Martin Bauer

I wish everyone a happy Christmas and some restful days at the end of the year!

12/12

If a child which expects Santa to appear would succeed in observing the |Santa> state, it would be unprecedented direct evidence of Santa Claus, but it would collapse Santa's wavefunction and all presents would be deposited in his or her living room at once

11/12

Santa Mechanics described by a wavefunction

α | Santa> + β | not Santa >

with a very low expectation value for
| Santa > provides a good explanation

But a successful observation would have catastrophic consequences!

10/12

The leading theory today is the model of 'Quanta Claus'.

Evidence for the quantum mechanical nature of Santa has been collected worldwide:

1. Santa is never directly observed, but indirect evidence of him abounds

2. 'Chimney Tunneling'

9/12

Alternative theories have been proposed:

- 'There is no Santa' by Grinch et al. Phys. Rev. NP 001/1965

- 'There are no good children' by Ruprecht et al. Phys. Rev. NP 013/1816

- More speculative ideas…

8/12

86000 tons travelling at 4x10^6 km/h create enourmous air resistance

This will heat the reindeer up

They will absorb 40 billion Joule of energy per second each. The reindeer will be vaporised in a fraction of a second

7/12

Even if flying reindeer could pull four times as much as their cousins we’d need 144 333 reindeers to pull that sleigh

6/12

This ignores, that there is no known species of reindeers that can fly

Also, if each household gets ~1kg worth of presents the sleigh is carrying at least 86 000 tons (not counting Santa)

5/12

Assuming evenly distributed houses with an average distance of 1.5 km, Santa will need to go 4 million km/h or ~1/250th of the speed of light (the corresponding relativistic length contraction has long been considered the secret behind Santa fitting through the chimney)

4/12

This works out to ~770 visits per second.

Santa has ~1/1000 seconds to

- park
- hop out of the sleigh
- jump down the chimney
- leave the right presents
- eat snacks
- move to the next house

3/12

The classical theory of Santa Claus is highly problematic:

- there are 2 billion children worldwide
- about 15% are Christian
- that makes 86 million households (with 3.5 children on average)
-Santa has ~31 hours to work with

2/12

What would really be the implications of taking Santa Claus seriously?

It's the time of the year to review the current state of the physics of Santa Claus

1/12

Really interesting event that would require black holes thatcan't be produced via any conventional mechanism!

A more careful formulation requires the embedding of the SM in a GUT (to get rid off the Landau pole) and can be found in the introduction of this nice paper (from which I also stole the figure)

arxiv.org/pdf/1305.6939

From this geometric perspective the Hierarchy problem is the question of whether there is a mechanism in some meow fundamental version of the Standard Model that selects or stabilises this very special trajectory

11/11

But from the point of view of the high energy fixed point, this trajectory is exponentially close to generic trajectories that fall directly into on of the RG attractors.

The SM trajectory requires very specific, highly fine-tuned initial conditions to realise this trajectory

10/11

The SM as realised in nature corresponds to a very special trajectory in this theory space

It stays for very long RG-time almost on the scaleless trajectory only to branch off into the broken phase

9/ 11

Importantly, both the mu^2>0 and mu^2<0 asymptotic low-energy theories are RG attractors

But the mu^2=0 theory is a repulsive fixed point. It is unstable

(Technically this is defined by the sign of the beta function).

8/11

the mu^2<0 branch corresponds to a broken electroweak symmetry phase

The mu^2=0 option is special, because it corresponds to the trajectory on which all particles remain massless and the theory remains scale-invariant (all operators are marginal)

7/11

But there're different low energy fixed points.

They correspond to the three different options for the Higgs mass term mu^2<0, mu^2=0 and mu^2>0

The mu^2>0 branch corresponds to the SM in which the electroweak gauge symmetry remains unbroken

6/11

One can then view the Standard Model as a specific trajectory in theory space from the high-energy fixed point to a low energy fixed point

5/11

Now imagine the SM in the opposite limit: almost 0 energy. In the effective field theory approach you have successively integrated out every massive particle and you're left with a theory of only massless states, which is also scale-invariant.

4/11

In the 'map of theories', this is a fixed point. Because it doesn't matter what the values if the mass parameters of the theory were different, in the limit of very high energies, physical observables would all look the same

3/11

For this it is important to understand the SM at different energy scales.

At very, very high energies, all the mass terms in the SM are irrelevant. The SM looks scale invariant in this limit, because all effects from dimensionful parameters (scales) can be ignored.

2/11

The hierarchy problem (finetuning) of the Standard Model of particle physics is often presented as the question 'why the weak scale is so much smaller than the Planck scale'

But there is also a geometric interpretation that can be understood with little maths (but a lot of physics)

🧵1/11

The Nobel laureates were the first to show this effect for systems containing billions of Cooper pairs. 'Macroscopic' objects described by a collective wavefucntion. Their work laid the foundations for superconducting qubits

They also showed other properties like energy quantisation

7/7

In superconductors you can build have states where many, many Cooper pairs (pairs of electrons) are described by the same wavefunction, which allows them collectively to tunnel through thin insulator barriers called Josephson junctions

6/7

But in quantum mechanics one wavefunction doesn't mean one particle. Many particles can be described by the same wavefunction. Entanglement is an example in which multiple particles are described by one wavefunction

5/7

It is also responsible for field electron emission, used in electron microscopes and tunnel diodes, nuclear fusion in stars, etc

4/7

This effect isn't uncommon in nature

It explains radioactive alpha-decay where a whole Helium nucleus is emitted from a heavy decaying element even if the binding forces wouldn't allow this process classically

3/7