I am a sucker for time travel stories. I love thinking about ways in which the past could be altered and considering ways in which that might be better or worse.
For example, if Hitler had not risen to power and started World War II, would we have had the civil rights movement in the 60s? Did it take the extremely negative example of the holocaust to convince a new generation growing up in the 50s that racism and prejudice of any kind are abhorrent? And what about surviving the nuclear arms race? Without Hiroshima and Nagasaki, would mutually assured destruction have worked as a strategy to reduce the likelihood of nuclear war? Would the human race have survived a period of nuclear proliferation without a negative example to draw on?
It is reminiscent of Leibniz's "Best of all possible worlds". I am not referring to the mockery that Voltaire made of that phrase in Candide when he suggested that the phrase meant there was no unhappiness in the world. I mean it as Leibniz meant it, that for all the unhappiness in the world, things would be even worse if we did not go through that unhappiness.
To me, that gives us two great types of time travel stories that I seem to see far too few of: ones where people try to change the world for the better only to have it get much worse, and those where people change the world for the worse knowing that the overall effect will be better.
But for all these time travel stories that I love, I find that there are few that I can call Science Fiction despite the fact that there are at least some reasons in science to think that time travel of some sort may be possible. I am not a physicist and if anybody is reading this and wishes to correct me on any of these points then feel free. I think that they are all rudimentary enough to pass muster, though, and it surprises me that no one ever seems to deal with them in any time travel stories that I have read.
I have a number of issues with the science in time travel stories although suspension of disbelief allows me to treat them as entertaining fantasy. This is my first objection. Others will follow in later posts.
Objection 1: Position and Momentum
Whenever someone travels in time, they always end up standing on the ground, usually in exactly the same place they left from. There are so many ways this is a troublesome concept.
a) Ground level changes. Moving any significant distance in time while maintaining the exact same place makes it likely you'd be buried in the ground or floating in the air. Thanks to plate tectonics, you may even be over or under the sea. If you were on a boat, a short trip of a few hours would put sea level at a different location thanks to tides, so make sure your time machine is a submarine that can drop from heights. Of course, none of this really matters because of the other positional problems that follow.
b) Choose a different time of day? The earth has just moved under you. If you stay in exactly the same place, you could be anywhere else on the same latitude. Assuming some kind of location displacement built into your time machine to account for this, you have to deal with momentum changes. Unless you are at the north or south pole, this will be problematic.
Assume a non-flying Delorean is time-travelling for a 12 hour displacement and is maintaining its position on the earth. In order to account just for the vector of the earth's rotation (and you can see from the length of this post that there are many other vectors) you would have to go from travelling in one direction to the complete opposite direction. Eric Idle tells us that the earth revolves at 900 miles an hour (this depends on where you are on the earth, but works for approximations), so to flip your direction of travel you would have to change your speed 1800 miles an hour. That is mach 2.4. Assuming the Delorean did not get ripped apart (a ridiculously big if), at this speed the air would start to lift the car into the air without massive stabilizers to keep you on the ground. Assuming your tires were in good shape, your coefficient of friction with the ground would be about 0.8. That means you would require 41km of road to break on, less if the stabilizers introduced a lot of drag. But you would have to worry about creating too much G-force if deceleration was too fast. A flying Delorean has to deal with similar speed issues, but fortunately doesn't need roads.
Of course, if you only moved in 24 hour increments you could more or less ignore this factor.
c) Choose a different time of month? The moon does not just orbit around the earth, the earth makes small movements toward and away from the moon as well. They each orbit a point between them called the barycenter point. The earth only shifts about 4700km which is just 3/4s of the width of the earth itself, but it still would be a shock to a time traveller to suddenly find themselves buried deep within the earth or thousands of miles above it. The speed of movement is only 41km per hour and even doubling it does not give a number anywhere near the others, so the momentum issue in this case can be ignored.
Again, if you choose the same time of the lunar month you can do away with this as a consideration.
d) Choose a different time of the year? The earth is no longer anywhere near you as it has travelled around the sun. This is not usually a problem for us because gravity emits a long, enduring pull to keep us travelling along with the earth. Since we skipped that part with our time travel, we are now either on the far side of the sun from the earth floating in space, or miraculously transported to the earth but now having to deal with the momentum change.
The earth travels at about 107,500 km/hour or 30 km/second. Every second of time travel, the earth gets 30 km away from us. Assuming we want to stick with the earth, making a 6 month time travel journey requires a momentum change of 215,000 km/hour, or Mach 200. There is no point to incorporating motion displacement into your time machine because you can't slow down quickly enough to make "maintaining your position" mean anything.
Again, we can eliminate this issue by only time travelling in 1 year increments. Since a year is not an even number of days or lunar months, though, the previous two issues come into play when we do that.
e) The sun revolves around the galactic centre of the milky way once every 250 Million years. Estimates of how fast vary, but a conservative estimate is about 200km per second. That means for every second we travel back in time, the sun and earth and everything we know is being dragged back the way we came by 200 kilometres. That amounts to over 700,000 kilometres per hour time-travelled.
The good news is that for trips of less than 500,000 years back in time, the vectors of motion will be similar enough that there is not much worry about momentum. The bad news is that your time machine still needs to be a spaceship so that you can try to catch up with the earth.
f) The milky way is moving at about 300 km/sec within the local group of galaxies. Reverse the direction when travelling backwards in time as the milky way will occupy its former position, but no forces are acting on your time machine to make that true for you. Again, there won't be much difference in momentum between you and the earth, it will just be much further away.
g) The local group of galaxies is moving toward something called the great attractor at 1000 kilometres per second. Same details as other categories.
h) The universe is expanding at an accelerating rate. That sounds like we'd have to move faster still to catch up to the earth, but in fact the reverse may be true, although the speed boost would be small. Since both we and the earth would be farther back in time, that means that the space between us would be smaller. It amounts to 0.007% smaller per million years. In any case, this does not seem to be a big enough effect to worry about.
The Net Result
So can we add up all these speeds and come up with an answer as to how fast our time machine would have to travel to catch up with the earth? Unfortunately, no. Many of the vectors for these speeds are at angles, sometimes turning back on each other which means that to some degree they may cancel each other out.
Most articles that discuss the speeds at which the earth and sun move through the universe talk about how you have to calculate the speed relative to something else. What we want to use is the position of the earth sometime in the past. This seems a singular request, so I have looked for something more neutral. The best answer seems to be to measure the earth's redshift against the cosmic background radiation, which is the most distant and stable source we can look at. The net result is that the earth is moving at 600 kilometres per second in the direction of the constellations Leo and Virgo. Moving back in time, the earth would recede in the opposite direction.
This means that a way to launch a spaceship out of the earth's gravity well, if time travel were possible, would be to wait until Leo and Virgo were overhead and then move a fraction of a second into the past. It would also mean that time travel could provide a way to cover interstellar distances provided we weren't picky about direction. Perhaps it could get us close to the star Virgilis 61, which has a Super Earth planet around it.
But 600 kilometres per second is awfully fast if we wanted to stick with the earth. It is over 2 million kilometres an hour, or 0.2% of the speed of light. The fastest spacecraft we have ever created, the twin Helios probes, reached only about a 10th this speed. The situation becomes even worse if you don't want to spend as many years in space travelling as your time jump. If you wanted to travel back just 5 years, the earth would be 95,000,000,000 kilometres away. Travelling at 600 kilometres a second would take you the same amount of time, 5 years, to reach it. Speed up to 150,000 kilometres a second, half the speed of light, you would still take more than a week to reach earth although time dilation would make it seem about a day shorter.
So perhaps some sort of warp drive would still be required for a functioning time machine, if only to keep it in the same general vicinity as earth. Changes in momentum with the earth and sun could all be dealt with during decelerating from half the speed of light.
Next up - Objection 2: Quantum Mechanics and Time Travel
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