# How does an electron behave in a closed time like curve?

#### MTd2

Gold Member
So, it goes in the first loop, no problem. In the second loop, no problem either, it could just change the spin. So, what about the third, will the electron interfere with its own past? Will it be destroyed? Will it mysteriously scatter and not interfere with its past.

This is the same for all ferminos, but bosons won't have this issue.

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#### humanino

Yes but bosons do help you very much in this problem. By interfering constructively, if I recall correctly, they will blow up your loop before it becomes a real problem

#### MTd2

Gold Member
Yes but bosons do help you very much in this problem. By interfering constructively, if I recall correctly, they will blow up your loop before it becomes a real problem
Really? Any source or reasoning?

BTW, I was thinking more about fermions because of the exclusion principle.

#### friend

So, it goes in the first loop, no problem. In the second loop, no problem either, it could just change the spin. So, what about the third, will the electron interfere with its own past? Will it be destroyed? Will it mysteriously scatter and not interfere with its past.

This is the same for all ferminos, but bosons won't have this issue.
Actually, QFT loses its particle nature in tightly curved spacetimes. Particles are described by plane waves in flat spacetime that propagate both forward and backward in time. But in curved spacetimes planewaves no longer act like planewaves.

#### humanino

Really? Any source or reasoning?
I originally read about it in Kip Thorne's "Black and time warps". I can dig up the references if you want.

#### Demystifier

2018 Award
So, it goes in the first loop, no problem. In the second loop, no problem either, it could just change the spin. So, what about the third, will the electron interfere with its own past? Will it be destroyed? Will it mysteriously scatter and not interfere with its past.

This is the same for all ferminos, but bosons won't have this issue.
The wave function is still of the form $$\psi({\bf x},t)$$, not $$\psi({\bf x}_1, {\bf x}_2, {\bf x}_3, ...,t)$$. In other words, it is still a 1-particle wave function. Consequently, the statistics is irrelevant, the concept of particle exchange does not make sense, there is no difference between bosons and fermions. The electron will have the same spin in each loop, simply because it is the same self-consistent electron.

The only interesting stuff is the following. Due to CTC, the wave function must be periodic in time. Consequently, energy is quantized even though the particle is not in a potential well.

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#### Demystifier

2018 Award
Actually, QFT loses its particle nature in tightly curved spacetimes. Particles are described by plane waves in flat spacetime that propagate both forward and backward in time. But in curved spacetimes planewaves no longer act like planewaves.
Wrong! QFT loses its particle nature when the time coordinate is not well defined. On the other hand, in our case the time coordinate may be well defined. Take for example a cylindrical universe, in which the compact coordinate is the time coordinate. In this case the metric is flat, but there is a CTC.

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