using GR classical mechanics on the large scale we get a background space-time on which QM field theory is superposed to to get microscale events.
What, then, is the fundamental difference between QM and GR?
Let’s start here.
1.
GR tells us that an oscillating electric charge always generates an electromagnetic wave, which robs energy from the oscillation.
QM tells us, and observation confirms, that this doesn’t happen for electrons (electric charge) oscillating in orbit around an atom. The Planck blackbody radiation function. This became known in 1901, I think.
2.
QM field theory tells us that there is a spin 2 subatomic particle called the graviton. But gravity acting by means of the graviton would not tell space how to curve so gives wrong results for things such as the gravitational bending of light. This became known in 1934, I think.
Wikipedia says this about gravitons:
“When describing graviton interactions, the classical theory of Feynman diagrams and semiclassical corrections such as one-loop diagrams behave normally. However, Feynman diagrams with at least two loops lead to ultraviolet divergences. These infinite results cannot be removed because quantized general relativity is not perturbatively renormalizable, unlike quantum electrodynamics and models such as the Yang–Mills theory. Therefore, incalculable answers are found from the perturbation method by which physicists calculate the probability of a particle to emit or absorb gravitons, and the theory loses predictive veracity. Those problems and the complementary approximation framework are grounds to show that a theory more unified than quantized general relativity is required to describe the behaviour near the Planck scale.”
The mention of “ultraviolet disturbances” takes us straight back grom gravitons to point 1 above, the Planck blackbody radiation curve.
But hold on.
I, personally, did a lot of work several decades ago on infinite numbers. Starting from a very simple hypothesis, I ended up with the Veronese continuum and with Robinson’s hyperreal numbers from the 1950s and 1960s.
This work on infinite numbers allowed me to numerically and analytically evaluate integrals involving the product of a smooth function and an oscillatory function that classical mathematics (ie. Cantor’s cardinality) failed to evaluate.
I turned from that work into how subatomic physics works and found that my methods got the same answers as renormalisation methods. The physicists had already incorporated my results into their own work, and if anything had gone beyond what I had been able to do.
So just perhaps General Relativity really is renormalisable in Quantum Mechanics. Using Robinson’s mathematics.
Or perhaps when GR is renormalised, the answers it gives differ from observation – that seems more reasonable.
Hmm.
This wasn’t where I was trying to get. I was trying to get to a symmetry breaking event at high energies between GR and QM.