Casimir effect and a finite length Tipler cylinder?

In summary: Casimir effect in general relativity and quantum mechanics.In summary, the Casimir effect may offer potential for constructing a finite length Tipler cylinder for CTCs, but there are many technical and theoretical challenges that need to be addressed before its feasibility can be determined.
  • #1
MvL1234
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Can the Casimir effect be used to enable a finite length Tipler cylinder to allow for CTCs?

Stephen Hawking proved that a functioning Tipler cylinder could not be built unless it either (1) was infinitely long or (2) violated the weak energy condition, meaning that the region can contain no exotic matter with negative energy. However, if a Tipler cylinder could be built, it has been shown in a solution to the equations of general relativity to allow for the possibility of closed timelike curves (CTCs) via frame dragging (http://en.wikipedia.org/wiki/Tipler_cylinder).

Now, here's where I thought of the Casimir effect. Morris, Thorne and Yurtsever pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time (http://en.wikipedia.org/wiki/Casimir_effect#Casimir_effect_and_wormholes).

Now, clearly the Tipler cylinder is an outcome of a solution to general relativity (as is frame dragging, which I'm not sure has been experimentally verified yet), whereas the Casimir effect is a well-established result in quantum mechanics. A mature, complete quantum theory of gravity might rule out even the theoretical possibility of a Tipler cylinder.

But assuming frame dragging really occurs in nature (and despite conclusive evidence there is no reason to believe that it doesn't), could a Tipler cylinder of finite length be constructed by somehow exploiting the fact that the Casimir effect can produce a locally mass-negative region of space-time (i.e. fulfilling the role for which some negative energy form of "exotic matter" might otherwise be required)? And if so, what, roughly, might this setup look like? Obviously if it would be possible to construct it is way beyond our technical capabilities at this time, but it is interesting to consider, and it is an area where general relativity and quantum mechanics sort of "collide".

Hope that all makes sense!
 
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  • #2




Thank you for your interesting question about the potential use of the Casimir effect in constructing a finite length Tipler cylinder for closed timelike curves (CTCs). This is definitely an area where general relativity and quantum mechanics intersect and it is worth exploring further. However, there are a few considerations that need to be addressed before we can fully answer your question.

Firstly, it is important to note that the Casimir effect is a purely quantum mechanical phenomenon and its effects are typically observed on a very small scale. In order to create a negative mass region of space-time using the Casimir effect, we would need to manipulate and control the Casimir forces on a macroscopic scale, which is currently beyond our technical capabilities. Additionally, the Casimir effect is highly dependent on the geometry and material properties of the plates used, so it may not be possible to create a negative mass region of space-time in the specific shape and size needed for a Tipler cylinder.

Secondly, even if we were able to create a negative mass region of space-time using the Casimir effect, it is not clear if this would fulfill the role of the exotic matter required for a Tipler cylinder. The negative mass region created by the Casimir effect is not the same as exotic matter with negative energy, which is required by the weak energy condition to enable CTCs. It is possible that the negative mass region created by the Casimir effect would not have the same properties as exotic matter and therefore may not be suitable for constructing a Tipler cylinder.

Lastly, as you mentioned, a complete quantum theory of gravity may rule out the theoretical possibility of a Tipler cylinder altogether. While frame dragging has not yet been experimentally verified, it is still a theoretical concept and it is yet to be seen if it can be confirmed in nature. Therefore, it is important to consider these limitations and uncertainties before exploring the use of the Casimir effect in constructing a finite length Tipler cylinder.

In conclusion, while the idea of using the Casimir effect to create a negative mass region of space-time for a Tipler cylinder is intriguing, there are still many technical and theoretical challenges that need to be addressed before we can determine its feasibility. It is an interesting area of research and perhaps in the future, with advances in technology and our understanding of quantum gravity, we may be able to explore this idea further. Until then, we can continue to study and theor
 

1. What is the Casimir effect?

The Casimir effect is a phenomenon in which two uncharged parallel plates placed in a vacuum experience an attractive force due to quantum fluctuations of the electromagnetic field.

2. How does the Casimir effect relate to the Tipler cylinder?

The Casimir effect is often used as an analogy to explain the concept of closed timelike curves (CTCs) in the Tipler cylinder. In both cases, the vacuum energy of the electromagnetic field plays a crucial role in the existence of these phenomena.

3. Can a finite length Tipler cylinder actually exist?

Currently, there is no known mechanism that can create a Tipler cylinder with a finite length. The only theoretical possibility is to artificially construct one using an infinitely long cylinder and advanced technology to cut it down to a finite length. However, this remains purely speculative and has not been proven to be feasible.

4. What are the implications of a finite length Tipler cylinder?

If a finite length Tipler cylinder were to exist, it would violate the principle of causality and create paradoxes such as the grandfather paradox. It would also require the existence of exotic matter with negative energy density, which has not been observed in nature.

5. Is the existence of a Tipler cylinder supported by scientific evidence?

No, the concept of a Tipler cylinder remains purely theoretical and has not been supported by any experimental evidence. It is a thought experiment used to explore the implications of closed timelike curves and the principles of causality in physics.

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