An entanglement of space and time.

My story starts almost half a century ago in a school in South East London.

Fig 1.  Gold Leaf Electroscope

used in Photoelectric Effect

On an October morning my physics teacher, Mr Poole, decided that it was time to demonstrate the wave–particle duality of light [1]. 

With two demonstrations, the 1887, Heinrich Hertz, Photoelectric Effect experiment [2] and the 1801, Thomas Young, Double-Slit experiment [3], we were first shown how light in the form of photons could liberate electrons from a metal plate and then how light in the form of waves could interact, producing an interference pattern.

Fig 2. Interference Pattern from Sodium Vapour Lamp via two slits

This early and limited glimpse into the strange world of quantum physics [4], provided me with a “world model” [5] that I was comfortable with and one which I did not question in my early career as a Microwave Systems Engineer.

As time moved on I progressed through roles such as Project Engineer, Internet Systems Developer and Research Programme Manager, finally almost 50 years later I found myself supporting a small number of very bright PhD students in their research. It was only then that the early world model I had created in my mind seemed insufficient. 

Fig 3. A scanning tunneling microscopy image of single-walled carbon nanotube

I had met with one of my PhD students and we were discussing the interaction of electric fields in adjacent carbon nanotubes [6], within a wire composed of the tubes [7]. 
I quickly realised that I needed a better understanding of quantum mechanics [8].

Fig 4. Allan Adams, MIT    

I read several texts on the subject but still did not really understand enough. So I looked to the open course material at MIT and specifically some video lectures by Allan Adams on Quantum Mechanics [9].

Suddenly it all began to fall into place and I felt confident again, that is until I watched Allan talk about an experiment carried out at the Hitachi Central Research Laboratory,  by Akira Tonomura (1987).  

Akira Tonomura recreated the famous Double-Slit experiment, but with individual particles (electrons) [10]. His conclusion was brief and its true significance was only to be realized later, he said, "We realized a two-slit interference experiment, once regarded as a pure thought experiment with no hope of precise execution, with a combination of both electron-counting and magnifying techniques. The resultant buildup of the interference pattern is exactly as predicted by quantum mechanics". (Subsequently this has also been shown with a light source producing small numbers of photons, which in effect pass though the slits individually) [11].

How could individual electrons passing through one or other of the two slits form an interference pattern, what were they interacting with? I was frankly shaken.

Fig 5. Interference pattern from single particles    

My nice comfortable model of particles and waves had suddenly been ripped apart. I was quite honestly I bit miffed, why had I not heard about this?

One of my colleagues at college explained that one of the challenges of quantum physics is that the electrons are particles and waves simultaneously. The particles can never produce such interference patterns on their own, they need to somehow gain the information that the “wave function” [12] provides, so all any other explanation is doing is replacing the wave function by something that does the same thing. (NB: The Schrödinger equation [13] determines how wave functions evolve over time)

However that said, apparently while I had been away being an Engineer, several arguments, some a little more complex and implausible than others, have been developed to explain how individual particles can produce an interference pattern in the experiment.

I consulted Google.

On one end of the spectrum was the idea that the particle changes into a wave, passes through both slits, and then changes back into a particle, which is subject to interference with itself, this seemed to be in quantum mechanical terms sort of reasonable [14], but I read on.

Fig 6. Mathematical plot of a Lorentzian wormhole (Einstein-Rosen bridge)   

At the other end of the spectrum of thought was the argument that the electron is somehow connected to other electrons in SpaceTime [15], by something like an “Einstein-Rosen bridge” [16] and although they do not pass through the slits at exactly the same time they still experience the effects of interaction, this being known as Quantum Entanglement [17].

From Wikipedia - Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently of the others, even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.

I had certainly heard of this, but only in terms of quantum computing [18].

But on reading further I found that this explanation might help in understanding why when an attempt is made to “observe” what is happening at each slit in the single particle experiment, the interference pattern ceases. However a physicist friend at college recommended I read, “Origin of quantum-mechanical complementarity probed by a `which-way' experiment in an atom interferometer, by S. Durr, T. Nonn & G. Rempe [19].

In this experiment when a `which-way' detector is employed to determine the particle's path, the interference pattern is destroyed. However the atom’s momentum is far too small to explain the disappearance in terms of Heisenberg's uncertainty principle [20]. (one standard explanation for the effect).

Fig 7. A cat, with its mirror reflection

Apparently Quantum entanglement theory tells us (Wikipedia), “it appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances”.

Reading all this I envisioned Schrödinger's cat [21], with a twin.

Having read various papers on the subject and consulted some physicist friends I was sort of comfortable again, but at the same time took some solace in the fact that both Einstein and Schrödinger were dissatisfied with the concept of entanglement [22], because it seemed to violate the speed limit on the transmission of light. I found the following quote from Niels Bohr, which made me feel a little better. 

If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet [23].

And I might have left it there but for an early arrival for lunch last week.

My college has an excellent collection of science periodicals, so having arrived 30 minutes early, I decided to catch up on the latest copy of Nature [24].

The title of one of the articles caught my attention, Cosmic test backs 'quantum spookiness' (2^nd February 2017) [25]. The article explained the latest attempts, using light that had taken 600 years to reach us, to prove quantum entanglement. I discovered that this type of experiment is known as a “Bell Test Experiment” [26] after John Bell, whose experiments are designed to demonstrate the real world existence of certain theoretical consequences of the phenomenon of entanglement in quantum mechanics.

I consulted Google again.

An earlier Nature article looked worth a read, “The quantum source of space-time” (16^th November 2015) [27]. The article explained that Mark Van Raamsdonk [28] had decided to tackle one of the deepest mysteries in physics: the relationship between quantum mechanics and gravity, he explains his theories in, “Building up spacetime with quantum entanglement”, (31^st March 2010) [29]

Fig 8. Tadpole Galaxy PS1 - NASA

Even though I had been away from the subject for a long time I certainly knew that there was really only one great challenge facing physicists today – a unified theory of everything [30] – a single theory which brings together the very large and the very small – quantum mechanics and gravity. I knew that the successful unification of quantum mechanics and gravity had eluded physicists for nearly a century.

I discovered that as well as Mark Van Raamsdonk, a second researcher, Leonard Susskind [31], had written some key research on the subject, “Cool horizons for entangled black holes” [32], in which he says, “General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein-Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex Einstein–Podolsky–Rosen (EPR) pair [33]. We suggest that similar bridges might be present for more general entangled states”.

So, apparently, the way around the problem with information travelling faster than the speed of light, in relation to entangled particles at a distance [34], is to speculate that a nano-scale wormhole [35] might exist between entangled particles? [36]

Are we any closer to a unified theory?

I really don’t know, but certainly there are some really big questions being asked and they are both opening up new lines of thought and questioning existing assumptions, which must be good.

But what I find truly amazing is that Einstein knew there was more to do. He believed quantum mechanics was correct, but desperately wanted to find a way to "complete" quantum mechanics so it made sense [37], something I would support!

Oh, and the cat is alive and well and living in Finland.

---

My sincere thanks to my son for proof reading this article, my daughter for her ideas and comments and my friends and colleagues in Physics for their comments and for pointing me at some quite amazing research papers.

References:

1. Wave-Particle Duality - http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html
2. Photoelectric Effect - https://en.wikipedia.org/wiki/Photoelectric_effect
3. The Double Slit Experiment - https://en.wikipedia.org/wiki/Double-slit_experiment
4. Quantum Physics - https://www.khanacademy.org/science/physics/quantum-physics
5. Mental Models - https://en.wikipedia.org/wiki/Mental_model
6. Advances in the science and technology of carbon nanotubes and their composites: a review, Erik T. Thostensona, Zhifeng Renb, Tsu-Wei Choua - https://www-prod.bc.edu/content/dam/files/schools/cas_sites/physics/pdf/Ren/p85.pdf
7. Electrical Properties of Carbon Nanotube Based Fibers and Their Future Use in Electrical Wiring, Agnieszka Lekawa-Raus, Jeff Patmore, Lukasz Kurzepa, John Bulmer & Krzysztof Koziol- http://onlinelibrary.wiley.com/doi/10.1002/adfm.201303716/full
8. Quantum Mechanics - https://en.wikipedia.org/wiki/Quantum_mechanics
9. Allan Adams on Quantum Mechanics  - https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-videos/
10. Demonstration of single-electron buildup of an interference pattern, A. Tonomura, J. Endo, T. Matsuda, and T. KawasakiH. Ezawa - http://aapt.scitation.org/doi/abs/10.1119/1.16104
11. Researchers observe single photons in two-slit interferometer experiment- https://phys.org/news/2011-06-quantum-physics-photons-two-slit-interferometer.html
12. Wave Function - https://en.wikipedia.org/wiki/Wave_function
13. The Schrödinger equation - https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation
14. Do atoms going through a double slit ‘know’ if they are being observed? - http://physicsworld.com/cws/article/news/2015/may/26/do-atoms-going-through-a-double-slit-know-if-they-are-being-observed
15. SpaceTime - https://en.wikipedia.org/wiki/Spacetime
16. Einstein-Rosen Bridge - https://en.wikipedia.org/wiki/Wormhole
17. Quantum Entanglement - https://en.wikipedia.org/wiki/Quantum_entanglement
18. Quantum Computing – https://en.wikipedia.org/wiki/Quantum_computing
19. Origin of quantum-mechanical complementarity probed by a `which-way' experiment in an atom interferometer, by  S. Durr, T. Nonn & G. Rempe - http://www.nature.com/nature/journal/v395/n6697/full/395033a0.html
20. Heisenberg's uncertainty principle - https://en.wikipedia.org/wiki/Uncertainty_principle
21. Schrödinger's cat- https://en.wikipedia.org/wiki/Schrödinger's_cat
22. Both Einstein and Schrödinger were dissatisfied with the concept of entanglement- https://en.wikipedia.org/wiki/Quantum_entanglement
23. If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet  - https://www.brainyquote.com/quotes/quotes/n/nielsbohr164546.html
24. Nature - http://www.nature.com
25. Nature, Cosmic test backs 'quantum spookiness' (2nd February 2017) - http://www.nature.com/news/cosmic-test-backs-quantum-spookiness-1.21401
26. Bell Test experiments - https://en.wikipedia.org/wiki/Bell_test_experiments
27. Nature - The quantum source of space-time - http://www.nature.com/news/the-quantum-source-of-space-time-1.18797
28. Mark Van Raamsdonk - http://www.phas.ubc.ca/~mav/vanraamsdonk.html
29. Building up spacetime with quantum entanglement - https://arxiv.org/abs/1005.3035
30. Will we ever have a theory of everything? - http://www.bbc.co.uk/earth/story/20150409-can-science-ever-explain-everything
31. Leonard Susskind - https://en.wikipedia.org/wiki/Leonard_Susskind
32. Cool horizons for entangled black holes, Juan Maldacena and Leonard Susskind – https://arxiv.org/abs/1306.0533
33. Einstein–Podolsky–Rosen (EPR)- https://en.wikipedia.org/wiki/EPR_paradox
34. Cosmic Test Bolsters Einstein's “Spooky Action at a Distance”- https://www.scientificamerican.com/article/cosmic-test-bolsters-einsteins-ldquo-spooky-action-at-a-distance-rdquo/
35. Wormhole - https://en.wikipedia.org/wiki/Wormhole
36. Creation of entanglement simultaneously gives rise to a wormhole - https://phys.org/news/2013-12-creation-entanglement-simultaneously-wormhole.html
37. Quantum mechanics so it makes sense -  https://phys.org/news/2014-06-einstein-quantum-mechanics-hed-today.html

Figures:

Fig 1. Gold leaf electroscope Kolbe 1908 – Wikipedia - https://en.wikipedia.org/wiki/Electroscope

Fig 2. Double slit experiment, with sodium vapour lamp – Wikimedia - https://commons.wikimedia.org/wiki/File:Young%27s_two-slit_experiment_and_Lloyd%27s_mirror.png

Fig 3. A scanning tunneling microscopy image of single-walled carbon nanotube – Wikipedia - https://en.wikipedia.org/wiki/Carbon_nanotube

Fig 4. Allan Adams MIT Lectures on Quantum Mechanics - MIT -  https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-videos/

Fig 5. Interference pattern from single particles – Thierry Dugnolle - Wikimedia - https://commons.wikimedia.org/wiki/File:Wave-particle_duality.gif

Fig 6. Mathematical plot of a Lorentzian wormhole (Einstein-Rosen bridge) - Wikipedia  - https://en.wikipedia.org/wiki/Wormhole

Fig 7. A cat and its reflection – image owned by author.

Fig 8. Tadpole Galaxy PS1 – NASA - . https://apod.nasa.gov/apod/image/1211/TadpoleGalaxyPS1V9snyder.jpg

Tags: #QuantumMechanics, #SpaceTime

DOI: 10.13140/RG.2.2.29498.80321