Newtonian physics describes what happens in systems that have large masses and slow speeds. There are three relevant
limits that are indicators that Newtonian physics is no longer the preferred model:
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Special relativity
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General relativity
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Quantum mechanics
These models are unified. For example, the model of special relativity could be used to solve all solvable
problems in physics, but it would just make the calculations unnecessarily difficult. Also, general relativity and
quantum mechanics are the two major (but separate) theories for how the universe works. They work well in their own
domain, but they are incompatible, especially when gravity is introduced. String Theory has been the only promising
candidate of reconciling the two.
In Newtonian physics, systems are reversible. Physical processes hold unitarity, which is the condition that the time
evolution of a state is mathematically represented by a unitary operator. Or, if you know everything about a system (like the positions and speeds of all particles), you can use the laws of physics
to figure out what it will do in the future. Importantly, you can also reverse the process and figure out what it was
doing in the past. This is called reversibility.
In this model, there is implicit determinism.
Systems are not as easily reversible in quantum mechanics because of the uncertainty principle and the probabilistic
outcome of measurement. Something about it being tricky when the system is moving fast and/or when gravity is introduced... I'm not qualified to go down that rabbit hole. The takeaway is that in Newtonian physics, the world is deterministic, implying
there is no freedom vis-a-vis natural laws. But in other more involved models of the universe, the world is not
deterministic, implying free will.
Leonard Susskind is a professor of theoretical physics at Stanford University and is one of the leading minds in string
theory and quantum mechanics. Here he talks about the indestructibleness of information. The conservation of the
information principle makes sense, but Susskind's explanation and this response suggests that the principle is a
consequence of unitarity. Is information only relevant in Newtonian physics?
Noether's theorem is a beautiful fundamental theorem of calculus that connects symmetries to conserved quantities. When
physics is independent of spatial position, momentum is conserved. When physics is independent of time, energy is
conserved. When you take quantum mechanics into account, Noether's theorem explicitly depends on unitarity. This theorem
conserves quantities in nature across every known model of the universe.
If information is indeed indestructible, it would seem that the conservation of information is caused by the unitarity
of the physical process from which the information came from. This is only compatible with Newtonian physics as
explained earlier. But I don’t see how this holds true when you consider that information exists on every scale.
In 1867, Maxwell proposed a thought experiment called Maxwell's demon. If you pour hot liquid into a system of cold
liquid, the resultant mix would have an average temperature of both liquids. The only way to stop that would be if there
was a small demon there to stop this from happening. Absent this demon, the second law of thermodynamics states that the
liquids will mix and reach an average temperature. Leo Szilard, a colleague of Einstein, noted that for the demon to be
able to do this, he'd need to have information about which molecules are hot and which molecules are cold. That way he
could keep the liquids separated and they wouldn't reach an average temperature. There is just as much
information as there is energy in the system.
Information and energy are two sides of the same coin. The laws of thermodynamics express facts about temperature, heat,
and entropy from the subatomic to cosmic level. Information exists on these scales as well.
Susskind's belief about the conservation of information implies that information exists in the deterministic landscape
underwritten by Newtonian physics. This is clearly not the case. Information exists beyond Newtonian physics if you
agree with Szilard, which I do.
Einstein's physics and quantum mechanics support an indeterminate nature of the universe, implying free will. But it
seems that our current understanding of the information landscape doesn't support that claim.
The physics of energy has achieved wonderful feats for
mankind. It is governed by mathematical models that describe the universe well independently, but aren’t reconcilable
with each other when gravity is introduced. I'm not a physicist, but I suspect that the disconnect has to
do with the physics of information. There is so much undiscovered about information creation, symmetry, and measurement.
Perhaps when we have clearer models on the physics of information and have revisited our current theories, will we
understand more about free will about our place in the universe.