There's a lot of hype around time travel into the past or into the future using blackholes or wormholes. But's its just hype created by a lot of people who want to sell you their books. The goal of this post is to summary my previous post and to highlight those aspects of the previous post that show why time travel is impossible (as depicted in sci-movies or as discussed by astrophysicts such as Richard Gott or Kip Thorne.)
Here's a short summary:
(1) We live on a wrinkled 3D surface of a 4D sphere.
(2) The 2nd Law of Thermodynamics states that there is no way to give a particle enough energy such that it has enough mass/energy to curve space-time enough to go back to the Big Bang.
(3) Time travel is impossible. Even if you give a particle enough energy such that it is locally further back in time than its surrounding environment, as soon as you de-accelerate the particle back to normal speeds, the particle goes back to being at the same radius (time) as its surrounding environment.
(4) When you account for acceleration and de-acceleration (i.e. General Relativity), the Twin-Paradoxes and the idea of Time Travel go away completely. Therefore, when we teach Special Relativity to students in the class room, it's important to simultaneously time some of the basics of General Relativity.
(5) In the long-run, growing life is the best and fastest way to generate entropy and to expand the radius and surface area of the universe. Culture grows, music expands, art thrives, and mathematics dazzles while we expand life from Earth to other planets. It's a win-win situation for everybody. We live into an unknown future, with only the past as a rough guide on how best to grow life and expand the universe.
Here's the longer summary of the previous post:
(1) Mass is energy; energy is mass. Mass/energy curves 4-D space-time into a surface of a 4D sphere. The surface is wrinkled because the mass/energy density of the universe is not constant. We and every particle in the universe resides on the same wrinkled 3D surface of this 4D sphere.
(2) Entropy is encoded in the wrinkled 3D space-time surface. Irreversible entropy production increases the 3D surface area of space-time. Time is the radius from the surface to the center of the 4D sphere. The radius to the surface is not constant, but the 2nd Law of Thermodynamics states that the average radius to the surface increases and then reaches a maximum. The speed of light (3∙108 m/s) is simply a conversion factor between spatial dimensions and what we call temporal dimensions. It tells you how fast force carriers can travel in a spatial direction during a given period of expansion of the universe.
(3) Time does not flow the same for all observers. If one observer is moving near the speed of light, he or she has a lot of energy and therefore he/she is not at the same radius in time as a different observer. The extreme case is an energetic particle in a particle-collider (like CERN). As the particle is circling around with velocities near the speed of light, it's not at the same radius in 4D space as the people working at CERN. Space-time is locally warping just around the proton or anti-proton. This means that photons from the particle have to travel in curved space-time to reach the observer.
(4) The speed of light is related to the maximum amount that space-time can warp. As you or a particle with rest mass increases its velocity, it increases it energy...causing space-time to warp. If the particle is accelerated by an outside force, the particle can continue to increase its energy, and it goes further and further back in time. There is a limit to which it can go back in time...The only way it could go all the way back in time is if it had the same energy as the Big Bang. But because of the irreversible processes associated with supplying the energy to accelerate the particle, the total space-time surface increases and therefore time increases on average, even though locally the particle is further back in time than the people working at CERN. The 2nd Law of Thermodynamics states that there is no way to go back to the Big Bang. In other words, there's no way to supply enough energy to a particle to get it to travel back to Big Bang. If you tried to supply enough energy, then you would be re-creating the Big Bang. But since the entropy of the Big Bang was much, much less than the entropy of the present universe, you could only re-create the Big Bang if you could violate the 2nd Law of Thermodynamics.
Note: I think that when we teach special relativity in classrooms, we must teach the basics of general relativity as well. If you only teach special relativity, it's hard to visualize why a yardstick shrinks when viewed by an observer at high speeds. It's a lot easier to visual why it shrinks when you realize that the yardstick didn't shrink. It's total length in 4D space is exactly the same as it was before (which is why it doesn't think that it shrunk.) The yardstick is now curved in 4D space-time. You can demonstrate this by purchasing a flexible ruler. Show students the ruler at full length, and then start bending it away from the students. They should start to see the yardstick become shorter because it's length in their viewing direction in less than before.
(5) There is no Twin Paradox in General Relativity, just as there is no "yardstick" shrinkage in space-time. If both twins start at the same location, the same gravitation field and have the same velocity, and then one of them gets in a spaceship with the capability of traveling near the speed of light, then that Twin will be able to distort time-space. However, as soon as the Twin puts on the brakes (in order to return to Earth), the Twin will be decreasing his/her velocity and will be lowering the local curvature of space back to the same curvature of his/her twin. The Twin who went on the spaceship (assuming that he/she brought a clock with him/her) would measure the same exact time duration as her/her twin who stayed back on Earth. After de-accelerating, both twins would be at the same radius from the center of the 4D sphere.
(6) Time travel to the past or to the future is impossible. Time travel to the future is easy ruled out by the fact that there is no way to create negative curvature of space-time. The 3D surface can only curve inward by mass-energy. But even if you could locally create a warping of space-time that moved you into the future (i.e. a radius further away from the center of the 4D sphere), the rest of space-time would still be at the same radius as before. You might have moved further from the center of the 4D sphere, but nobody else did. But as I said before, space-time doesn't appear to be able to curve in the direction to be able to move particles forward in time. It is possible (as I mentioned with the particles at CERN) to give some particles enough energy such that they are further back in time (i.e. closer in radius to the Big Bang.) But this is a local phenomena. The rest of space-time is at the same radius as before. And as soon as you de-accelerate the particle, you bring it back to our radius.
(7) In other words, time travel (as in sci-movies) is impossible. There's no way to re-create the past. You could spend a lot of energy and get the Earth to travel at speed near the speed of light...and this could move the Earth back further in time (i.e. a radius closer to the center of the 4D sphere), but if you slowly accelerated the Earth (and the whole Solar System), nobody here would notice (except for a few astronomers.) In other words, we wouldn't magically start goes backwards culturally. We wouldn't start walking backwards, singing disco backwards, reliving WWII backwards, discovering steam engines in backwards time. We'd keep on living life in a forward direction...inventing new technologies. Time travel in the movies luckily is impossible both according to the theory of General Relativity and the 2nd Law of Thermodynamics. There is no way to revisit the past (and hence, there's no way to murder your grandfather.) The wrinkled 3D surface of space is constantly changing. There's no way to transport yourself back to the past because there's no way to run time backwards for the entire universe.
(8) Because the expansion of the universe is due to the amount of irreversible entropy generation, there is no way to run the universe backwards to model the Big Bang. Astrophysicists can estimate the amount of irreversible entropy generation between the time that the cosmic microwave background radiation first formed and the present, but it is nearly impossible to model the Big Bang at times earlier than when the cosmic plasma of electrons and protons combined into hydrogen atoms. To model the Big Bang at earlier times, you have to make a guess at what the acceleration of the universe was, but how would you estimate the amount of irreversible entropy generation if you have no experimental data to tell you what the universe looked like? When astrophysicists tell us that they can predict the amount of hydrogen, helium and lithium in the universe, be very skeptical. (First of all...their current models don't do a good job of predicting the amount of lithium, and second, their models are completely time reversible, violating the second law of thermodynamics. Future models of the Big Bang need to incorporate irreversible thermodynamics into the model as a means of estimating the expansion rate of the universe. Only then can we hope to develop models of the Big Bang that actually predict the correct amount of hydrogen, helium and lithium in the present universe. But even then, we should be skeptical of our predictions.
(9) Here are some more open questions not listed in the previous post:
(a) Is the growth of the 3D surface area (due to irreversible processes) a local phenomena or a global phenomena? My guess is that it's a somewhat local phenomena...i.e. the 3D surface area increases locally due to irreversible processes. But entripy is related to the relationship between particles, so you can't assign the increase in entropy to any one particle. My analogy is to a computer that has to increase its hard drive space (by growing new hard drive space) in order to store more information. The hard drive space stores the symmetry group of the universe. As the symmetry group increases, the computer has to increase its storage space. I believe its a somewhat local phenomena because the symmetry groups of the universe can be de-composed into sets of groups, each of which can expand independently of the other groups.
(b) If the average radius of the 4D sphere is related to the amount of entropy, what's to stop the universe from continuing to increase in size? My guess is that there will be a limit to the expansion of the universe once everything turns into a symmetric sea of cold photons and cold neutrinos. But this is billions or trillions of years away.
(c) Can we predict the final state of the universe? My guess is that we can't calculate the precise final state of the universe given the present state of the universe. It might be some mix of blackholes, photons and ultra-cold neutrinos. The surface will measure the total entropy and ultimately the surface size/shape will tell the story of what happened during the history of the universe. Since the entropy is proportional to the exchange symmetries similar particles, and since the symmetry group of the future contains the symmetry group of the past, then the past stays with us, etched into the symmetry group of the present and the future.
Our purpose, ultimately, is to increase the size of the universe, and we do this by growing life throughout the universe. As we grow life, there will be inevitable irreversible entropy generation. By growing life, we positively etch our names into the symmetry group of the universe and help make the universe a little bit larger. If you've seen some of my previous posts, you'll hopefully realize that the best way to generate entropy is not to waste exergy...it's to use the exergy to generate useful work in power plants, and to use the generated useful work to make more power plants. (By power plant, I mean both living creatures and the normal definition of the term 'power plant.') Ultimately, growing life is a better and faster way to generate entropy than to just waste exergy. Culture grows, music expands, art thrives, and mathematics dazzles. It's a win-win situation for everybody. We live into an unknown future, with only the past as a rough guide on how best to grow life.