## 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)]

Sqrt2^5

In[]:=

Out[]=

UnitConvert[%]

In[]:=

Out[]=

In[]:=

Out[]=

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