Static vs Dynamic: Can Massive Particles Have Parallel Spacetime Trajectories?

[zonde]

Can two massive particles have parallel spacetime trajectories? It seems that the answer is - no. And the closer they are the more they can't.

But in that case we can't have static structure consisting of massive particles. Any composite structure would have to have something like phasespace itself to appear semi-static.

Comments? Objections?

 

[Matterwave]

If I have 2 objects just sitting on my desk, wouldn't you call those 2 objects to be moving on "parallel spacetime trajectories"?

They maintain the same proper distance between them at all times.

 

[TrickyDicky]

Maybe zonde had in mind free-falling trajectories?
That would leave out the objects mentioned by matterwave.

 

[zonde]

If I have 2 objects just sitting on my desk, wouldn't you call those 2 objects to be moving on "parallel spacetime trajectories"?

They maintain the same proper distance between them at all times.

Yes they would be moving on "parallel spacetime trajectories". Basically it would sound simpler if I would say that particles can't be at rest in respect to each other.

Ok, back to your question. As you say in classical domain we can have two identical objects at rest in respect to each other. So we can prepare ensemble of identical objects that move along exactly the same trajectory.

But if we talk about QM domain does it hold or no? It seems to me that it doesn't. We have Pauli exclusion principle and Fermi–Dirac statistics. So we can't prepare ensemble of identical particles that move along exactly the same trajectory.

 

[Darwin123]

Yes they would be moving on "parallel spacetime trajectories". Basically it would sound simpler if I would say that particles can't be at rest in respect to each other.

Ok, back to your question. As you say in classical domain we can have two identical objects at rest in respect to each other. So we can prepare ensemble of identical objects that move along exactly the same trajectory.

But if we talk about QM domain does it hold or no? It seems to me that it doesn't. We have Pauli exclusion principle and Fermi–Dirac statistics. So we can't prepare ensemble of identical particles that move along exactly the same trajectory.

I would say yes. We can prepare such an ensemble. The reason is that most objects can't be described as fermions.
Not all particles are fermions. Some are bosons. The Pauli exclusion principle doesn't apply to bosons. Bosons satisfy Bose-Einsten statistics, not Fermi-Dirac statistics. Mesons and photons are bosons, not Fermions.
A corporate particle made of many entangled fermions could act as a boson. If all the fermions are entangled and if an even number of spins are coupled together, then the corporate particle will act as a boson. A group of such corporate particles would not satisfy either the Pauli exclusion principle or Fermi-Dirac statistics.
Atoms with zero spin belong in this category. Nuclei with zero spin belong in this category. The ground state C60 molecule belongs in this category. Collections of such things are regularly prepared in laboratories around the world.
A corporate particle consisting of incoherent wavicles would act like a classical particle. It would satisfy Maxwell statistics. Of course, this is an approximation. In the limit of an infinite number of incoherent wavicules, a corporate particle acts like a classical body.
This last category probably includes all the common objects that we recognize in the macroscopic world. You and I belong in this category. Planets belong in this category.
The Pauli exclusion principle is satisfied only by a relatively small set of bodies. Most large objects would not satisfy the Pauli exclusion principle. So even taking into account quantum mechanics, massive objects could travel in parallel space-time paths.

 

[zonde]

I would say yes. We can prepare such an ensemble. The reason is that most objects can't be described as fermions.
Not all particles are fermions. Some are bosons. The Pauli exclusion principle doesn't apply to bosons. Bosons satisfy Bose-Einsten statistics, not Fermi-Dirac statistics. Mesons and photons are bosons, not Fermions.

Good point. So in order to talk about Pauli exclusion principle as universally applicable to all massive matter there should be arguments why Bose-Einsten statistics does not apply to bosonic composites.

A corporate particle made of many entangled fermions could act as a boson. If all the fermions are entangled and if an even number of spins are coupled together, then the corporate particle will act as a boson. A group of such corporate particles would not satisfy either the Pauli exclusion principle or Fermi-Dirac statistics.
Atoms with zero spin belong in this category. Nuclei with zero spin belong in this category. The ground state C60 molecule belongs in this category. Collections of such things are regularly prepared in laboratories around the world.

I believe it's bound fermions not entangled fermions.
And it's integer spin not only zero spin.
And C60 is generally mixture of ¹²C₆₀ (bosonic composite) ¹²C₅₉¹³C₁ (fermionic composite)

A corporate particle consisting of incoherent wavicles would act like a classical particle. It would satisfy Maxwell statistics. Of course, this is an approximation. In the limit of an infinite number of incoherent wavicules, a corporate particle acts like a classical body.
This last category probably includes all the common objects that we recognize in the macroscopic world. You and I belong in this category. Planets belong in this category.
The Pauli exclusion principle is satisfied only by a relatively small set of bodies. Most large objects would not satisfy the Pauli exclusion principle. So even taking into account quantum mechanics, massive objects could travel in parallel space-time paths.

One nice example where Fermi-Dirac statistics apply is electrons in metals. And it has nothing to do with coherence of electrons.

 

[zonde]

Good point. So in order to talk about Pauli exclusion principle as universally applicable to all massive matter there should be arguments why Bose-Einsten statistics does not apply to bosonic composites.

And here are the arguments.
The only case where we talk about Bose-Einsten statistics as applicable to bosonic composites is Bose-Einsten condensate (BEC). But:
1. BEC appears suddenly as phase transition. If Bose-Einsten statistics would always apply to bosonic composites then we would expect smooth transition from Maxwell–Boltzmann statistics to Bose-Einsten statistics.
2. Fermionic composites too can undergo phase transition to superfluid state. Certainly before this phase transition Fermi–Dirac statistics applies to them (so why not for bosonic composites?)
3. In this lecture it says http://nobelprize.org/nobel_prizes/physics/laureates/2001/cornellwieman-lecture.pdf:
"A normal thermal gas (in the collisionally thin limit) released from an anisotropic potential will spread out isotropically. This is required by the equipartition theorem. However, a BEC is a quantum wave and so its expansion is governed by a wave equation. The more tightly confined direction will expand the most rapidly, a manifestation of the uncertainty principle. Seeing the BEC component of our two-component distribution display just this anisotropy, while the broader “uncondensed” portion of the sample observed at the same time, with the same imaging system remained perfectly isotropic (as shown in Fig. 8), provided the crucial piece of corroborating evidence that this was the long awaited BEC."

This "manifestation of the uncertainty principle" can be understood as degeneracy pressure and so it would indicate that Fermi–Dirac statistics apply to bosonic composites.

 

[Cthugha]

The only case where we talk about Bose-Einsten statistics as applicable to bosonic composites is Bose-Einsten condensate (BEC).

Is that so? The effects of Bose-Einstein statistics are typically less visible than those of Fermi-Dirac statistics. BEC is the most prominent case, but definitely not the only case. Check for example the really cool experiment by Jeltes et al. (Comparison of the Hanbury Brown–Twiss effect for bosons and fermions, Nature 445, 402-405 (2007), also available on the ArXiv:http://arxiv.org/abs/cond-mat/0612278).

In a nutshell they just take a bunch of Helium-3 atoms (composite fermion) and Helium-4 atoms (composite boson) and drop them. At the ground the positions of these atoms are detected and it is clearly demonstrated that the Helium-3 atoms have a tendency to avoid each other, while Helium-4 atoms have a tenddency to group together. This is quite a clear demonstration that B-E statistics does apply to composite bosons - and the system is far from being in a condensed state.

 

[zonde]

Is that so? The effects of Bose-Einstein statistics are typically less visible than those of Fermi-Dirac statistics. BEC is the most prominent case, but definitely not the only case. Check for example the really cool experiment by Jeltes et al. (Comparison of the Hanbury Brown–Twiss effect for bosons and fermions, Nature 445, 402-405 (2007), also available on the ArXiv:http://arxiv.org/abs/cond-mat/0612278).

Indeed this is really cool experiment, thanks.

In a nutshell they just take a bunch of Helium-3 atoms (composite fermion) and Helium-4 atoms (composite boson) and drop them. At the ground the positions of these atoms are detected and it is clearly demonstrated that the Helium-3 atoms have a tendency to avoid each other, while Helium-4 atoms have a tenddency to group together. This is quite a clear demonstration that B-E statistics does apply to composite bosons - and the system is far from being in a condensed state.

Two equally sized samples of He-3 and He-4 are released and are expanding at about the same rate. And yet particles in one sample tend to have more close neighbours but in other sample less close neighbours while about the same number of far neighbours in both samples.
I wonder what should Bohmian trajectories look like to get such an effect. And is it possible at all.