space time from quantum entanglement 201103011710

8/7/2019 Space Time From Quantum Entanglement 201103011710

http://slidepdf.com/reader/full/space-time-from-quantum-entanglement-201103011710 1/36

1

Space-timefromQuantum Entanglement

DRAFT

Richard Bradford and Gordon Rogers

Abstract 20110424

A basis for the Lorentz groupderives from quantum entanglement and the associated basic measures from first principles. A

four-space manifold generates and decomposes into a related one time and three space domains from this basis. That

simultaneity and frame independence are necessary and sufficient conditionsdemonstrates over all space with local special

cases generating the general condition of arbitrary event ordering globally.The material is presented in reverse order of its

development as this allows for the presentation of the most significant of the findings first. For thorough

systematicdevelopment, chapters read in reverse order.

Correspond at

[email protected]



2

Chapter 1:A Space-Time and Quantum Entanglement in a General Manifold.

Assume there are a manifold and any pair of quantum-entangled points on the manifold.Given no violations of therules of

quantum mechanics for entangled points, there is a law conservation law of probable outcomes for the joint relative

measurements of a particular attribute.This conservation law implies symmetry that all pairs of points on a manifold are

equivalent for the description of the connected entanglement. As a result, the link between arbitrary points is simultaneous.

Let two points in the manifold be entangled and labeled A and B. The entangled state is a quantum connection between A and

B and requires a quantum medium to enable the connection. Starting from A the point infinitsesimally close to A is

simultaneously entangledand connected to point A and iteratevly onto point B. Then, there is a path from A to B where its

points contained are entangled and simultaneously connected along with points A and B. The actual paths of the simultaneous

entanglement link between two points are not known, however. Thus, all paths from one end point to the other in the manifold

are necessary to describe the entanglement connection between points A and B and the points in the paths within.The paths

are all equivalent since the quantum entanglement outcomes are the same for any pair of points. Define a general quantum

field as all entanglement paths connecting two arbitrary entangled points on a manifold.

There is necessarily a third point, O, where entanglement of points along with their pathsoriginate.Consider two points that are

infinitesimally close to O and each other. They are then simultaneously entangled and connected to each other and to O. The

iterative process continues to point A and likewise to point B. The general quantum field links the points A, B, and O together

along with points contained in the paths. There are quantum entanglement paths that connect A to B through O. Define this as

a TypeI quantum bundle. Also, there are quantum entanglement paths connectingpoints A and Bthat do not pass through

O.Define these as aTypeII quantum bundle. Given a manifold with a general quantum field and an entanglement origination

point O for pair wise entanglement of two points, the two types of quantum bundles and their relationship with O exist.Thus,

theentire general quantum field is composed of the sum of theType I and II quantum bundles.

Ways of connecting entanglement to points on the Type I quantum bundle together pair wise using Type I and II quantum

bundles introduces sets of connections. All possible entanglement paths of the TypeI and II quantum bundles are similar to all

possible paths for a particle wave function in quantum field theory as given by Feynman and so hascardinality C, the continuum.

If C paths connect two points, then there is C number of possible ways of connections. If one point connects to C number of

points using one path, the number of ways is again C. If one point connects to C number of points with C number of paths, the

set of connections is CXC = C2

and so on. The order of the connection is the number of cross products.

Connections of points in Figure1.2 illustrates by an example the number of quantum connections depends on the number of

paths and points involved. As shown, there are two paths in the Type II quantum bundle that links together two points on OA,

A1 and A2, to two points, B1 and B2, on OB on the Type I quantum bundle giving a total of 2X2X2 = 23

= 8 possible ways to link

the two pairs of points with two paths. The order is three.The two pairs of points arealso auto linked together by the two paths

of the Type I quantum bundle since they were all connected by their origination from O.The total order is represented as

23+2.Thus the general quantum bundle has order 3 plus order 1. This is a special case and in other cases the number of

connections by unequal numbers of points and paths leads to different a form not of mn+nsuch as three paths of Type II

quantum bundle connecting two points on OA to two points on OB, which is 3X2X2. Connecting three points to two points with

three paths is 3X3X2. They are third order, however. In the limit as the number of points and paths of TypeII connections on the

Type I bundle approach C,it is ultimately independent of the numbers of points and paths possibly not equal to each other. It is

given as CXCXC = C3

which is third order. On the Type I bundle the limit is C paths auto connecting C points through O. The total

order is C

3

+C.

Figure1.3again illustrates the topology of theType I and II quantum bundles. The paths of the Type I quantum bundle pass

through O while the paths of the Type II quantum bundle do not.Figure1.3 also showsthat a one-dimensional manifold would

be degenerate.

A Type II quantumbundle that connectstwo point wise entangled points onOAandOB is a quantum connection withall

entanglementpaths not through O and contains C connections. Given anyarbitrary locations of A and B, there is C numbers of

possible points on all possible curves onOA and C forOB for the Type II quantum bundle to connect. Connecting a point on



3

OAwith C number of points on OBwith the Type II bundleis CXC. To connect all the C number of points on OA to all C number of

points on OB, the number of connections with a TypeII quantum bundle for arbitrary points on OA and OBis CXCXC = C3. This

would bean order 3 connection on the manifold. In addition, there is C numbers of paths in the Type I quantum bundle thatauto

connects C number of points on OA and OB since they all originatedat O.The total order of connectionson the manifold is TypeI

+TypeII or an order three plus order one connection andrepresented as C + C3

since they are of a distincttype.These distinct

quantum connections apply to all manifolds that have dimension greater than one.

Below is Table 1 that compares dimensions ofmanifolds to the orders of theType I and II quantum bundleconnectionsfor

arbitrary points A and B.

Dimension of Manifold Order of OA + OBType I Order to connect OA to OBTypeII Comment

2 1st

order or C1

C3

or 3rd

order C+C3

Order Connection

3 1st

order or C1

C3

or 3rd

order C+C3

Order Connection

4 1st

order or C1

C3

or 3rd

order C+C3

Order Connection

5 1st

order or C1

C3

or 3rd

order C+C3

Order Connection

Table 1.

As seen in Table1 any manifold of dimension greater than onehas an order three plus an order one connection. Each set of

entanglement connections represents a degree of freedom and has a mapping onto another distinct manifold. The third order

plus first orderentanglement connection then has four degrees of freedom and maps onto afour-dimensional manifold.TheType

I quantum bundle +Type II quantum bundle gives four dimensions. All quantum-entangled connections of entangled points

contained in the quantum fieldgenerate a four-dimensional manifold.

Below, a two-dimensional manifold has a 3rd

order connection where each color represents a connection. Each order of

connection represents a degree of freedom. Each degree of freedom is mapped to another manifold and becomes a dimension.

Here it is 3.

Figure1.1

R1 R

1 R

1

Manifold with third

order connections Each connection equals a degree

of freedom and is mapped to a

dimension



4

Figure 1.2

Ways of connecting points on Type I Quantum Bundle with Type I and II quantum Bundles:

Two paths of the Type II Quantum Bundle connect two points, B1 and B2 on OB to A1 and A 2 on two paths

of OA. The number of ways to connect the points is 23=8. The Points B1 and B2 auto connect to A1 and A2

by two paths of Type I. The total number of ways to connect this set is 2

3

+2 =10



5

Figure1.3.

What does the Type I and II quntum bundles along with their connections mean in the four-dimensional manifold?

The Type I and II quantum bundles are equivalent in terms of describing point entanglement. The TypeI quantum bundle is

distinct from the TypeII quantum bundle in that the Type I bundle was associated with a single degree of freedom or one

dimension, while the TypeII bundle had three. The three degrees of freedom or dimensions involve the simultaneous quantum

point-wise entanglement on the Type I quantum bundle and forms a subgroup of the four-dimensional manifold. The one

degree of freedom of the Type I quantum bundleinvolve simultaneous quantum connections of its points with each other and O

forms its own subgroup. Both bundles are interconnected however. Let the subgroup of the Type II quantum bundle with three

dimensionsbe known as space and theType I quantum subgroup of one dimension be known as time.The manifold is space-time

and points within are events.

To see the relationships induced by the Type I and II quantum bundles work in thelocal tangent space at event O on the general

manifold. The general manifold is affine and has curvature defined with affine geodesics. The tangent space has a flat affine

curvature. There a quantum entanglement field exists.Thus, there is a Type I quantum bundle through event O and aType II

quantum bundle that connects eventstogether on the Type I quantum bundle.The events in the tangent space-time have four

unique coordinates x1, x2, x3, x4. The coordinates are parameters with no metric units attached and the value of the coordinates

are equivalent to sets of elements given in set theory. Define a coordinate system corresponding to the entanglement

connections defined above whereone coordinate axis is time and the other three axes are space.The orientation of the time

axis is such that its positive direction, in order to sequence the emission and detection events, is between the detectors or OA

and OB and in the direction of A and B from O as measured by a perpendicular segment to the time axis at O.The coordinate

axes originate at event O.

Resolution of the General Quantum Bundle into Type I and II Quantum Bundles

for AOB path sets. The General Quantum Bundle equals Type I plus Type II

Type II quantum bundle do not

pass through O

Type I quantum Bundles pass through O



7

at one time coordinate leads to a breakdown of the distinct frames of reference having thetransformations developed

above.Given above that all distinct frames of referenceequivalently described by quantum-bundles,thisspecial case would then

be a limiting and not equal to relationin order to preserve the distinct frames of references and the transformations associated

with them. Thus, in order to preserve differentiation and the associated structure of frames of reference in the tangent space-

time introducea finite parameter that measures the amount that OA is not diametrically opposed to OB. Since the quantum

particles follow paths to A and B from O that allow space and time coordinates to vary and different frames of reference to

exist implies no particle can exceed a limiting speed. The parameter and speed is unique by logical arguments i.e. if the speedsare different, then the greater speed is in violation. Thus, the speed is unique. In the diametrically opposed case, the speed is

infinite for particles in space-time.Therefore, in the limit of approach to diametric opposition of A and B from O the space-time

would transition from one that has different frames of reference with transformed time and space relationships into a special

case of spaces merged existing at one time.

The other extreme is the case whereOA and OB merge. Again, the Type II and Type I quantum bundles merge. In this case,

however, the timeparameters on an entire time axis present. All the spaces that exist together simultaneously or at different

times on the time axis merge into a set of simultaneous merged spaces at each instant of time. The association of spaces

occurring at two different times on the time axis preserves, however.The result is conservation of the transformation

relationship to another frame of reference. Here the motion of the entangled particles is rest would lead them to the detector

along the time axis while conserving the structure of different space-time frames of viewpoint developed above. Both

entangled particles at rest travel through time at the same rate. If that were not the case then there would be two-time axisone for each particle but the space is four-dimensional however leading to one time axis. Thus, the particles at rest travel

through time at the same rate. The quantum bundles also merge in this case implying that the events all along the time axis are

simultaneous with each other. Since a transformed time axis can be primary, that time axis connects throughout

simultaneously.

The difference between the merge case and the diametrically opposed case in terms of the time parameter is that in the

merged case all time parameters presents at once establishing the space-time relationships whereas in the diametrically

opposed case the time parameters carry simultaneous spaces with it upon each increment of the time parameter. That

relationship is unchanging so the connection between space and time is unchanging and the structure of the space-time with

interrelated space and time relationships developed above no longer holds. The general case is the establishment of the

different frames of reference with transformations of space and time as opposed to a time parameters given for each

simultaneous space.

The two extremes of the Type I and Type II quantum bundles represent the two quantum simultaneous connections. One is

where the all spaces at one time are connected quantum simultaneously and the other represents a quantum simultaneous

temporal connection.This establishes a quantum entanglement basis set have a null tetrad structure. The space-time with the

quantum entanglement basis generates the relationships between different frames of reference with its null tetrad.

In summary, the existence of a quantum field with the topology of simultaneous connections of quantum-entangled particles

with Type I and II quantum bundlesis necessary and sufficient for the existence of a Lorentz-type space-time group.

Figure1.5 and 1.6illustrates the loss of frames of reference when OA becomes diametrically opposed to OBthat leads to a

parameter, which measures the amount of OA not diametrically opposed to OB.This implies the equivalence of frames of

reference. This leads to a finite upper speed for quantum particles where there is a change in the spatial coordinate with

respect to the time coordinate. The parameter is unique because of logical arguments.



8

Figure1.4

Figure 1.5

A O

B

Events a and b are connected quantum simultaneously. Given t1 and t2 are the same for spaces a and

b, implies events a and b are simultaneous with respect to time. This represents an organization of all

event coordinates in the tangent Space-time. Events c and b form a different quantum simultaneous

connection. This implies that there exists a simultaneous space with a common time coordinate but on a

different time axis T because the new connection requires a different organization of events coordinates

with respect to the original coordinates. Events that are concurrent on T occur at two distinct time

coordinates of T. If T2-T1 is a constant, then a frame of reference in T and X is defined.

Spaces with paired connections: All combinations are simultaneous at O. Space is simultaneous in

time. Special case of Frame of reference and collapse of the structure of reference frames.



9

Figure 1.6

TT

B A

Finite

Parameter

suggests

limiting motion

for entangled

articles

Maintaining distinct frames of reference introduces an angle between OA and OB, herein

called . This necessarily finite parameter implies limiting motion rate for entangled

articles.



10

Chapter 2:A Space-Time Description of Quantum Entanglement.

Initially there are three assumptions for the discussion. The final assumptions follow after a correspondence between quantum

entanglements with the initial assumptions is established.

1. There exists a four-dimensional flat manifold where there is athree-dimensional space and aone-dimensional time

and all particles and observers trace by their events and world lines in the manifold.

2. The speed of light is the same for all local observers.

3. The particles in the manifold are quantum-entangled and follow quantum rules for entangled particles in determining

the probabilities for measurement outcomes at detectors.

As an example use quantum-entangled photonsand the attribute to measure is polarization-using polarizers that can have any

relative orientation using two detectors. Assume there is an event O where a pair of quantum-entangled photonsemitted.

Space

Time

O

A B C D

The Entanglement Basis formed where AO and OB are

diametrically opposed in Space-time and OC and OD coincident.

The Type I and Type II Quantum Bundles are co- mingled and

establish a null tetrad basis set. The merge of OC and OD retain

all time and space relationships with simultaneity along the

time axis.OB and OA opposed gives simultaneity across space at

one time.



11

There is a pair of detectors where one is located at A and the other is located at B. Both detectors are at rest relative to O.

Assume that B is closer to O where one entangled photon reaches B first then the other reaches the detector at A. When the

detector at B makes a measurement of polarization on the incoming photon the other photon is simultaneously encoded or

correlated with the resulting information from the first measurement and then becomes untangled. The untangled photon

reaches its detector at A and it is measured. The result of the measurement outcome follows the rules of quantum mechanics

for entangled or correlated photons for all relative orientations of the polarizers. The outcome at detector A reflects by the

measurement of the first photon at some orientation of the polarizer at detector B when it was in an entangled state. Theprocess of non-entanglement is simultaneous on a space-like surface because the quantum rules for outcomes of either photon

when measured with any relative orientation of the detectors must result when the detectors are at an equal distance from the

source. That probability obeys a specific relation with the relative orientations of detectors measuring polarization of the

entangled photons and the probabilistic outcomes follow the same quantum rules as isreadily shown using a time-like surface.

This then leads to the hypothesis that the transmission of quantum information occurs simultaneously in space-time and that

quantum entanglement is closely associated in the fact that there is a distinct time and space side of space-time.

In the paper,space-time diagram cases are when the detectors are at rest with respect to the emitter, when there are observers

in relative motion, and with detectors at unequal distances to illustrate quantum entanglement of two correlated photons on

space-like planes of simultaneity in space-time and an illustration of quantum entanglement on a time-like slice in space-time.

Lastly, the case where there are more than two quantum-entangled photons is considered. Consider the first case where there

are two detectors, A and B, at rest and are at equal distance from theemitter at event O. This is the stationary frame. As shownin Figure2.1, the quantum-entangled photons at each instant of time are on simultaneous space-like planes. When the photons

reach their respective detector, the result of a measurement on one occurs simultaneously with the measurement result on the

other since they are both on a simultaneous space-like plane at one instant of time. More importantly, the results are

simultaneous because of assumption 3 above. Ideally, what happens if they reach their detectors at exactly the same time?

Which one measured first? The answer is that they measure at the same time and the probabilities of measurement results for

each detector are by the quantum rules even if the polarizers have different relative orientation. The simultaneous

transmission of the quantum information links the two detectors and two photons. The probabilities of the measurement

outcomes are correct for both. Quantum uncertainties leads to fuzziness in space-time that could lead to a path of equal

distance to both detectors from event O and assuming both detectors are identical the measurement may also occur at the

same time. The probabilities of measurement outcomes conserve in that instance. The quantum uncertainties also contain

paths that have slight unequal distances or times to where the detectors are located. The rules of quantum mechanics for

entangled photons must still apply in these cases as well. More detail is later in the paper. In Figure2.2,the perspective is the

space-like planes of simultaneity taken at each instant 1 thru 6 from Figure2.1. There the two photons remain entangled or

connected starting at instant 2 at O thru instant 5 where measurement of both occurs. The photons entangle simultaneously at

each instant of time in space. The entanglement remains space-like as long as both photons untouched remain on the

successive space-like slices in space-time. The photons are space-like entangled.



12

Figure2.1

Space

Time

O 1 2

3 4

B A 5

Space-time: stationary observer Simultaneous detection at A

and B on Card 5

6



13

Figure2.2

O

A

B

1 2

4

3

5 6



14

Next, consider the entanglement of two photons from the perspective of a relatively moving observer. Two

entangled photons are emitted from O and a moving observer is looking at the process from his or hers

perspective. Detectors A and B are at equal distance from event O in the stationary frame. Assume that the

moving observer is moving toward detector A and away from detector B. Due to the relative motion toward Athe

space and time axis of the moving observer are tilted toward each other and thus the space-like planes of

simultaneity of the moving observer are tilted compared to those of the stationary observer. This is the result of the extra structure added to the space-time manifold locally by the constant speed of light for all observers. The

moving observer will see an entangled photon first measured at detector Aand the quantum information transmits

on its plane of simultaneity to the other photon travelling towards detector B. That photon will then untangle and

placed into a correlated state with its partner at some event before it arrives at detector B. When the untangled

photon travels on and reaches B it has correlation with the result of the measurement of its entangled partner

when it was measured at A and at detector B the probabilities of its measurement results are correctly given by

the quantum rules for any relative orientation of detectors at B when it arrives. If the observer were moving

toward B, the space-like planes of simultaneity would tilt in the other direction with respect to the stationary

observer. As a result, the measurement of the entangled pair of photons occurs first at detector B. At that event,

the photon traveling toward detector A becomes untangled and correlated on a space-like plane of simultaneity of

the moving observer with the result of the measurement from B. The photon arrives at detector A and theprobable result of a measurement outcome there determined by the quantum rules for entangled particles.

Which of these viewpoints is the correct one if A measured before B or B before A and different outcomes may

result at A or B depending on the relative orientation of the polarizers? The answer is that both viewpoints are

equally valid since the probabilities of measurement outcomes between them are by the same quantum rules for

entangled photons so it still obeys a conservation rule even though there are two different descriptions.As

mentioned above given a quantum uncertainty associated with the fuzziness of space-time this tie in with an

uncertainty associated with the measurement events. The conservation of probabilities must hold true and thus

are independent of space-time uncertainties.

Figure2.3 illustrates the space-time diagram of a relatively moving observer. The space and time axis of the moving

observertilt toward each other and make equal angles with the space and time axis of the stationary observer. Its

space-like planes of simultaneity are tilted with respect to the planes of simultaneity of the stationary observer so

what is simultaneous for the stationary observer is not simultaneous to the moving observer. In the figure it is

shown in the particular case on the space-like plane marked at time t=6 that the measurement of an entangled

photon at detector B occurs simultaneously with an event on the photons world line to detector A according to

the moving observer. At that event, they are simultaneously untangled. The untangled photon is then in a

correlated state and travels on to the detector A where its measurement of polarization occurs with the correct

quantum probabilities of the measurement outcome. Figure 2.4 illustrates the space-like surfaces of simultaneity

for the moving observer.At time t=2 O emits two entangled photons. At t=3, 4 the photons are spatially

entangled. At t=5 one entangled photon is measured at detector B and becomes untangled with the photon

traveling toward detector A which is in a correlate state due to the measurement of the photon at B. At t=6 one

photon not entangled but correlated travels on to detector B and is measured at t= 7. The correct quantum

probabilities of measurement results at B apply there. During the time the two photons entangle together, they

connect on space-like slices of simultaneity. The photons spatially entangle. At t=6 there is only one event from

one photon and thus there is no longer an entanglement. The photon is in a correlated state however. The

quantum entanglement is space-like.



15

Figure2.3

Space

Time

1 2 3 4

..............................

Figure 2.3

Time

7

5 B 6

4 3

O

0000000 7 6

B Space

A



16

Figure 2.4

With respect to T

O

1 2

4

3

5 6 7

A

B



17

Next consider the case of two detectors one at event A the other at event B but are at an unequal distance from

the emitter at event O. The detector at B is closer to O. The observer is at rest with respect to both detectors. Here

the photon travelling toward detector B will be measured first and untangle with its partner at an event

simultaneous on a space-like plane with B on its world line to detector A. The photon then correlates with its

measured partner and will travel on to detector A. There the probabilities of measurement outcomes at detector A

given by the quantum rules for entangled photons. The space-time diagram is in Figure2.5. Shown in Figure2.6

arethe space-like slices of the planes of simultaneity. At time t=2 the entangled photon pair is emitted at event O.

At t=3 and t=4 the two photons are in an entangled state and both are connected together simultaneously on a

space-like plane. When measurement is made at detector B the photon is simultaneously untangled at t=five. At

t=six the one correlated photon reaches the detector at A where the correct probabilities of measurement

outcomes occur. Losing one photon event on its world line signals the end of the entanglement with its partner.

Note that Figure2.6 is similar to Figure2.4 for an observer moving in the direction of detector B when both

detectors are at equal distance from event O. If detector A in any direction is farther away from O than detector B

and both detectors at rest with respect to event O then there is a relatively moving observer that sees

simultaneous measurements at detector A and detector B. Likewise for detector B farther away than detector A.

Both descriptions are qualitatively the same.

All states of motion and all positions of detectors relative to any stationary observers are equivalent for describing

events and quantum measurements at the detectors for any relative orientation of polarizers at the detectors.

With assumption 3, leading to the space-like entanglement of photons and conservation of quantum rules for

entangled photons for all observers and positions of detectors imply the simultaneous connection of quantum

entangled particles on any space-like plane.



18

Figure 2.6

A

B

4

O

0 1 2

5 6 7

3



19

Consider now a slice of space-timetaken parallel to the time axis in a stationary frame. The slice is composed of the

sum of all thespace-like plane slices of simultaneity occurring throughout all instances of time. The one

simultaneous time-like slice then encompasses all observers, geometries of the locations of the detectors, and the

world lines of the entangled photons. The time-like slice then represents all the measurement events and world

lines of the quantum-entangled particles that from the perspective of the time-like slice occur simultaneously

throughout time.

Given that the emitter of entangled photons is at event O, a pair of entangled photons is emitted one toward

detector A and the other toward detector B. Assume that detector B is closer to a stationary observer at event O

than detector A. The world lines of the photons existsimultaneously in time for all the time the world lines exist in

this particular slice. The two photons entangled and their world lines connect simultaneously in time and to their

respective detectors. Thus, the entangled photons and detectors connect simultaneously throughout time as well

as space but the time viewpointgives a direct connected representation of why the entangled particles give the

correct probabilities of the measurement outcomes and the conservation principle at the detectors for any relative

orientation of the polarizers. The assumption that the quantum rules apply for a time-like complete connection

between quantum-entangled photons and their measurements is a more natural one than that explicitly assumed

for a space-like quantum entanglement connection between two events. Figure2.7illustrates how the time-like

slice and how the world lines connect throughout time. The unbarred time and space axis represents a stationary

observer whereas the barred space and time axis represents a relatively moving observer. The space-like planes of

simultaneity of the moving observer is contained in the time-like slice of space-time.Figure2.8 shows a

simultaneous time-like connection. The time-like connection illustrates the simultaneous continuous connection of

entanglement and of the detectors A and B together with event O where the entangled photons emitted. Here

there is a time-like connection.



20

Figure2.7

Time

Time

Space

Space

2

1

B

A

O

B

Events Aand

Band all

axes are

coplanar,

but are

shown in



21

Figure 2.8

O

A

B

A

B

O



22

The above arguments also hold for threeor more entangled particles or photons. There would still be space-

likeplanes of simultaneity at each instance of time to connect the entangled particles or photons. The detectors

(more than 2) could be equidistant from the emitter or all at unequal distances from the emitter. Observers in

various states of motion are equivalent for describing the occurrence. Instead of one time-likenarrow slice through

space-time for two particles, there would be a time-like wider slice defined by the spatial locations of all entangled

particles. The time-like slice could actually encompass all of space-time. The time-like wide slice would thenconnect together all of the simultaneous time-like connections from O to the entangled photons and detectors.

The detectors connect simultaneously in time and the quantum rules for entangled photons would naturally apply.

The time-likespace-time slice mentioned above for two entangled particles is a special case of the time-like slice

for more than two entangled particles.Figure2.9 illustrates the time-like wide slice. It is the sum of all space-like

planes of simultaneity and thus defined for all time. Four entangled photons emitted from event O and travel

toward detectors at A, B, C, and D.

Each space-likeplane of simultaneity at an instant of time would give a space-like connection between all the

entangled particles or photons. All of the previous arguments would apply. In a space-likedescription, one photon

reaches detector B first where it is measured. The other photons untangle themselves on a space-like plane of

simultaneity and correlate with the result of the measurement result on the one photon at B. They travel on to

their respective detectors where the quantum rules for entangled photons give the correct probabilities for

measurement outcomes at the remaining detectors. . In Figure 2.9, there are three planes of space-like

simultaneity shown. At time t=one the photons are all entangled and traveling toward their respective detectors.

At t=two a measurement is performed at detector B and thus all photons are untangled simultaneously and are all

correlated with the measurement result at detector B. At t=three there are only three photon world lines cut by

the space-like plane. The photons are then in an untangled state and travel on to their respective detector where

they are measured and the results are given correctly by the quantum rules for entangled photons.

Figure2.10 illustrates the time-like slice as a 2-D projective plane showing howall the world lines connect

simultaneously in time. Figure2.10 also shows the space-like entanglement. At time t=two where all photons are

entangled and a measure on one of them at detector B is occurring and untangle after measurement occurs. At

t=three the remaining three photons carrying the information of the measurement at B are untangled and travel

on to their respective detectors where they measure. The measurement and subsequent disappearance of one

photon event on a space-like plane of simultaneity signals the end of entanglement between them all. The

remaining photons are in a correlated state with the measurement on the first one.



23

00

Space-like Slices: 1, 2

1

2

3

Time

Time-like Wide

O

Figure 2.9

Space



24

Figure 2.10

A

O B

D C

B

Entangle UntangleTime-like 2-Dimensional

projection of Wide slice

with O, A, B, C, D

Entangled in time

2 3 1



25

An entangled state can be described as a simultaneous connection in space-time through a space-like slice of

simultaneity at a given instant of time and/or a simultaneous connection through time as a time-like slice. These

are the descriptions of the simultaneous untangling of entangled particles or simultaneous measurement of

entangled particles as a space-like phenomenon and a direct link of entangled particles to each other and to their

detectors and thus a linking together of detectors as a time-like phenomenon. Both descriptions must lead to the

correct probabilities of measurement outcomes given by the quantum rules for entangled particles given by thethird assumption.

To have a space-like connection for entanglement from two events, which are the positions of the photons,

requires the assumption of having the correct probabilities of measurement outcomes when the quantum-

entangled particles measure at two detectors whereas it is a natural outcome from the time-like slice viewpoint

because both particles connect in their paths throughout time. Time-like slices slice in any number of ways to

obtain space-like planes of simultaneity for any observer or geometric location of detectors and likewise a time-

like slice builds out of summing space-like planes. Thus,time-like and space-like connections are on the same

footing but the time-like slice provides for a more natural description of assumption 3. Quantum entanglement

may then be responsible for distinguishing a time orientated direction and a three space orientation on a four-

dimensional flat manifold. The constancy of the speed of light gives space-time an additional structure for specific

geometric transforms for observers in relative motion. If the vacuum electrical characteristicschangethe constant

velocity of photons change but the description of space and time in terms of entanglement would remain the

same.Thus, quantum entanglement is more fundamental than the space-time structure given by any constant

finite speed. The generation of a space-time with the formation of a space and a distinct orientated time may then

occur from some sort of constituent universe building blocks each with some natural orientation or spin direction

that are initially amorphous by having quantum entanglement as a basic property in the primitive universe. The

spin direction alignment would then be a key to having a time direction. A locally constant velocity of any

magnitude of light would also be present since the vacuum state would exist in the primitive universe. Particles as

well as space-time constituents and vacuum fluctuations dependent upon the Heisenberg Uncertainty Principle are

also present and they all will conform to the quantum entanglement rules.

Assumption 1 above stated that there is a four-dimensional flat manifold with a distinct one-dimensional time and

three-dimensional space. The discussion that followed showed that quantum entanglement in space and time was

equivalent with the distinction in assumption 1. Quantum entanglement could be the reason for giving a purpose

to and reason for the distinction and so could actually be the cause. To go one natural step farther, quantum

entanglement could be the generator of a space-time from orient able building blocks of the universe. In terms of

the three assumptions at the beginning of the chapter and the discussion of quantum, entanglement related to the

1 + 3 dimensions on the manifold the number of assumptions isone.

Thus,the only assumption required isa four-dimensional flat manifold that contain paths of quantum-entangled

particles.

The view now is that there exists a four-dimensional flat manifold without any distinction as to the types of

dimensions and paths of entangled particles are traceable in the manifold. Due to the entanglement,three planes

must exist in order to slice through the paths of the particles in such a way that only two points in the case of two

entangled particles would exist on the plane in order to have entanglement simultaneity between the two points.

This would define all of the three planes of simultaneity on the manifold. On the other hand,there exists only one

plane, which contains the entire path of both particles required by the simultaneity of quantum entanglement.

Thus, a four-dimensional manifold divides into one plus three dimensions. Quantum entanglement demands that.

The distinction of a one-dimensional direction that includes the paths of both particles would be a result of a



26

simultaneous connection of the pair of entangled particles. The need for the other three planes is that it provides

the other simultaneous point wise connections between a pair of entangled particles. Thus, quantum

entanglement provides a fundamental structure for distinguishing a one-dimension direction from the three other

dimensions. Quantum entanglement then constructs a space-time. Adding an observer independent propagation

that depends upon the properties of quantum vacuum adds structure to the manifold that determines how the

one dimension and the three dimensions are related.

Chapter 3 An Argument for the Simultaneous Transmission of Quantum Information.

The argument in this paper assumes that the quantum information of the measurement result on one photon,

which is one of a pair of entangled photons, transmitted to the other at a finite speed. This leads to an

instantaneous transmission as a way to solve the problems associated with a finite speed for transmission of

quantum information.

The rules of quantum mechanics for measurements on an entangled pair of photons must apply in all frames of

reference in Minkowski space-time. Consider an experiment where there is an emitter of two quantum-entangled

photons at an event O that travel to two detectors A and B that are stationary with respect to event O. When one

of the entangled photons has a measurement at its detector it will signal, the other photon the result of themeasurement so that the other photon acquires a particular correlated state. Once having a state, it will interact

with a polarizer at its detector and the result of the measurement has a determination given by the rules of

quantum probability for polarizer that has any relative orientation. For example, let the relative orientation of a

polarizer at the detectors be 90 degrees, one vertical at B and one horizontal at A and the result of the

measurement at B is up. Then the measurement result on B has transmitted to the other entangled photon and it

becomes down. The down photon by the rules of quantum probability has a 50% chance outcome to the left or

right by the horizontal polarizer at detector A. If the polarizer at detector A was vertical then there would 100%

chance of a down measurement. Even if the polarizer is relative, orientation changed at the last split second the

results still follow the rules of quantum mechanics even outside the light cone.

First, consider the case that quantum information travels at a finite speed. It has been cited that the finite speed of quantum information is as low as 10,000*c to greater than 100,000*c. Let an approximate average of 50,000*c be

taken as the speed of transmission of quantum information. Away from event O where two entangled photons are

emitted there are two detectors A and B stationary with respect to event O. Detector B is 0.01 Light Years or

9.4608X1010

km from event O and detector A is 0.01 Light Years plus 10 Light Seconds or 9.4611X1010

km away from

event O. If the entangled photons emitted in opposite directions, the distance between the detectors is

1.8922X1011

km. After the two entangled photons emitted, one entangled photon reaches detector B first and

passes through a polarizer giving a particular state outcome there. The quantum information is transmitted out at

50,000*c or 1.5X1010

km/s. It takes 12.6s for the quantum information to reach detector A from detector B. With

this particular experimental arrangement, the other photon reaches its detector A 2.6s before the quantum

information arrives. The photon arriving at detector A has not acquired a specific correlated state from the result

of the measurement of its entangled partner at detector B because the quantum information has not arrived.Thus, the photon at detector A is random or no correlated state and could give a different out come from a

measurement there. For example, the two polarizers may be vertical, the photon measured at detector B is up,

the other photon traveling to detector A has not received the information yet, and it may measure as up as well.

This would not be a proper result by the quantum rules for entangled photons. Any similar experimental

arrangement could be set up to give results of this type regardless of any finite speed of transmission of quantum

information as illustrated in Figure 3.1.



27

Figure3.1

Having a finite speed for the transmission of quantum information can lead to difficulties as shown above. Next,

consider the case where the speed of quantum information depends upon the experimental arrangement of two

detectors A and B and an emitter of two entangled photons located at event O in a stationary Minkowski frame.

The two entangled photons emitted in opposite directions from event O. Let detector B be always at a constant

distance from event O given by c*t1 where c is the speed of the photon (light) and t1 is a given time interval.

Detector A on the other hand has a distance from event O that varies. The minimum distance that detector A will

be from event O is c*t1. This will not affect the argument since only the relative positions of the detectors matter.

Each experimental configuration is initially static long enough so that the relative positions of all its parts areknown to each other by some kind of a quantum information transfer process. Then the experiment proceeds.

Assume that the information about the result of a measurement on one entangled photon at one detector

transmitted to the other detector when the other entangled photon arrives there to receive the information. Then

it placed into the proper correlated state and produced outcomes when measured by the rules of quantum

mechanics for entangled states. The two light like world lines one to detector B and the other to detector A form a

right angle at event O and 45 degree angles to the space and time axis on the Minkowski diagram. The hypotenuse

50,000 C= ~1.5 e10km/sec

Time B to A+~12.6 sec

Simultaneous

1/100L.Y=9.4608 e10 km

Distance B to A = 1.89221e11km

1/100L.Y + 10L.S. = 9.4608e10 +10 L.S

km= 9.4611e10

Spa

Time

2.6 sec



28

then represents the world line of the transmission of the quantum information. When detector A is at the

minimum distance c*t1, both detectors A and B are on a space-like plane of simultaneity and the transmission

speed of quantum information becomes instantaneous but the present assumption is based on a finite speed.

Then the space-like plane is an asymptote. However, at that location the world line of quantum transmission is at

a 45-degree angle to both the light like world lines so the 45-degree angle is also an asymptote.

Now detector A increases its distance a small amount from event O from its minimum distance. The world line of

quantum transmission is no longer in the space-like plane of simultaneity but is space-like and thus has a finite but

large speed greater than c. The angle that it makes with the light like world line at detector A becomes less than 45

degrees. As the distance of detector A from event O approaches infinity the world line of quantum transmission

approaches 0 degrees with the light like world line to detector A and approaches parallel to the light like world

line. The speed of quantum transmission approaches c as a minimum. The world line of quantum transmission is

thus always space-like.

Time, t, is time beyond, t1, of detectors A minimum distance to event O or c*t1. Thus as detector A moves farther

away from event O the extra distance is c*t. When detector A is farther away than detector B, the entangled

photon traveling to detector B measured there first at time t1. This also is the time when the other photon reaches

detectors A minimum distance. The quantum information is sent to detector A from detector B with the necessary

speed required so that it arrives there in time, t, when the photon arrives there in time, t. The distance to detector

A from detector B is then c*t1 (-c*(t1+t)) = 2*c*t1+c*t. Thus, when the photon at detector B is measured the

speed of the quantum information needed to reach detector A when the other photon arrives is: VQI =

[2*c*t1+c*t]/t. When time, t, approaches 0, VQI approaches infinity and when t approaches infinity, VQI approaches

c as argued above. Figure3.2 illustrates the details of the experimental setup.



29

Figure3.2

The geometry is in place from assuming that the speed of the quantum information depends upon the

experimental arrangement of the detectors and the emitter so that the quantum information arrives at the

detector when the entangled photon arrives after a measurement on its partner has occurred. Holding detector B

at a constant distance from event O, detector A moved while the experiment is in progress particularly shortly

before a measurement has occurred at detector B. Now that the relative positions of the detectors have changed

among themselves and with respect to event O, knowledge of the new configuration has to know amongst itself.

This requires some sort of quantum information transmission of its relative position from detector A to detector B

so that the speed of transmission of quantum information of the result of a measurement from detector B will be

correct so that the information arrives when the photon arrives at detector A.

Time

Space

t

t B

VQI

A

-C (t1 +t) -Ct1 Ct1

Ct1

is constant V

QI= [2Ct

1 +Ct]/T

t

t

A

A

A45

(t)

Origin of t



30

Consider an example. Detector B is 0.009 Light Years from event O. Detector A is originally at 0.011 Light Years

from O. One of the two photons emitted from event O travels to detector B. 100s prior to arriving at detector B,

detector A blown up. A new detector A is going to be constructed out of pieces that are not separately any sort of

photon measuring device. The new detector A will be located 0.01 light years from event O. Time, t, for detector A

at its original location is (0.011L.Y.-0.009L.Y.)/c = 6.3072X104sec. (1L.Y. = 9.4608X10

12km) Time, t, at the new

location is (0.01L.Y.-0.009

L.Y)/c = 3.1536

X10

4

s. The time required to build the detector and have it ready when thephoton reaches detector B is 6.3072X10

4s-3.1536X10

4s + 100s = 3.1636X10

4s. Assume that the new detector A

completed in half the time or 1.5818X104s.

Once detector A is at the new location, a quantum signal transmitted to detector B in order to give its relative

position but that requires 3.1536X104s. The photon arrives at detector B in 100s and thus at detector B when the

polarized measurement is made the relative position of detector A at its new position is not known. The position

signal arrives at detector B late. The speed of transmission of the quantum information of the result of the

measurement at detector B based on detector A at its original location the last known position of detector A. The

time of transmission of the quantum information of the measurement outcome at detector B is 6.3072X104s. In

the meantime the partner to the photon at detector B arrives at detector A in its new location in time t =

3.1536X104s + 100s = 3.1636X104s which is less than time, t = 6.3072X104s. The quantum information of the result

of the measurement of the photon at detector B is late at arriving at detector A in its new location. The photon

arriving at detector A is not in any correlated state with the one at detector B so the results of a measurement at

detector A may violate the rules of quantum mechanics for entangled photons.

The only way that the quantum information of the result of a measurement on an entangled photon at detector B

is to arrive at detector A in its new location is if detector A at its new location is completed 3.1536X104s before the

entangled photon arrives at detector B. This result is not general and thus the speed of transmission cannot

depend upon the geometry of the detector locations if transmission of all quantum information is finite.Figure3.3

illustrates the geometry of the argument.



31

Figure 3.3

Time

Space

6.3072 e4 sec

=T old

3.1536 e4sec

=T new

Photon B

A new

A old

0.011 L.Y. 0.010 L.Y. 0.009L.Y. 0.009L.Y. Anew completed in 1.5818 e4 Sec

t0



32

The arguments above with the particular experimental arrangements show that having a finite speed for the

propagation of quantum information leads to untenable results. First, there was a particular finite speed of

transmission of quantum information from one detector where a result of a measurement on one entangled

photon transmitted to the other photon. An experimental arrangement was set up in such a way that the

quantum information not transmitted to the other photon in time. This would be the case for any finite speed of

transmission of quantum information since an experimental arrangement could be set up to produce the sameoutcome.

If the speed of transmission of quantum information depends upon the geometry of the locations of the detectors

then there are problems associated with this assumption. The particular example where there was a relatively

quick change in the location of one of the detectors before measurement of one entangled photon occurred

illustrated a problem. The same problem can occur if the change in a detector location occurs after a measurement

on an entangled photon occurs while the quantum information transmission of the detectors new position is

somewhere along the way.

How fast would quantum information need to travel then to solve a problem associated with finite transmission

speeds of quantum information? Consider the same situation where the speed of transmission of quantum

information depends upon the experimental arrangement of the detectors. The largest possible experimental

arrangement would be one where two photons entangled across the universe. That distance would be 2*13.7 =

27.4 billion light years if the two photons emitted in opposite directions from event O to the limits of the

observable universe. In kilometers, it is 2.55X1023

km. The difference in the distance between the two legs of travel

then would determine a speed for transmission of quantum information. For instance if the difference in the time

of arrival between the two entangled photons at their respective detectors is 1 second then the speed that

quantum information has to travel is 2.55X1023

km/s in order for the quantum information of the measurement

outcome at one detector to reach the other when the other photon arrives.

As an experiment assume the difference in distance between the two detectors, A and B, after billions of years of

set up time is 1cm. Assume detector A is 1cm farther than detector B. That represents a difference in the time of

travel of a photon of 1cm/3X1010

cm/s = 3.33X10-11

s. The photon will arrive at detector B 3.33X10-11

s before itspartner arrives at detector A. The speed for the transmission of quantum information then has to be

2.55X1023

km/3.33X10-11

s = 7.65X1033

km/s for the quantum information to arrive when the photon does at

detector A. Assume as in the scenario above detector A is moved closer to the source by 0.5cm to position A at

the same time as one of the photons arrives at detector B. The movement process occurs in a time equal to say

1.67X10-11

s. One of the entangled photons reaches detector B 1.67X10-11

s before the other reaches A. The

information of detector A being at its new position reaches detector B in 1.67X10-11

s. Again, it is late. At detector B

when the measurement is made the speed of transmission of the quantum information is based upon detector As

position and will be late arriving at detector A. The photon arriving at detector A has no knowledge of the

measurement outcome at detector B and thus is not in a correlated state. The only way for this scenario to work is

if detector A is in position 1.67X10-11

s prior to the entangled photon arriving at detector B. Again, this is not a

general result so having a finite speed for the transmission of quantum information leads to problems.

The argument continues on to a limit determined by quantum uncertainty of position or time. That would be

random fluctuations of the positions of the detectors and time of measurement. Each outcome of a measurement

of position is determined probabilistically and so each measurement of position would lead to slightly different

outcomes. The problems cited above would still exist even for the extremely high speed for the transmission of

quantum information. The conclusion is that the speed of transmission of quantum information is in principle

instantaneous.



33

Next, consider the case where the transmission of quantum information of the result of a measurement on one

photon instantaneously transmits to the other placing it in a correlated state. Then the measurement of that

photon would lead to the correct probable outcome given by the quantum rules for entangled photons.

Figure 3.1 illustrated the geometric relations of two detectors, A and B, and the space-like world line for a

transmission speed of 50,000*c. As can be seen from the diagram and the corresponding analysis the information

transmitted to detector A of the measurement results of one photon of an entangled pair at detector B was 2. 6s

late. The photon traveling to detector A would not correlate. If the quantum information is given simultaneously

then the entangled photon traveling toward detector A would receive that information at event A and be placed

in a correlated state 10s prior to arriving at detector A. See Figure3.4. When it arrives at detector A the correlated

photon measures and its outcome is by the quantum rules for entangled photons. This would be true for detectors

at equal distance form event O, the emitter, as well as for any difference in the distances of the detectors from

event O.

In Figure 3.3 along with the corresponding analysis showed that moving a detector A(old) to A(new) within certain

time constraints leads to possible untenable results from a measurement at detector A (new) according to the

quantum rules for entangled photons. Figure3.3 redrawn in Figure3.4 showing the inclusion of a world line of

simultaneous creation of a correlated state at event A (simul) on one entangled photon when its partner measures

at detector B. Thus the photon traveling toward the detector located at A (old) will be correlated when it arrives at

the detector A (new) after the detector at A (old) is moved to A (new) within 3.1536X104s. If the detector at A (old)

is placed at A (new) at a time greater than 3.1536X104s and less than 6.3072X10

4s which is after the correlated

photon passes the position of A (new) the photon will not of course be measured at the detector at A (new) or A

(old). The photon however will be in a correlated state given by the outcome of the measurement of its entangled

partner at detector B determined by the quantum rules for entangled photons. Placing another detector farther

away in the path will confirm the correlation. A finite speed for the transmission of quantum information can lead

to violation of quantum rules for entangled particles. However, simultaneity of a correlation state of an entangled

photon from a measurement on its partner always leads to the entanglement following the quantum rules for

entangled photons even for an experiment the size of the observable universe.



34

The arguments given above leads to the need for instantaneous transmission of quantum information or that

measurement on one of an entangled pair of photons leads to a simultaneous placement of the other into a

50,000 C= ~1.5 e10 km/sec

Time B to A+~12.6 sec

Simultaneous

OB=.01 L.Y=

~9.4608 e10 km

Distance B to A = 1.89221 e11km

OA=.01 L.Y +10 L.S

~9.4611 e10km OA =.01 L.Y ~9.4608e10 km

Spa

2.6 sec

Figure 3.4

A

A B



35

correlated state. This is true for a correlation through space as shown. The limit of a relative spatial distance

measurement between two detectors is the inherent quantum uncertainties associated with the probable

outcomes of measurement of their relative positions. Moving the detectors in space-time along the null path of

the photon requires both a space and time location change relative to the stationary observer. The simultaneous

placement of an entangled photon into a correlated state after a measurement on its partner as described above

occurs on a space-like plane of simultaneity but there is also a movement of the detectors in time as well. Thus, anequally good description of the simultaneous placement of an entangled photon into a correlated state occurs

simultaneously throughout the time of their existence as well. The limit in the relative temporal locations of the

two detectors is the inherent quantum uncertainties in the measurement of time. Thus, there is a spatial as well as

a temporal link between the two entangled photons. The photons entangled in the complete space-time and the

limit is the inherent quantum uncertainty of space-time itself. Since the outcomes of measurements on entangled

pairs of photons must follow the rules of quantum mechanics for entangled photons, the space-time link between

a pair of entangled photons is in principle instantaneous or simultaneous across space from where one entangled

photon is located to the other and during all their time of existence until both being absorbed in measurements.

Quantum entanglement is independent of those uncertainties.

As a final experiment let the emitter of the pair of entangled photons explode after the photons emitted. Is the

time link between the two entangled photons through the emitter broken? After the photons emitted they

entangle and the outcomes measured by a pair of detectors must follow the quantum rules for entangled photons.

Thus, the temporal link is not broken. The space-time event of their emission is what is important since they

entangled there. Figure3.6 illustrates the temporal link between two entangled photons.

In conclusion, entangled particles simultaneously linked together in a four-dimensional flat manifold leads to

dividing the manifold locally into 1 plus 3 dimensions. These dimensions identify as a space and a time. The

entangled particles link in space-time simultaneously. That the link is simultaneous or instantaneous leads to the

quantum entanglement transcending any boundaries of space-time. To ascribe a finite speed to the transmission

of quantum information during measurements on entangled particles is untenable and so time and space does not

apply in determining any sort of a transmission speed. Quantum entanglement besides being instantaneous does

leave its mark as paths when viewed from the space-time perspective since objects have different event locations.

The quantum entanglement effect occurs in a domain more fundamental than that of space-time and is actually

the generator from some fundamental building blocks. Virtual particles in a quantum vacuum create as entangled

particles that obey the quantum uncertainty principle. The quantum fluctuations of space-time manifest itself

strongly on small scales of distance and time or at extreme high energies at the Plank scale, which are at the limits

of classical space-time of general relativity. At the Plank scale quantum, fluctuation effects would produce

fluctuations, which have extreme gravitational space-time curvatures. Chaos would upset coherent connections in

space-time itself at that level. Quantum entanglement generates and transcends space-time is then necessary to

maintain coherent causal structure and the distinct dimensions from fundamental building blocks in a chaotic

world of extreme quantum fluctuations of space-time



36

Figure3.5

Space

Time

O Temporal Link: OA +OB

A

B

space time from quantum entanglement 201103011710

Documents