# What Are Some Shocking Surprises in Quantum Mechanics?

*Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.*

Quantum mechanics is a mess. It is a hard to grasp the theory of something where if you phrase certain aspects of it incorrectly it only causes further confusion, especially to the masses who are trying to understand it. But just because quantum mechanics is thick doesn’t mean it has revealed all its secrets. In fact, I’d say we keep finding new ways to upend our notions of reality as we go down the quantum rabbit hole…

## Conservation Laws?

Something that I had always wondered about was the effects of quantum mechanics on Conservation Laws, or central pillars of physics that we are so confident in their validity that we hold them to be always true. In fact, the symmetry in time of these laws, or the fact that they never change as we progress forward, is a key to our confidence in them. But…that viewpoint really holds up in a classical way only. How about quantumly? (Sudarsky)

Well, to know the energy of a system you would need to take some measurement of it, and in quantum mechanics that causes the wave function governing it to collapse into a definite state. Prior to that, it is in a superposition of states with no conclusion to it. Does the system then actually exist if you don’t measure it? Three popular interpretations of quantum mechanics dealing with this problem are the pilot-wave theory (where the wave feature just guides, or pilots, the particle along a path), a multiverse (where each system state ends up existing in its own reality), and the spontaneous-collapse model (which ensures a random action forcing a definite state no matter what we do) (Ibid).

So Tim Mauldin, Elias Okon, and Daniel Sudarsky developed thought experiments to see what conservation laws do under these three systems. Consider photons that are quantumly superimposed and one path sends them to a galaxy and then back to us, causing a net loss of energy due to the expansion of the universe red shifting the photon. Another path will involve no loss of energy. Until you make a measurement, quantumly a photon can go down either path but then we would seem to have an energy discrepancy. Some say the measuring device takes energy to operate and so the conservation is maintained, but entanglement can ensure I don’t have to be directly connected to the act of measurement. If spontaneous collapse is true, then a non-conservative action happens because it falls into one of those states after a given timeframe. The pilot-wave theory would have the waves themselves interfere upon their return to the lab to ensure that non-conservative behavior occurs. And as for the multiverse approach, the *overall* average of energy will be conserved but not along each branch (Ibid).

Oh, boy. Did we just show that energy conservation is in trouble? Well…what we were talking about was *local energy conservation*. A possible solution was developed by Thibaut Josset, Alejandro Perez, and Daniel Sudarsky has been found by slightly modifying general relativity which allows for local violations. If you take a system and look at the total local violations, the behavior causes an accelerated expansion of the universe, just like dark energy! (Ibid)

## Frauchiger-Renner Paradox

This is one of those oddities that once you get though the (seemingly) complex set-up reveals troubling contradictions in some basic ideas. Developed by Daniela Frauchiger and Renato Renner (Swiss Federal Institute of Technology Zurich), the thought experiment involves 4 people participating in a quantum experiment. Alice (A) is recording her friend (AF) inside a laboratory, who is recording the result of a coin toss with a 1/3 chance of being heads and a 2/3 chance of being tails. If the coin comes up heads, a particle with spin down is generated by AF but if the toss is tails then AF will put the particle in a superposition of up and down based upon the assumption of a wave function governing particle mechanics. Bob (B) also brought a friend (BF) to this experiment and is also recording BF and his laboratory. AF sends her particle, whichever one it is, to BF. BF can then figure out the coin toss from what he receives. Meanwhile, A takes a measurement herself, of both AF and her laboratory and B does a similar action with BF and his lab. Both treat each package as a quantum system, an assumption about the universal nature of quantum mechanics. As long as we are clear as to our systems, we should be able to apply quantum mechanics to them. And A hasn’t a clue as to AF’s coin toss result, so the lab *and* AF are in a superposition of heads and tails and therefore by extension AF is in superposition with BF until A has made a measurement. Until then, AF can conduct her experiment and BF can have his measurement but to A its still uncertain. But then A takes her own measurement of the system, somehow, and comes to her own conclusion as to the coin toss results. Meanwhile, B has done something similar and makes his own conclusion as to AF’s result based on BF’s measurement (Ananthaswamy, Cavalcanti).

You would think A and B should agree with their results, but we actually made another hidden assumption. We think everyone is collecting their data in the same way, but the way we infer a quantum state has drastic implications as to what result we get. If you measure property 1 and someone else measures property 2, even though they are related to each other, the averaging of results yields contradictory results. But if two different people use the same methods on the same system, no contradictions should arise. And yet, once the probabilities are all solved, scientists found that around 8% of the time A and B arrive at different conclusions as to the coin toss result (Ibid).

So one (or more) of the three assumptions (wave function, universal quantum laws, and non-contradictory results for consistent systems) has something wrong with it. So what gives? Well, quantum mechanics works great on micro scale, but no evidence yet for macroscopic effects. Maybe that is a clue as to a scale-limiting factor to it, therefore meaning its not a universal rule. This would support spontaneous collapse models, which then do put a strict limit on the arena quantum mechanics can play with. It could be that the many-worlds interpretation, where each measurement happens in a branching off universe, is actually correct. If so, then there would be no contradiction because the wave function never collapses into a single state but exists…somewhere else. Or this could point to a new, thus-far unknown, interpretation of quantum mechanics. These types of paradoxes can be viewed as frustrating but in reality are crucial tools in examining our scientific theories and pushing for new theoretical findings. For now, the best option is to find a *real* version of this and see if the thought and the action match each other (Ibid).

## Clock Ambiguity

Andreas Albrecht was looking at the Universe just a short, short while after the Big Bang and happened to find a paradox. You see, clocks are a man-made construction used to note the passage of time. At the time of the Big Bang, no clocks were present as well as no one to note the transition of events. A few moments after the Big Bang, when the Universe was about a grapefruit sized object, quantum mechanics reigned supreme. Probabilities of future events were…complicated, especially without a clock to notate the transition. In fact, without a clock it was impossible to determine which future we would take, for its readings would cause the wavefunction of the Universe to collapse. Was time actually needed? Albrecht removed it from the equations of the moment and therefore lost relativity at that moment also. What he found was that the potential Universes were all crazy and no consistent theory of physics dominated any of them. Is this evidence that quantum cosmology is in trouble? For if not, then “the fundamental physical laws are not fundamental” but determined in some unknown capacity (Frank).

## Quantum Scars

The second law of thermodynamics may be one of the most underappreciated scientific concepts to the layman, and yet all can attest to its implications. No one ever sees a broken glass reassemble itself, but if you did then you would know something was terribly wrong. Now, imagine seeing the breaking and reassembling of the glass over and over again. Now *that* would be something. Something somewhat analogous to that has been seen on a quantum scale. A team of scientists looked at 51 rubidium atoms lined up and held in place with lasers so that the order of them alternated between excited energy states and ground ones. The goal was to test out potential quantum processes for quantum computers. Thermodynamics anticipated that the system should balance out so that all 51 fall into a random order. And they did…but then reverted back to their original pattern, and then mixed again, reverted, over and over again. Known as ‘quantum many-body scarring,’ it implies that “an imprint of the past” causes them to go back to what they originally were. Instead of remaining entangled, the atoms became *disentangled*, then *reentangled*! This is a wild result. If anything, it should collapse into a different state every time the system is released because of probability stating the exact same outcome is highly unlikely...and yet, there it is (Woo).

The answer to the phenomena rested in work by Eric Heller from the 1980s. He looked at a Bunimovich stadium, essentially a track and field configuration of a rectangle ended on both sides by semicircles. If you launch a ball around in it, the path it takes is chaotic, or seemingly without pattern. But, if you happen to hit upon a special angle, then the path the ball takes can be predicted. Heller then replaced the ball with a quantum particle. The unfolding wave function of probability should make things even more chaotic, but shockingly the wave functions sometime stack into a way that allows the waves to “develop a memory of this special trajectory” where the path is retraced. *The particle interferes with itself over the unfolding probabilities of the wave function*. Because the mappings of these paths looked like scar tissue, Heller named the phenomena quantum scaring in 1984. But at the time, it was just a thought experiment. Now, it has been shown to be true with many bodies, hence the idea of quantum many-body scarring. Mysteries still endue, but isn’t that always the case with quantum mechanics? (Ibid)

## Works Cited

Ananthaswamy, Anil. “New Quantum Paradox Clarifies Where Our Views of Reality Go Wrong.” *Quantamagazine.com*. Quanta, 03 Dec. 2018. Web. 22 Sept. 2020.

Cavalcanti, Eric. “Raising questions about physical reality.” *Cosmosmagazine.com*. The Royal Institution of Australia, 24 Aug. 2020. Web. 23 Sept. 2020.

Frank, Adam. “Who Wrote the Book of Physics?” Discover. Apr. 2010. Print. 34-5.

Sudarsky, Daniel. “Is the Law of Conservation of Energy Cancelled?” *nautilis.is.* NautilisThink, Inc. 12 Dec. 2019. Web. 22 Sept. 2020.

Woo, Marcus. “Quantum Machine Appears to Defy Universe’s Push for Disorder.” *Quantamagazine.com*. Quanta, 20 Mar. 2019. Web. 21 Sept. 2020.

*This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.*

**© 2021 Leonard Kelley**