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Artificially constructed spacetime with closed timelike curves to test the plausibility of Godel’s universe
The objectives of this research are to discover if in this set up we can prove blabla. The aim is to open up a door that leads to a more serious interest and complex research on this topic.
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There hasn’t been a lot of experimental research done to actually test CTCs, and in particular Godel’s model. The aim of this project is to conduct a simpler model of experiment that would prove that time travel is possible in an artificially constructed spacetime according to Godel’s model to include closed timelike curves, unlike the conditions that actually exist in our universe. Following Godel’s theory, this project aims to create a CTC otherwise not possible in our universe and test if it can work to send a quantum particle back in time, if only just for one billionth of a second.
Time travel is one of the most controversial topics in the theoretical physics realm. Theoretical physicists have been trying to prove and disprove time travel for decades. The biggest transition from science fiction to real physics happened when Van Stockum (1937) first described the possibility of a closed timelike curve the INVENTION of closed timelike curves, first mentioned by KOJBESE and established as a theory by Kurt Godel in 1949. Kurt G¨odel in 1949 discovered an exact solution to the EFEs of a uniformly rotating universe containing dust and a nonzero cosmological constant, as discussed in depth and analyzed by Lobo, 2010.
The key aspect of this experiment is successfully creating a Godel mini-universe in a box that we will call the time machine. The box will be constructed to have all the parameters needed for the creating of Godel’s closed timelike curves (Godel, 1949), using a combination of techniques as presented in several attempts to experimentally create them . In the entrance of the machine we set up a photon source that emits only one photon. At the exit of the machine we place a black box – completely impenetrable to outside influences, with one single opening at the exit of the time machine. In the black box we insert a single-photon detector (such as a Quanta Image Sensor (QIS)), completely untampered with .
We connect a strontium atom clock to the photon source. We start the simulation of the machine, therefore creating a space-time with potential CTC’s. After a billionth of a second the exit automatically closes, closing all entrances to the black box, after this time nothing else can enter or exit the black box. In the same instance that the exit closes, the photon source emits a single photon.
After the experiment is over we open the black box. If the photosensitive film is eluminated, it effectively means that the photon managed to enter the CTC and exit one billionth of a second before it was emitted, to the time when the entrance to the black box was still open, and enlighten the film. This confirms that the experiment was completely successful.
We shall observe positive results if the photosensitive film is eluminated, and negative results if it remains unaltered.
However, if the photosensitive film remains as it was, it doesn’t necessarily mean that the entire experiment is unsuccessful. This can be due to two reasons. The first one is obviously the lack of precision of the technology used, because we are talking about a time frame of one billionth of a second in which two simultaneous things have to happen – the exit must close, and the emitter must follow with emitting the photon precisely after that. Of course that follows another validity, should the film be eluminated, it doesn’t necessarily mean that the experiment was successful, it can mean that the technology failed to get this two actions in the correct order, and emitted the photon a billionth of a second after the exit closed. To validate this in the event of a positive outcome, we must test the technology, and we should gradually increase the timeframe, and possibly prove that the CTC can bring back the photon more than just one billionth of a second in the past. This brings me to the second reason why the experiment might yield negative results, the CTC is effective but it brings the photon back less than one billionth of a second in the past. With the latest technology we have today, there is a smaller fraction of a second that the watch can measure, up until 10-11 fraction of a second, but it would be impossible to create both conditions in such a time-frame, emitting the photon and closing the exit. Unfortunately we are bound by the latest technology in that aspect, and until we can improve to move faster that one billionth of a second, we cannot test this plausibility. That remains our biggest constraint.
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The third possibility is that the time machine does in fact work, creating CTC’s, but the photon failed to get into the right one at the right time. This can only be by doing multiple attempts, but never fully disproved.
The limitations of this experiment are that neither reason for a negative outcome completely disproves the hypothesis, as well as none of the reasons for a positive outcome completely confirms it. However, in the case of at least one positive outcome, a new door for subsequent further experiments opens.
For the development of this experiment, we would use technologies for CTC’s already created, and a very simple and cost efficient set-up.
Godel tried to propose solution to the Einstein equation by introducing a cosmological constant. 
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