A question about velocities in Bohmian mechanics

[indefinite_123]

Hi all,

In 'Bohmian mechanics,' (BM) velocities are given by the 'guiding equation' as explained, for instance, in this article of the Stanford Encyclopedia of Philosophy https://plato.stanford.edu/entries/qm-bohm/#DefiEquaBohmMech
These velocities can, in principle, be greater than c. This is not a problem in a non-relativistic context.

Is there an upper limit to velocities when relativity is taken into account?

I know that non-locality is the main issue for finding a 'relativistic' version of BM. In contrast, it seems that faster than light velocities are not a problem.

Thanks in advance!

 

[Demystifier]

Welcome to the forum!

Speeds higher than c, by themselves, are not in contradiction with relativity. See http://de.arxiv.org/abs/1205.1992 Sec. 8.2.2, especially the text between Eqs. (8.13) and (8.14).

For a different approach to relativity in Bohmian mechanics, which now I think is more promising, see "Bohmian mechanics for instrumentalists" linked in my signature below.

 

[indefinite_123]

Thank you for the informative answer and for the welcome!

Speeds higher than c, by themselves, are not in contradiction with relativity. See http://de.arxiv.org/abs/1205.1992 Sec. 8.2.2, especially the text between Eqs. (8.13) and (8.14).

Ok! I agree that strictly speaking they are not a problem for Lorentz invariance.

However... particles that move faster than light move backwards in time.
Personally, I find this problematic (mainly for philosophical reasons...). But, anyway, I agree that it does not violate Lorentz invariance.

So, if one builds a Lorentz-invariant 'version' of BM it seems necessary that particles can travel backwards in time. Am I right?

Edit: in other words, superluminal particle velocities are an inevitable feature of BM? I ask this because in the article only non-locality is mentioned as a possible cause of friction with relativity.

For a different approach to relativity in Bohmian mechanics, which now I think is more promising, see "Bohmian mechanics for instrumentalists" linked in my signature below.

Well, it is a very interesting proposal! I am too open to the possibility that 'elementary particles' might not be fundamental

 

[Demystifier]

So, if one builds a Lorentz-invariant 'version' of BM it seems necessary that particles can travel backwards in time. Am I right?

Edit: in other words, superluminal particle velocities are an inevitable feature of BM? I ask this because in the article only non-locality is mentioned as a possible cause of friction with relativity.

Traveling backwards in time is not a necessary feature of relativistic BM. For instance, it seems that it doesn't occur for particles with non-integer spin http://de.arxiv.org/abs/0806.4476

 

[indefinite_123]

Traveling backwards in time is not a necessary feature of relativistic BM. For instance, it seems that it doesn't occur for particles with non-integer spin http://de.arxiv.org/abs/0806.4476

Ok, I see. Thank you very much!

Kind regards!