Science merges the concept of three-dimensional space with time to create a dimension called spacetime. With Einstein’s theory that time is relative, an avalanche of ideas spread of how spacetime can be manipulated, which lead to theorizing time travel.
There have been a lot of different theories for time travel and computer modeling, but not a lot of experimental research. In particular there hasn’t been a lot of experimental work to test Gödel’s model on closed timelike curves.
The aim of this research is to discover if an artificial universe made by the metric of Gödel’s theory for closed timelike curves can be used for time travel otherwise not possible in our universe. We aim not to find a strong prove of the existence of time travel, but to understand its possibilities and limitations. If the experiment is successful it would lead to a more serious interest and complex research on this topic.
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The objective is to use already made computer models and defined parameters to see if we can successfully construct an artificial mini-universe complying with Gödel’s metrics. This mini-universe needs to rotate with a sufficient speed to form closed timelike curves. Using it as a time machine, we will conduct a simple experiment to test if the CTC’s can send a quantum particle one billionth of a second back in time. If we get a positive result we can further decrease the timeframe to less than one billionth of a second to create a stronger argument.
Physicists have been trying to prove and disprove time travel for decades. A big turning point happened when Van Stockum (1937) first described the possibility of closed timelike curves, which was later established as a theory by Kurt Gödel in 1949 (Gödel, 1949). We define these CTC’s (closed timelike curves) as a path in spacetime that when travelled will lead one back to a point where one started, while never travelling faster than the speed of light (Deutsch & Lockwood, 1994). The existence of CTC’s is one of the theories that make time travel possible. Gödel established the theory for CTC’s when analyzing Einstein’s field equation and suggested a new solution. According to his suggestion, in order for CTC’s to exist the universe has to be homogenous (Gödel, 1949). So far that is assumed to be correct (Hawking, 1996). However in his solution Gödel (1949) also suggests a cosmological constant that is not equal to zero which means that the universe needs to be in rotation. This has been proven to be incorrect (Hawking, 1996). Even though that means that we cannot apply Gödel’s theory in our universe, it doesn’t mean that we cannot use the characteristics of such a universe to create CTC’s and explore the plausibility and characteristics of time travel.
Recent simulations for experiments on time travel have been conducted based on Deutsch’s model for wormholes (Lloyd, Maccone, Garcia-Patron, Giovannetti & Shikano, 2011; Ringbauer, Broome, Myers, White & Ralph, 2014) and have been unsuccessful. We want to take a simpler approach with Gödel’s model.
If we manage to create a mini-universe by Gödel’s measurements in a laboratory and artificially create a spacetime with CTC’s, we can test the possibility of time travel. The CTC’s will have to exist prior to starting the experiment, because a CTC can only take you back to a time when it existed, not earlier (Deutsch & Lockwood, 1994).
At the entrance of this mini-universe we will put a single-photon emitter and at the exit a closed box with a single-photon detector. We allow some time to pass; we seal the exit door that leads inside the box, and emit a single photon through the set up. In normal conditions, the photon would not be able to enter the box. In our set up, the photon would go through the mini-universe, into a CTC that would lead it back to a past moment when the door to the box is open, enter the box and get caught on the detector. We will further explore the limitations of this experiment.
The first step is creating the mini-universe that we will call the time machine. The time machine will be a cylinder that rotates fast enough to create CTC’s (Majer & Schmidt, 1995), with optimal acceleration as suggested by Natário (2012). This has been visualized and theoretically explained by Buser, Kajari & Schleich (2013). In the entrance of the machine we put a single-photon emitter. At the exit of the machine we place a box completely impenetrable to outside influences, with one single opening – at the exit door of the time machine. In the box we insert a single-photon detector by the newest technology; a Quanta Image Sensor (QIS). We use the QIS because it can detect single photons at room temperature, at relatively low cost (Gnanasambandam, Elgendy, Ma & Chan, 2019). We set the exit door and the photon emitter to an automated computer setting, connected to a strontium atom clock. Using such program will allow us with a press of a button to create two simultaneous actions; close the exit door of the time machine (closing the only entry to the box), and emitting a photon from the emitter just one billionth of a second later.
After the experiment is over we open the box, and develop the QIS. When developed, if the QIS had caught a single photon, it would show as a silver grain (Gnanasambandam, Elgendy, Ma & Chan, 2019). We shall note positive results if the QIS shows a silver grain and negative results if it remains unaltered.
There are two reasons for a positive result. The first is 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 get caught on the QIS. The second reason for getting a positive result is that the technology failed to get the two actions in the correct order; and emitted the photon a fraction after the exit door had closed. To validate this, we must test the precision of the technology, and gradually increase the time frame, to prove if the CTC’s can bring back the photon more than just one billionth of a second in the past.
The first result for a negative result is that the CTC’s only bring the photon back less than one billionth of a second in the past. With the latest technology we have today, it would be impossible to create both conditions in a shorted time frame. This remains our biggest constraint.
The second reason is that the time machine creates CTC’s, but the photon failed to get into the right one at the right time. This can only be tested by doing multiple attempts, but never fully proven.
The limitations of this experiment are that neither reason for a negative outcome completely disproves the hypothesis, as well as neither reason for a positive outcome completely confirms it. However, if there is at least one positive outcome, a new door for subsequent experiments opens.
Create mini-universe according to Gödel’s parameters in a lab
Install the set up
Run the experiment
Decrease time frame
Test the equipment on speed and precision
Doesn’t comply with conditions
Complies with conditions
Repeat the experiment
Increase time frame
Figure 1. Diagram of framework
*In case of a positive result when the equipment fails the testing on precision, we increase the time frame and run the experiment again. If we come to the same result for the second time, we cannot increase the time frame any further so we must conclude that our experiment is limited by the technology
The complex topic of time travel remains paradoxical and vastly uninvestigated. Every step we take, especially with experimental work leads us to a better understanding of its complexity.
For the development of this experiment, we will create a time machine using the optimal conditions of a universe containing CTC’s according to Gödel’s metrics. We will run a simple experiment with a box at the exit door of such a time traveling machine with a QIS, and emit a photon through the setup only after closing the exit door. At the end we look at the potential outcomes if the QIS detects a photon. We will run the experiment multiple times and test the equipment to make sure it complies with our conditions. This is a simple and cost efficient method to test new opportunities in the realm of time travel. Even though a positive result won’t definitely prove the hypothesis, it will be one step closer to understanding the existence and functions of closed timelike curves and it will open a new door for further research.
- Buser, M., Kajari, E., & Schleich, W. (2013). Visualization of the Gödel universe. New Journal Of Physics, 15(1), 1-36. doi: 10.1088/1367-2630/15/1/013063
- Deutsch, D., & Lockwood, M. (1994). The Quantum Physics of Time Travel. Scientific American, 270(3), 68-74. doi: 10.1038/scientificamerican0394-68
- Gnanasambandam, A., Elgendy, O., Ma, J., & Chan, S. (2019). Megapixel photon-counting color imaging using quanta image sensor. Optics Express, 27(12), 17298-17310. doi: 10.1364/oe.27.017298
- Gödel, K. (1949). An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation. Reviews Of Modern Physics, 21(3), 447-450. doi: 10.1103/revmodphys.21.447
- Hawking, S. (1996). The illustrated A brief history of time. New York: Bantam.
- Lloyd, S., Maccone, L., Garcia-Patron, R., Giovannetti, V., & Shikano, Y. (2011). Quantum mechanics of time travel through post-selected teleportation. Physical Review D, 84(2). doi: 10.1103/physrevd.84.025007
- Majer, U., & Schmidt, H. (1995). Reflections on Spacetime: Foundations, Philosophy, History. Dordrecht: Kluwer Academic Pub.
- Natário, J. (2012). Optimal time travel in the Gödel universe. General Relativity And Gravitation, 44(4), 855-874. doi: 10.1007/s10714-011-1308-1
- Ringbauer, M., Broome, M., Myers, C., White, A., & Ralph, T. (2014). Experimental simulation of closed timelike curves. Nature Communications, 5(1). doi: 10.1038/ncomms5145
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