What is “measurement relativity”?
What is “measurement relativity”?
Ordinary general covariance: you can change coordinates and get same answer
Inertial motion in branchial space:
evolution of an observer who is not affected by the environment
Observer is “on a plan” to do a sequence of measurements
[like a brainless observer is like a rocket without propulsion]
evolution of an observer who is not affected by the environment
Observer is “on a plan” to do a sequence of measurements
[like a brainless observer is like a rocket without propulsion]
Limited computational capability
Limited computational capability
SR: very trivial computation
Invariance under measurement speed (?)
Invariance under measurement speed (?)
e^(i H t), scaling the H ??
Can you run a quantum computer at any speed?
Cf mechanical motions can run at any speed in Galilean mechanics
Faster measurement: more uncertainty about energy
Faster measurement: more uncertainty about energy
Imagine that branchial space is exponential
Imagine that branchial space is exponential
If exponential, then you get to the edge of space in logarithmic steps
Then is there still a maximum speed??
Observer is defined by a branchlike hypersurface
Observer is defined by a branchlike hypersurface
In the evolution causal graph:
The branchlike hypersurface defines how you foliate state space
Claim about branch space: only the causal graph matters
The branchlike hypersurface defines how you foliate state space
Claim about branch space: only the causal graph matters
In the branching in the multiway causal graph, a bifurcation could be space separation, or it could be branch separation.
In the branching in the multiway causal graph, a bifurcation could be space separation, or it could be branch separation.
Observers in QM treated relativistically (?)
Observers in QM treated relativistically (?)
Geodesic in multiway space is evolution of a pure state
Geodesic in multiway space is evolution of a pure state
Wave-particle duality: branch separation vs. space separation
Wave-particle duality: branch separation vs. space separation
Confusion between branch-like and space-like bifurcations (?)
Spin
Spin
Configuration in the spacetime causal graph
vs. configuration in the branchtime causal graph
vs. configuration in the branchtime causal graph
Claim: flipping between branches has a characteristic time;
Claim: one period of “quantum revolution” = 1 branch time
Claim: spin is way of detecting branchial structure
Claim: spin is way of detecting branchial structure
Analogous to how light can probe the structure of spacetime
To probe spacetime, have an event that produces propagating light
To probe spacetime, have an event that produces propagating light
Light is what communicates from event to event
States in multiway graph are like events in causal graph
States in multiway graph are like events in causal graph
Combined description of multiway + real space
Combined description of multiway + real space
Evolution causal graph has both kinds of edges
Spacelike separation is “spanned” by photon propagation
Branchlike separation is “spanned” ( exp( i H t / ℏ) )
[ If i H t is big compared to ℏ, then we get decoherence ]
Why can’t we measure faster?
1. Zeno’s paradox
2. “Maxwell demon’s effect”
Why can’t we measure faster?
1. Zeno’s paradox
2. “Maxwell demon’s effect”
Twin paradox
Twin paradox
“Aged twin” is more decohereed
Think of branches as eigenstates
Think of branches as eigenstates
Therefore MW evolution is evolution of a superposition
Network of interferometers
Network of interferometers
Interferometers measure coherence
In spacetime, you take a “journey” and progressively sample more
In measurement space, you are taking a journey and entraining more dof
In spacetime, you take a “journey” and progressively sample more
In measurement space, you are taking a journey and entraining more dof
In measurement space, you are taking a journey and entraining more dof
Aka measuring less correlated observables because those observables were more branchlike separated
[ Operators are the updating events ]
[ Measurements are updating events with a choice ] (aka critical pairs)
[ Operators are the updating events ]
[ Measurements are updating events with a choice ] (aka critical pairs)
[ Measurements are updating events with a choice ] (aka critical pairs)
Pure time evolution is “measurement” without branching
In sampling more, you could do that space-ly, or branch-ly, or both
In sampling more, you could do that space-ly, or branch-ly, or both
E.g. move and see more spins; or spins could be delivered to you
World line in branch space:
World line in branch space:
Your memory of the past is the way you entangle previous dof
The analog of β=v/c is (your decoherence rate)/ℏ
The analog of β=v/c is (your decoherence rate)/ℏ
Your rate of gobbling more dof
Decoherence: you’re entangled with so much stuff, it’s like a heat bath
Basic claim: “knowledge is confusion”: the more dof you’ve sampled, the more decohered you are
Maximum measurement rate
Maximum measurement rate
What is the analog of Maxwell’s equations that should tell us this already ?
Anything that “depends on ℏ” won’t depend on observer
Anything that “depends on ℏ” won’t depend on observer
Spin eigenstates are “frame independent”
position/momentum are frame dependent [but commutators are not]
Energy levels of harmonic oscillator ℏω
position/momentum are frame dependent [but commutators are not]
Energy levels of harmonic oscillator ℏω
Commutation relations
Commutation relations
"AAA"r1"ABA"r2XXXX"AAA"r2"BBA"r1XXXXX
If it takes n steps to converge
[ “Elementary distance between states” : iℏ/2 ] : “after 2 steps” you get a “full commutator”
Metric: minimum between states based on optimal rewrite sequence
Energy
Energy
Spacetime energy/momentum vs quantum energy (iHt energy)
[ Number of causal connections crossing spacelike/timelike hypersurfaces ]
[ Evolution connections crossing branchlike hypersurfaces ]
[ Evolution connections crossing branchlike hypersurfaces ]
Kinetic-like energy
vs. quantum (“frequency”) energy
Kinetic-like energy
vs. quantum (“frequency”) energy
vs. quantum (“frequency”) energy
Kinetic-like : connections in spacetime causal graph slicing spacelike hypersurfaces
Quantum : connections in branchtime causal graph slicing branchlike hypersurfaces
Quantum : connections in branchtime causal graph slicing branchlike hypersurfaces
There is a wavepacket that spans some part of the branchial graph; extent of the wavepacket in the branchial graph effectively determines its energy : broader wavepacket in branchial space => more causal connections => more energy
[ Elementary energy associated with every causal edge ]
There is a wavepacket that spans some part of the branchial graph; extent of the wavepacket in the branchial graph effectively determines its energy : broader wavepacket in branchial space => more causal connections => more energy
[ Elementary energy associated with every causal edge ]
[ Elementary time ]
time units * i ℏ ==== distance gone in branchial graph
time units * elementary energy
ℏ / elementary time = elementary energy
time units * elementary energy
ℏ / elementary time = elementary energy
1 causal edge ~ (c [elementary time])^d in volume
energy density associated with 1 causal edge = ( i ℏ / elementary time ) / (c [elementary time])^d
G T is dimensionless
G ~ 1/energy density
8 π G/c^4 T = R
1 causal edge is associated with a certain spatial volume, and a certain branchial volume
Planck area: ℏ G / c^d
energy density associated with 1 causal edge = ( i ℏ / elementary time ) / (c [elementary time])^d
G T is dimensionless
G ~ 1/energy density
8 π G/c^4 T = R
1 causal edge is associated with a certain spatial volume, and a certain branchial volume
Planck area: ℏ G / c^d
Think of speed of light as escape velocity of a black hole
Think of maximum measurement rate as [[ maximum energy added to an elementary region without gravitational collapse ]] ℏ/τ = ( c τ )^d
Think of speed of light as escape velocity of a black hole
Think of maximum measurement rate as [[ maximum energy added to an elementary region without gravitational collapse ]] ℏ/τ = ( c τ )^d
r = 2 G m / c^(d-1)
( c τ ) = 2 G E / (c^(d+1))
E = c^(d+2) τ / ( 2 G) = ℏ / τ
( c τ ) = 2 G E / (c^(d+1))
E = c^(d+2) τ / ( 2 G) = ℏ / τ
τ = Sqrt[2 G ℏ / c^(d+2)]
Measure one spin every Planck time
Units:
Units:
Energy/ℏ is the analog of c
c t = spatial length
1. energy/ℏ t = entanglement length
2. ℏ [time units] = entanglement length
< 1 unit of entanglement >
1. energy/ℏ t = entanglement length
2. ℏ [time units] = entanglement length
< 1 unit of entanglement >
The meaning of general covariance
The meaning of general covariance
You can make a mesh of world lines that ignore almost every form of curvature that can show up [??]
Acceleration vs structure of space
Acceleration vs structure of space
Can a change of dimension masquerade as a feature of motion?
Early universe implications
Early universe implications