Timelike Curves leads to violation of heisenberg uncertainty Relation

In summary, the paper considers a party with access to CTCs which allows them to perfectly distinguis h among a set of non-orthogonal quantum states. Their work supports the conclusions of another paper which claims that an observer can use interactions with a CTC to allow them to discriminate unknown, non-orthogonal quantum states.
  • #1
audioloop
463
7
General Relatitivity predicts Timelike curves and there are nonlinear extensions of mechanics which resolve the paradoxical aspects of CTC's *i.e. Time Travel, on the other hand Hawking proposed a conjeture to rule out CTCs, the Chronology Protection Conjecture*
there are a class of Timelike Curves, Open Timelike Curvatures, OTCs which leads to violate Heisenberg's Uncertainty Principle






http://arxiv.org/pdf/1206.5485v1.pdf

...and show that the Heisenberg uncertainty principle between canonical variables, such as position and momentum, can be violated in the presence of interaction-free CTCs...

...We refer to the interaction-free case as an 'open time like curve' (OTC) because the disconnected paths of the time-traveller's trajectory appear to form an open loop rather than a closed curve...

...We have speculated on the extension of this idea to curved spacetimes in general by conjecturing that gravitational time dilation can be modeled as an OTC effect. This leads to a modied theory of quantum optics that becomes nonlinear in the presence of curvature. This speculation could be testable with current technology via experiments on entangled systems in Earth's gravitational feld*...




*D. Deutsch, Phys. Rev. D, 44, 3197
J. B. Hartle, Phys. Rev. D, 49, 6543
H. D. Politzer, Phys. Rev. D, 49, 3981
S. Lloyd, L. Maccone, R. Garcia-Patron, V. Giovannetti,
Y. Shikano, S. Pirandola, L. A. Rozema, A. Darabi,
Y. Soudagar, L. K. Shalm, and A. M. Steinberg, Phys. Rev. Lett., 106, 040403.
T. C. Ralph and C. R. Myers, Phys. Rev. A 82, 062330

*Hawking, S.W. Phys. Rev. D46, 603-611.

*T. C. Ralph, G. J. Milburn, and T. Downes, Phys. Rev.A, 79, 022121
 
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  • #2
As I read it, this paper is more about the discrimination of models. I really wouldn't expect to see a violation of the HUP.
 
  • #3
Deutsch avoids time-travel paradoxes in QM by rejecting the superposition principle of QM. In my opinion there is much simpler and more natural way to avoid the paradoxes, by retaining the superposition principle but rejecting the assumption of free will:
http://xxx.lanl.gov/abs/1006.0338 [accepted for publication in Advanced Science Letters]
 
  • #4
Phys. Rev. Focus 27, 5. 2011


...Oxford University physicist David Deutsch proposed a consistency condition to avoid time-travel paradoxes: a particle that loops back in time in this way should be in the same quantum state when in reappears in the immediate past of the interaction as it was when it departed the interaction for the immediate future.

To see how this condition works, imagine a quantum particle having states labeled 0 and 1. It travels around a CTC and, on its return, interacts with an “external” particle in such a way that 0 becomes 1 and 1 becomes 0. Such a particle presents a quantum grandfather paradox: when it comes back around the loop, it flips its former self to the opposite state. However, Deutsch showed that consistency is possible if the particle is in a superposition–a state that is equal parts 0 and 1. The interaction exchanges the 0 and the 1, but the state overall remains unchanged. For this to work, the external particle must also be in a superposition that flips back and forth...

then

...the paradox is avoided, but a difficulty arises if the external particle is measured. Then it cannot remain in a superposition but must become definitely either 0 or 1–which means that the CTC particle cannot remain in a superposition, either. To preserve consistency, Deutsch argued that the CTC particle must exist in two parallel universes–the “1-universe” and the “0-universe”–and continually switch between them, so that no contradiction occurs in either one...

Deutsch appeals to the multiverse

but

...Lorenzo Maccone*, of the Massachusetts Institute of Technology and the University of Pavia, Italy, and his colleagues propose a more stringent condition that avoids these difficulties. They require that any measurement of the particle going into the future should yield the same result as measuring it when it returns from the past. So any state that would alter the past when it came around again is disallowed, and no grandfather-type paradoxes can arise...


*Phys. Rev. Lett. 106, 040403 (2011)
 
  • #5
and

Todd A. Brun, Foundations of Physics
March 2012, Volume 42, Issue 3, pp 341-361

...considering that a D-CTC-assisted quantum computer can violate both the uncertainty principle* ...*Phys Rev Lett, 102(21):210402, May 2009.----
...show how a party with access to CTCs, or a "CTC-assisted" party, can perfectly distin-
guish among a set of non-orthogonal quantum states...

T. A. Brun, Phys Rev Lett, 102(21):210402, May 2009.

----
...and can be interacted with in the way described by this simple model, our results confirm
those of Brun et al that non-orthogonal states can be discriminated...

...Our work supports the conclusions of Brun et al that an observer can use interactions with a CTC to allow them to discriminate unknown, non-orthogonal quantum states – in contradiction of the uncertainty principle.

T. C. Ralph, Phys. Rev. A 82, 062330 2010.
 
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FAQ: Timelike Curves leads to violation of heisenberg uncertainty Relation

What are timelike curves and how do they relate to the Heisenberg uncertainty relation?

Timelike curves are a theoretical concept in physics that describe a possible path of an object through spacetime. They are related to the Heisenberg uncertainty relation, which is a fundamental principle in quantum mechanics that states that certain pairs of physical properties, such as position and momentum, cannot be simultaneously measured with perfect precision.

Why does the existence of timelike curves lead to a violation of the Heisenberg uncertainty relation?

The existence of timelike curves implies the possibility of time travel, which would allow for the measurement of past values of physical properties. This would violate the Heisenberg uncertainty relation, as it would allow for the simultaneous measurement of incompatible properties with perfect precision.

What implications does this violation have for our understanding of the laws of physics?

The violation of the Heisenberg uncertainty relation by timelike curves would challenge our current understanding of the laws of physics, particularly in regards to causality and the concept of time. It would also potentially open up the possibility of paradoxes and inconsistencies in the laws of physics.

Are there any proposed solutions to this violation of the Heisenberg uncertainty relation?

There are several proposed solutions to this violation, including the idea that timelike curves may not actually exist in our universe, or that the Heisenberg uncertainty relation may need to be modified in the presence of time travel. However, these proposed solutions are still highly debated and have not yet been definitively proven.

What are the potential consequences of resolving this conflict between timelike curves and the Heisenberg uncertainty relation?

If a solution is found to this conflict, it could greatly impact our understanding of the fundamental laws of physics and potentially open up new avenues of research and exploration. It could also have implications for technologies that rely on our current understanding of the Heisenberg uncertainty relation, such as quantum computing.

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