This repository features documentation, code, and instructions to perform an at-home demonstration of quantum entanglement. It works by detecting statistical correlations in the Compton scattering of high-energy entangled photons produced from an electron positron matter-antimatter annihilation event.
This experimental design is based on an experiment performed and described by George Musser on his blog and as featured in a 2013 article in Scientific American.
This experiment has been updated to take advantage of more recent tools and technology:
- It uses two MightyOhm Geiger Counter Kit which enable easy wiring to an Arduino microcontroller.
- It uses an Arduino-based ESP32 with headers, which enables easy wiring to the Geiger counters for coincident detection, as well as data logging by connecting to a computer over USB.
- It uses LEGO-compatible blocks to make the positioning of detectors, the positron source, and aluminum scattering blocks both flexible and repeatable.
Above is an image of the assembled kits, both wired into an Arduino, and connected to a computer via USB for logging and analysis.
Aside from demonstrating Quantum Entanglement (recognized in the 2022 Nobel Prize in Physics, this experiment also demonstrates a number of other outstanding breakthroughs in 20th century science:
- Ernest Rutherford's discovery of the radioactive transformation of elements earning him the 1908 Nobel Prize in Chemistry as this experiment involves the radioactive transformation of Sodium metal into Neon gas.
- Arthur Compton's discovery of Compton scattering winning him the 1927 Nobel Prize in Physics as this experiment directly relies on Compton Scattering gamma rays off of Aluminum blocks.
- Albert Einstein's proof that light is made of photons, through his analysis of the photoelectric effect, earning him the 1921 Nobel Prize in Physics as this experiment's Geiger-Müller tube can only detect photons carrying enough energy to dislodge electrons from the tube's wall.
- Paul Dirac's prediction of, and Carl Anderson's later experimental discovery of antimatter and in particular, positrons earning Dirac and Anderson the 1933 and 1936 Nobel Prizes in Physics, respectively. This experiment uses positrons, and their antimatter annihilation to create an entangled photon pair. Incidentally this also demonstrates Einstein's mass-energy equivalence (E = mc2) as the energy of the gamma rays equals the rest-mass of the electron and positron (511 keV).
- Victor Hess's discovery of cosmic rays which earned him the 1936 Nobel Prize in Physics as when these two Geiger counters are stacked vertically, it functions as a cosmic ray telescope, able to detect muons that travel both Geiger tubes.
- Walther Bothe's invention of the Coincidence Method which earned him the 1954 Nobel Prize in Physics as this experiment uses the simultaneous detections of two detectors to determine when that two photons resulted from the same radioactive decay/annihilation event. This is the same principle upon which PET scans work.
In total, the experiment can be put together for a total cost of around 500 USD (pricing information as of mid 2026).
Here is a link to the parts list.
Note: If one already has the equipment for soldering it can be done for much less.
Warning
This project involves high voltages, lead soldering, and radioactive sources. Follow all applicable laws and regulations regarding, source-license requirements, radiation-safety practices, and apply lead-handling and ventilation precautions when soldering. Be sure to familiarize yourself with safe and legal practices before obtaining, handling, or disposing of any radioactive sources.
This experiment uses a kit to make each of the two Geiger counters. This requires some soldering. The kits arrive with the following parts:
After soldering and attaching some screws, the assembled Geiger counters look like this:
The instructions for assembling the Geiger Counter kits can be found at this link.
Conveniently, each Geiger Counter has pin headers which send a 100 microsecond pulse which can be interpreted by an Arduino device with headers. Using a breadboard together with male-to-female jumper wires, the Geiger counters can be directly wired to the Arduino device without soldering.
The Geiger counters are sensitive to beta and gamma radiation, and any significant source of these can trigger the counter. The counters will also detect background radiation at a level of around 20 counts per minute at sea level. By arranging the detectors vertically, simultaneous detections will trigger about once a minute due to cosmic-ray-generated muons passing from the upper atmosphere down to earth and passing through both detectors.
Below is a link to a video demonstrating testing of the two detectors with a 1 μCi test source of Na-22. A source of positrons, such as Na-22, is required in order to perform some of the entangled photon pair experiments detailed later in this document.
As a sanity check to ensure proper function of the Geiger counters, you can expect numbers around these approximate values:
- Expect 15 - 25 Counts Per Minute for Geiger Counters at sea level without proximity to a radiation source (higher rates at greater elevations).
- Expect 800 - 1,200 Counters Per Minute when 1 μCi test source of Na-22 is within close proximity to the Geiger tube.
- Expect ~1 CPM of simultaneous pair detections when tubes are stacked one on top of the other at sea level (higher rates at greater elevations).
Before the Arduino device will work as intended for this project, it must be loaded with software. To do this, you must have the Arduino IDE installed.
You may download the Arduino IDE for your operating system from this link.
Once it is installed, connect the Arduino device to your computer via a USB-C cable, make sure the cable supports data (some USB cables are for power only).
Then open the Arduino IDE by opening the micro-controller source code (known as a sketch) located in the microcontroller-code directory.
Then select the board from the drop down list at the top of the interface:
Before you can compile the sketch you must add the appropriate library dependencies. To do this, click on the icon that looks like a set of books on the left hand side of the IDE, to make the Library Manager appear, then in the search box, search for, and then add, each of the following libraries:
- Adafruit BusIO
- Adafruit GFX Library
- Adafruit SSD1306
- DFRobotDFPlayerMini
Once each of the library dependencies have been added, you can compile and upload the code to the Arduino device. To do this, click the icon at the top left which looks like a right-ward facing arrow. Note that it may take a few minutes to compile and transfer the code. Once it does, you will see lights flicker on the Arduino device and then it should simply show a solid blue LED light up. This indicates the sketch has been successfully compiled and transferred to the device and it is now running.
The following represents the pin diagram for the Nano ESP32 with headers:
To wire the ESP32 to the two Geiger counters, a LED, a buzzer, and an optional speaker output, connect the wires to the pins as shown below:
Arduino Nano ESP32
TOP VIEW
USB-C connection to Computer or Power Supply
↑
LEFT HEADER RIGHT HEADER
─────────── ────────────
D13 D12
OLED, buzzer VCCs → 3V3 D11
B0 D10
A0 D9
A1 D8
A2 D7
A3 D6 ← buzzer signal
OLED SDA → A4 / SDA D5 ← 330 Ω → LED anode
OLED SCL → A5 / SCL D4
A6 D3 ← 1 kΩ → Geiger RIGHT J6 pulse
A7 D2 ← 1 kΩ → Geiger LEFT J6 pulse
VUSB GND ← Geiger GNDs, LED cathode, buzzer GND
B1 RESET
OLED GND → GND D0 / RX0
VIN D1 / TX0
The end result should look something like the following when all wired up:
Note when connecting the pulse wires to the Geiger counter kit, the MightyOhm Geiger Counter has a section labeled J6 Pulse, with 3 pins Left to Right:
| Pin 1 | Pin 2 | Pin 3 |
|---|---|---|
| VCC | PULSE | GND |
Note: Pin 1 is marked with a small white triangle. Pin 1 is not used and not connected to the ESP32.
Only Pin 2 and Pin 3 on each Geiger Counter needs to connect to the breadboard. Pin 2 on the Left Geiger counter should connect to D2 while Pin 2 on the Right Geiger Counter should connect to D3. The grounds (Pin 3) on each Geiger counter should connect to GND on the ESP32. Ideally, there should be a 100 kΩ pull-down resistor between the Pulse lines D2 and D3 and GND. This will increase the stability of the signal and prevent false positives due to loose wires, static build up, or the wires picking up signals acting as antennae.
To verify operation, you can test with either a positron source placed between the detectors as shown in this video:
After everything is wired:
- Power on both MightyOhm Geiger Counters by flipping the power switch
- Connect USB power to the Arduino board from a computer using a USB-C data cable
- Start python logger to read data over USB
You should see events on the screen each time either Geiger flashes.
Or alternatively, you can stack the detectors one on top of the other, as is shown here:
And wait for a cosmic ray muon to trigger simultaneous detection. A simultaneous detection event should trigger a flash and beep, as well as the OLED display to update the count of the number of simultaneous detections.
For playback of an arbitrary sound file as an audio alert upon detection of a photon pair, the following:
First, obtain a microSD card and make sure it is formatted with the FAT32 filesystem. If it is not already formatted with this file system, you will need to reformat it. The size should be 16 GB or less.
Add the desired MP3 file to be played to the following path on that microSD card: /MP3/0001.mp3
That is, first create a directory named MP3 at the root level of the microSD card's filesystem, then place the MP3 file in that directory, and rename it to 0001.mp3. This file will then play at the moment of any simultaneous detection by the Geiger counters.
All wiring between the ESP32 and the DFPlayer is done on the left-side of the DFPlayer:
Connect via jumper wires the following four pins from the ESP32 to the DFPlayer:
Nano ESP32 5V/VBUS/VIN-side → DFPlayer VCC
Nano ESP32 GND → DFPlayer GND
Nano ESP32 A2 pin → 1 kΩ resistor → DFPlayer RX
Nano ESP32 A1 pin → DFPlayer TX
In the end, the DFPlayer Mini should appear like this:
DFPlayer Mini
TOP VIEW
LEFT HEADER RIGHT HEADER
─────────── ────────────
ESP VIN → VCC BUSY
ESP A2 → 1 kΩ resistor → RX USB-
ESP A1 → TX USB+
DAC_R ADKEY_2
DAC_I ADKEY_1
speaker terminal 1 → SPK_1 IO_2
ESP GND → GND GND
speaker terminal 2 → SPK_2 IO_1
Note that polarity to the speaker terminals does not matter.
DFPlayer SPK_1 → speaker terminal 1
DFPlayer SPK_2 → speaker terminal 2
The speakers should be 3 Watt, 8 Ohm speakers. Note that JST-PH 2.0mm 2 Pin Male Connectors may simplify the connection of speakers to a breadboard, especially if the speakers come with JST-PH 2.0 connectors.
Once the speakers are wired correctly to the DFPlayer, you can verify that the MP3 file plays correctly upon a coincidence detection, as shown in this video:
This project comes with scripts to collect and analyze data, and even comes with a number of pre-set experiments to perform. These scripts, and experiments, can be found in the experiments directory. The two scripts are:
log_geiger.py
analyze_geiger_run.py
These are python scripts and require python3 in order to run.
Before attempting to run these commands, you may need to setup your python3 environment first. For example, by running the following set of commands:
$ git clone https://github.com/jasonkresch/quantum-entanglement.git
$ cd quantum-entanglement
$ ./setup.sh
$ source .venv/bin/activateWhen the Arduino device is connected to a computer via USB, the log_geiger script will connect to it and start outputting data to the screen. Each time either the left or right detector registers a detection event, it will output which detector sent the signal, and a microsecond-accurate timestamp of when it occurred. Periodically, the script will also report summary data.
The detection event lines are prefaced with E while the summary report lines are prefaced with S:
Events Sample Output:
E,123456789,L,2,0,0
E,123456843,R,3,1,0
The fields are: E, t_us, detector (L/R), pin (2/3), prompt_matches, delayed_matches.
Summaries Output:
S,60000000,895.000,902.000,2.700,2.500,895,902,3,2,0
The fields are: S, t_us, left_cpm, right_cpm, prompt_cpm, delayed_cpm, total_left, total_right, total_prompt, total_delayed, dropped.
When you have collected sufficient data, you can end the logging script by sending an exit command (generally Ctrl+C on most systems).
Note that running this script requires specification of the USB port to which the Arduino device is attached, this can vary from system to system, below are some examples:
# Windows
python3 log_geiger.py --port COM5 --out output_file.csv# Linux
python3 log_geiger.py --port /dev/ttyACM0 --out output_file.csvOn Linux, typical USB device names can by found by looking at: /dev/ttyACM* or /dev/ttyUSB*
# macOS
python3 log_geiger.py --port /dev/cu.usbmodem206EF13166CC2 --out output_file.csvOn MacOS, typical USB device names can by found by looking at: /dev/cu.usbmodem* and /dev/cu.usbserial*
Note that the particular USB device name can vary from system to system. The Arduino IDE displays the exact device name to when you correctly select the board.
After collecting data and storing it to an output file, for example output_file.csv the analyze script can be run to report various statistics:
python3 analyze_geiger_run.py output_file.csv \
--out-prefix run_perpendicular_geometry \
--run-id R1 \
--half-window-us 3 \
--center-us 0 \
--orientation perpendicular \
--geometry "Al blocks, 90-degree scatter" \
--detector-separation "100mm" \
--source-position "centered" \
--shielding "none" \
--aluminum "present" \
--notes "overnight run, no bumps observed"This will result in the following output to the screen:
The output information includes the run duration, total number of left and right events, as well as counts per minute for both detectors. It then reports, for various time windows ranging from 1 microsecond to 1000 microseconds, how many coincident events were observed within each of those windows. Generally the 3 microsecond half-window is the most robust, as it is narrow enough to register all genuine coincidences, without being so wide that it includes spurious events that occur near the same time but are not genuinely correlated. Note that this setting means any other detection event happening within -3 µs to +3 µs within another event is counted as simultaneous.
The rate of these spurious events are continuously estimated by looking for coincident events if the right or left detector's reported events are time-shifted by a significant period (say half a second). These are reported as lag counts and should be subtracted from the raw observed counts to yield a more accurate net count.
In addition, it will also generate the following files:
<out-prefix>_signed_delta_histogram.png
<out-prefix>_window_scan.png
<out-prefix>_window_scan_summary.csv
<out-prefix>_run_log.csv
<out-prefix>_run_log.json
<out-prefix>_run_log.txt
Where <out-prefix> was the parameter supplied to the script under --out-prefix.
Here is an example of a generated histogram. It shows a genuine signal within the ±5 microseconds bucket, indicating a true excess of correlated events not observed for any of the other greater time-difference buckets:
The minimum experiments required to demonstrate quantum entanglement are defined below. Note that for each of these experiments, a sub-directory has already been setup within the experiments directory, which contains a bash script to log and analyze data for that run.
Phase 0 tests are meant to validate the equipment, establish a baseline for environmental background radiation, and verify detection of coincidences. These tests are not strictly required to prove quantum entanglement, but are important to run before proceeding to ensure the equipment is working as expected.
- 0A: Detectors close, no source present (estimate background radiation, validate equipment and electronics working)
- 0B: Detectors horizontally separated, no source present (expect lower cosmic ray coincident effect)
- 0C: Detectors vertically stacked, no source present (expect high cosmic ray coincidences, crude cosmic ray telescope)
The expected results are that general CPM rates should be more or less consistent regardless of placement, but that coincident event detection rates should drop when the detectors are separated by a larger horizontal difference in test 0B and should sharply increase when the detectors are stacked vertically in 0C.
The next phase is meant to demonstrate that entangled photon pairs are emitted in directions that are 180° off from one another, heading in opposite directions along the same axis.
- 1A: Detectors in demonstration position, no source (establish baseline environmental background radiation and coincidences)
- 1B: Positron source is added centered and inline with axis between the detectors (measure increase in singles counts and coincidences)
- 1C: Positron source is moved off-axis from the line between the detectors (expect small drop in singles detections, but large drop in coincidences)
The expected result is that coincident detections sharply increase from 1A to 1B when the positron source is placed exactly between the two detectors, but that the coincident rate drops when the source is raised relative to the detectors (taking it off-axis) and making it unlikely for two entangled photons traveling in opposite directions to reach both detectors.
This phase along with the next is where properties of entangled photons are measured. It uses a technique known as Compton Polarimetry. Because the polarizations of the entangled photons are perpendicular to one another (offset by 90° relative to the other) when one of these photons scatters, its preferred scattering angle will be along a plane that is perpendicular to the preferred scattering angle of its entangled partner photon.
By placing aluminum blocks in the path of the photons, and placing detectors in either the same plane (parallel) or in a perpendicular plane (perpendicular) we can expect to observe different rates of coincident detections.
- 2A: Detectors in Parallel Geometry Positions, no source present (establish baseline background radiation)
- 2B: Detectors in Parallel Geometry Positions, source present without aluminum blocks (establish baseline coincidences without effect of scattered photons)
- 2C: Detectors in Parallel Geometry Positions, source present with aluminum blocks (establish additional coincidences from scattered photons in parallel case)
The rate of coincident detections for the parallel case is expected by theory to be lower by an amount of roughly 2.6× compared to the perpendicular orientation of the detectors.
In this phase, we establish baseline background levels with and without the positron source, and detection rates with and without the presence of the aluminum blocks. But unlike Phase 2, in this case the detectors are placed in planes that are perpendicular to each other. This maximizes the rate of detection of coincidences for entangled photon pairs that are scattered by interacting with electrons in the aluminum blocks.
- 3A: Detectors in Perpendicular Geometry Positions, no source present (establish baseline background radiation)
- 3B: Detectors in Perpendicular Geometry Positions, source present without aluminum blocks (establish baseline coincidences without effect of scattered photons)
- 3C: Detectors in Perpendicular Geometry Positions, source present with aluminum blocks (establish additional coincidences from scattered photons in perpendicular case)
We expect that after accounting for and subtracting background events, and detection levels without the aluminum blocks present, that the observed number of detections in experiment 3C will be 2.6× greater than was observed in experiment 2C after similarly subtracting out background events.
The following section presents a summary of experimental data from the phase 2 and phase 3 runs, and concludes with evidence of entanglement. Together these represent over 75 hours of data collection, and resulted in over 200 megabytes worth of raw event timing data.
The following are data from parallel geometry runs.
Run summary
-----------
Input file: 2A.csv
Duration: 36624.2 s = 610.40 min = 10.173 h
Left events: 14,644
Right events: 14,885
Left CPM: 24.0
Right CPM: 24.4
Window scan
-----------
half_window_us prompt_count avg_lag_count net_count approx_z li_ma_z prompt_cpm lag_cpm net_cpm
1 0 0.000 0.000 NaN 0.000 0.000 0.000 0.000
2 2 0.000 2.000 1.414 3.203 0.003 0.000 0.003
3 2 0.000 2.000 1.414 3.203 0.003 0.000 0.003
5 2 0.000 2.000 1.414 3.203 0.003 0.000 0.003
7 2 0.000 2.000 1.414 3.203 0.003 0.000 0.003
10 2 0.000 2.000 1.414 3.203 0.003 0.000 0.003
Run summary
-----------
Input file: 2B.csv
Duration: 44309.5 s = 738.49 min = 12.308 h
Left events: 198,362
Right events: 204,420
Left CPM: 268.6
Right CPM: 276.8
Window scan
-----------
half_window_us prompt_count avg_lag_count net_count approx_z li_ma_z prompt_cpm lag_cpm net_cpm
1 2 2.833 -0.833 -0.379 -0.504 0.003 0.004 -0.001
2 17 4.750 12.250 2.627 4.070 0.023 0.006 0.017
3 19 6.083 12.917 2.579 3.930 0.026 0.008 0.017
5 24 10.000 14.000 2.401 3.545 0.032 0.014 0.019
7 28 14.167 13.833 2.130 3.078 0.038 0.019 0.019
10 36 19.250 16.750 2.253 3.237 0.049 0.026 0.023
Run summary
-----------
Input file: 2C.csv
Duration: 41085.5 s = 684.76 min = 11.413 h
Left events: 193,788
Right events: 200,681
Left CPM: 283.0
Right CPM: 293.1
Window scan
-----------
half_window_us prompt_count avg_lag_count net_count approx_z li_ma_z prompt_cpm lag_cpm net_cpm
1 1 3.250 -2.250 -1.091 -1.422 0.001 0.005 -0.003
2 21 5.167 15.833 3.095 4.874 0.031 0.008 0.023
3 23 6.500 16.500 3.038 4.701 0.034 0.009 0.024
5 24 10.000 14.000 2.401 3.545 0.035 0.015 0.020
7 30 13.667 16.333 2.472 3.612 0.044 0.020 0.024
10 34 20.500 13.500 1.829 2.594 0.050 0.030 0.020
The following are data from perpendicular geometry runs.
Run summary
-----------
Input file: 3A.csv
Duration: 35696.6 s = 594.94 min = 9.916 h
Left events: 14,063
Right events: 14,151
Left CPM: 23.6
Right CPM: 23.8
Window scan
-----------
half_window_us prompt_count avg_lag_count net_count approx_z li_ma_z prompt_cpm lag_cpm net_cpm
1 0 0.000 0.000 NaN 0.000 0.000 0.000 0.000
2 5 0.000 5.000 2.236 5.065 0.008 0.000 0.008
3 5 0.000 5.000 2.236 5.065 0.008 0.000 0.008
5 5 0.083 4.917 2.181 4.517 0.008 0.000 0.008
7 5 0.083 4.917 2.181 4.517 0.008 0.000 0.008
10 5 0.167 4.833 2.126 4.195 0.008 0.000 0.008
Run summary
-----------
Input file: 3B.csv
Duration: 39149.7 s = 652.49 min = 10.875 h
Left events: 193,816
Right events: 183,066
Left CPM: 297.0
Right CPM: 280.6
Window scan
-----------
half_window_us prompt_count avg_lag_count net_count approx_z li_ma_z prompt_cpm lag_cpm net_cpm
1 1 3.250 -2.250 -1.091 -1.422 0.002 0.005 -0.003
2 19 4.833 14.167 2.902 4.551 0.029 0.007 0.022
3 23 7.333 15.667 2.845 4.336 0.035 0.011 0.024
5 26 11.083 14.917 2.450 3.607 0.040 0.017 0.023
7 29 14.417 14.583 2.213 3.204 0.044 0.022 0.022
10 36 20.083 15.917 2.125 3.039 0.055 0.031 0.024
Run summary
-----------
Input file: 3C.csv
Duration: 45934.5 s = 765.57 min = 12.760 h
Left events: 231,635
Right events: 226,705
Left CPM: 302.6
Right CPM: 296.1
Window scan
-----------
half_window_us prompt_count avg_lag_count net_count approx_z li_ma_z prompt_cpm lag_cpm net_cpm
1 2 3.333 -1.333 -0.577 -0.763 0.003 0.004 -0.002
2 35 6.000 29.000 4.529 7.470 0.046 0.008 0.038
3 37 8.083 28.917 4.307 6.886 0.048 0.011 0.038
5 42 12.833 29.167 3.939 6.036 0.055 0.017 0.038
7 46 17.083 28.917 3.641 5.448 0.060 0.022 0.038
10 54 23.417 30.583 3.476 5.108 0.071 0.031 0.040
Let us review a summary of the data to determine if we have witnessed any evidence of quantum entanglement in the simultaneously detected photon pairs.
Taking the 2 microsecond time window from each of the above, we observe the following rates in terms of events per hour:
| Run | Runtime (Hours) | Net Events (at 2µs) | Events/hr |
|---|---|---|---|
| 2A - Parallel No Source | 10.173 | 2.000 | 0.197 |
| 2B - Parallel No Blocks | 12.308 | 12.250 | 0.995 |
| 2C - Parallel | 11.413 | 15.833 | 1.387 |
| 3A - Perpendicular No Source | 9.916 | 5.000 | 0.504 |
| 3B - Perpendicular No Blocks | 10.875 | 14.167 | 1.303 |
| 3C - Perpendicular | 12.760 | 29.000 | 2.273 |
A few things stand out from this. Despite both geometries having similar Right and Left CPMs (around 300), the No Source perpendicular has a significantly higher background coincidence rate (0.504 vs. 0.197 events per hour). This may be due to the fact that the elevated position of one of the detectors made it more sensitive to cosmic rays.
As expected for both geometries, the addition of the aluminum blocks increased the rate of coincident detections:
- The Perpendicular Geometry (3C) 2.273 events/hr > The Perpendicular Geometry without Blocks (3B) 1.303/hr
- The Parallel Geometry (2C) 1.387 events/hr > The Parallel Geometry without Blocks (2B) 0.995/hr
This indicates that the aluminum blocks, when present, are scattering the photons towards the detectors.
Also as we would expect, the addition of aluminum blocks in the perpendicular geometry has a greater net effect increase, than it does in the parallel geometry:
- Perpendicular: 3B No Blocks 1.303 events/hr → 3C With Blocks 2.273 events/hr, net increase of 0.970 events/hr.
- Parallel: 2B No Blocks 0.995 events/hr → 2C With Blocks 1.387 events/hr, net increase of 0.392 events/hr.
These values: 0.970 events/hr and 0.392 events/hr, best reflect the raw data after subtracting out background noise of detections that come straight from the positron source without being scattered by hitting an aluminum block, and so are the most useful values for direct comparison.
We observe that for the ratio of these values, between the the perpendicular geometry (0.970) is 2.47× the value for the parallel geometry (0.392). So in other words, the effect in increasing detection events by adding the blocks is 2.47× greater for the perpendicular geometry.
Of note, this value is consistent with, and close to, the idealized theoretical ratio of 2.6× for annihilation photons Compton-scattered at 90°.
According to the Klein–Nishina Compton-scattering formula, a 511 keV annihilation photon scattered at 90° has polarization analyzing power a = 2/3. Thus for an idealized photon pair created from an electron-positron annihilation in which both photons are Compton-scattered at 90°, the perpendicular-to-parallel coincidence ratio is:
(1 + a^2) (1 + (2/3)^2) (1 + 4/9) 13
R = __________ = _____________ = _________ = ____ = 2.6
(1 - a^2) (1 - (2/3)^2) (1 - 4/9) 5
This bias in detection rates after Compton scattering suggests that the photons are not merely simultaneous in their detection, but are also quantum entangled, in that each photon has an (undetermined before measurement) but nevertheless a related polarization angle with its entangled twin. If these detectors were spaced at arbitrary distances (say many light-years) we would still observe the same correlations, despite there being no possibility for classical influences to occur between these photons at sub-light or even at light speeds.
So how then do the photons know how to reflect appropriately off the aluminum to preserve these correlation statistics?