Matthew – Year 12 Student
Editor’s note: Year 12 student Matthew bravely tackles the complexities of quantum entanglement, a branch of quantum physics that is now being implemented in the treatment of cancer and other diseases. Matthew writes clearly and concisely, demonstrating an ability to communicate complex ideas as simply as might be expected given the nature of the topic. This is Matthew’s second publication in The GSAL Journal; you can read more from Matthew here. CPD
From the 18th century to the end of the 19th century, research in physics concentrated on mechanics, astronomy, optics, thermodynamics & electromagnetism. These areas of physics are now regarded as fields of classical physics. Alternatively, research into physics from the beginning of the 20th century and onwards is regarded as modern physics. This includes particle & nuclear physics, general & special relativity as well as quantum physics.
Spooky action at a distance…Albert Einstein
Quantum physics studies fascinating phenomena such as quantum tunnelling, quantum superposition, wave-particle duality and quantum entanglement. It was Einstein himself who described entanglement as ‘spooky action at a distance’ and he, along with two other physicists, formulated a paradox involving entanglement called the EPR (Einstein-Podolsky-Rosen) paradox. However, research into quantum entanglement has developed since the EPR paradox was formulated and, despite there still being no answer to the EPR paradox, entanglement is now being used to treat cancer patients among many other things.
The EPR paradox was formulated in 1935 by Einstein, Podolsky and Rosen. It states that if two particles are entangled as soon as you measure the spin of one particle, you collapse the wavefunction and the other particle immediately has the opposite spin. This is because the particles are in a superposition where both particles are simultaneously spin up and spin down. When the entangled particles are separated by long distances, (theoretically this could be millions of light years apart) if a measurement is made on one particle, the other particle is affected immediately. Scientists have been able to prove that entangled particles interact with each other faster than the speed of light. If we were to entangle two particles, keeping one on Earth in the Milky Way, and placing the other in the Andromeda Galaxy, as soon as we made a measurement of the particle on Earth and collapsed the wavefunction, a detector in the Andromeda Galaxy would measure the particle’s spin immediately. However, the Andromeda galaxy is 254 million light years (the distance light travels in a year multiplied by 254 million; the speed of light is 300 million metres per second), so clearly interactions between entangled particles happen faster than the speed of light. This is the EPR paradox.
Many experiments in electromagnetism prove that light is an electromagnetic wave, and therefore, according to James Clerk Maxwell, light travels at c (where c = 3×10^8 m/s) the speed of electromagnetic waves in a vacuum. Furthermore, Einstein was able to show in his Theory of Special Relativity, that nothing travelled faster than the speed of light. For many years, the speed of light was seen as the cosmic speed limit. So which theory is correct? The more classical approach of Maxwell who stated that light, like all EM waves travels at a constant speed, which later Einstein realised was the maximum speed in the universe? Or, the more modern approach of quantum physics which states that perhaps there is no cosmic speed limit? Physicists still don’t know the answer to this question. Quantum entanglement appears to be highly theoretical, but it actually has many uses. One idea for the future of quantum entanglement is in medicine, specifically in PET scans.
Doctors use PET (Positron Emission Tomography) to image metabolic processes in the body. This can involve imaging cancerous tumours, monitoring brain activity etc. Doctors will inject a radiotracer into the body e.g. fluorine attached to a sugar, which travels around the body and is absorbed into tissues. Radiotracers accumulate in areas of high metabolic processes, including rapidly dividing cells, e.g. cancerous tumours. PET scans require positron emission.
All nuclei want to be stable. For nuclei with a mass number of less than 20 (this involves all the radiotracers), the ratio of neutrons to protons should roughly equal 1. Therefore, there should be equal numbers of protons and neutrons.
Nuclei with more neutrons than protons decay by beta-negative decay:
n -> p + e– (+ anti-electron neutrino)
Nuclei with more protons than neutrons decay by beta-positive decay:
p -> n + e+ (+ electron neutrino)
Beta-negative decay involves a neutron decaying into a proton and releasing an electron & an anti-electron neutrino. Whereas, beta-positive decay involves a proton decaying into a neutron and releasing a positron & an electron neutrino. A positron is an anti-electron. PET scans use beta-positive decay; therefore, they need nuclei with more protons and neutrons. These include:
- Carbon-11 (6 protons & 5 neutrons)
- Nitrogen-13 (7 protons & 6 neutrons)
- Oxygen-15 (8 protons & 7 neutrons)
- Fluorine-18 (9 protons & 9 neutrons)
One of these unstable nuclei is attached to a sugar and injected into the body. For example, if fluorine-18 decays by positron emission (beta-positive decay) into oxygen-18. This produces a positron and when matter and anti-matter collide, they annihilate and produce two photons (particles of light) that travel in opposite directions. Therefore, the emitted positron travels a few millimetres before colliding with an electron and annihilating to form two photons. The two photons then travel out of the body and are detected by detectors that surround the patient. The photons travel in opposite directions at the same speed; therefore, two detectors located opposite each other both detect a photon at exactly the same time. If we were to draw a line joining the two opposite detectors that also travelled through the body, then we know the decay of fluorine-18 happened along this line. This line is called the Line of Response.
If many more decays occur, then many more pairs of photons will be produced. Different pairs of detectors, located opposite to each other will detect photons at the same time. Therefore, lines of response can be drawn passing through the body. All the lines will intersect each other and we can form a very good image of that part of the body. This is the ideal scenario and is called a true event.
However, photons can scatter in the patient, in the air and in the detector. If this occurs, the line of response would not be accurate. Furthermore, two decays can happen at (almost) exactly the same time. Therefore, four photons are produced and detected at the same time and this makes it difficult to know where to draw the line of response. 30% – 50% of detected events include scattered photons, or the line of response is incorrectly drawn. This is a very high statistic; therefore, medical researchers have found ways to lower this statistic so that more lines of response are accurately drawn.
Quantum entanglement can remove incorrectly drawn lines of response. This is because the two photons produced by the decay are quantum entangled. If two photons on the line of response are entangled then the line of response is accurately drawn. However, if two photons on the line of response aren’t entangled, then the line of response is incorrectly drawn. If we disregard all the lines of response where the two photons aren’t entangled (this includes scattered events because scattering destroys entanglement), then all the lines of response will be accurate because we are only drawing them if the two photons on the line are entangled with each other.
How do you measure entanglement? When each photon hits the detector, it scatters at an angle x. If you plot the difference between the two entangled photons scatter angles (Δx = x1-x2), for two unentangled photons Δx is flat because there is no relationship. Whereas for two entangled photons, Δx looks like a cosine function:
Now that we can measure entanglement, we can get more accurate lines of response and therefore, a higher quality image.
- York University Nuclear Physics Masterclass (https://www.york.ac.uk/physics/public-and-schools/nuclear-masterclass-homepage/)
- Wikipedia (https://en.wikipedia.org/wiki/Quantum_entanglement)
- Wikipedia (https://en.wikipedia.org/wiki/History_of_physics)
- GeoGebra (https://www.geogebra.org/?lang=en-GB)