Archive for the Theory of Time Travel Category

Making Time Travel Consistent: Part II

Posted in science fiction, Theory of Time Travel on August 30, 2013 by Alex

Item 2: All observations are probabilistic.

This is true whether we invoke quantum mechanics or not. What quantum mechanics brings to the table is the specific sort of probabilities being used. What must be true is that there is a minimum interval of time measurable by any object. What is this interval? In principle, it is the time it takes for light to pass from one end of the object to the other. For time intervals shorter than this, there is no coherent notion of “before” and “after” which could be used to distinguish between events. There is therefore an inherent uncertainty in the measurement of time. This creates uncertainties in the measurements of all the properties of distant objects. For example, if you wanted to know how fast your semi-truck was bearing down on you, you would have to measure the length of the time interval between successive photons hitting the back of your eye. Ultimately, all types of measurements reduce to measuring the time interval between local events. Most of the time, it’s much worse than this, as more detailed observations require more information, which means more photons hit your detector, which means a compounding of the errors in the measurements being done. Steps can be taken to reduce the compounding of the error, but it definitely cannot be reduced to zero. Every honest observation would be a statement like “I am 99.997 percent sure that the truck is between 25.5233357 and 25.5233359 feet away from me, and I am 99.9982 percent sure that its speed is between 45.213 and 45.214 MPH.”

The mathematically inclined would make a graph of “position of the truck” vs. “probability it is currently THIS distance from me.” This graph is called a probability density function (or sometimes simply a distribution.) We would expect it to look like a bell curve (which is called the ‘normal’ distribution) and if we are very sure of the location of the truck, it will be a skinny curve, whereas if we are not terribly sure of the location of the truck it will be a wide curve. The width of the curve (more specifically, the variance) is what is referred to as the “uncertainty” in the measurement.

I should note that this type of uncertainty is completely unrelated to Heisenberg’s Uncertainty Principle, which gives us another bound on the accuracy of a measurement due to the specific types of probabilities (more accurately: “amplitudes”) used in quantum mechanics.

In the quantum mechanical picture, the amplitudes of different ways an event might be observed to occur can interfere with one another, potentially creating distributions (which are computed from the absolute value of the amplitudes) that are very different from what one sees with just regular old probabilities. For example, it is entirely possible (if exceedingly unlikely) that the semi-truck bearing down on you could have a 50% chance of being 100 feet from you and a 50% chance of being 2 feet from you, based on your observations of the photons hitting your eyes. A situation like this is called a “discrete” distribution, since there are only two discrete options for the location of the truck. This is in stark contrast to a continuous distribution, which is what we see in the normal, “classical,” picture.

I should point out that in this scenario, the quantum mechanical picture can give rise to either discrete distributions or continuous distributions, or sometimes a combination of the two, whereas the classical picture would only give rise to a continuous distribution. Also, these probabilities do not tell us the “true” position of the truck, just the probability that the truck will be in one position or the other (in the discrete case,) or within a certain interval of positions (in the continuous case.) Information from future photons will help us distinguish between the two cases.

I am going to make an attempt in the next section to use discrete probabilities to create a good-enough-for-science-fiction resolution to the famous “Grandfather Paradox.”

Stay tuned.

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Making Time Travel Consistent: part 1

Posted in science fiction, Theory of Time Travel on August 11, 2013 by Alex

In the previous post, I gave you a little teaser about my next writing project: The Causeway. One of the difficult things about writing a story about time travel is the issue of consistency. Time travel is difficult to write about in any way that makes sense. It jumbles up cause and effect into an unintelligible mess, and has a tendency to leave readers passed out in the fetal position, hands fiercely gripping the sides of their head.

What I wish to do in this space is slowly work out my thoughts on the mechanics of time travel in a way that will (hopefully) make sense, or at least be consistent for the purposes of my story. This will be done in a series of posts, tackling one item at a time.

I will not dwell on the specific technology that would be used to implement time travel (more specifically, closed timelike curves that can interact with our normal, causal world,) but on what mechanisms known to science today can be used to explain its possibility.

Item 1: All observations are local.

This is a principle that is easy to ignore when speaking of the so-called paradoxes of quantum mechanics and special relativity. When you see an object (say, a semi-truck bearing down on you), what is it that you really see? You do not see the truck itself, for it is far away and is not directly in contact with you (at least, not yet.) What you see is the image of the truck projected onto your retina. Photons bounce of the surface of the truck, pass through the intervening space, are focused by the lenses in your eyes and strike a screen in the back, slightly altering the nerves there. Electrical signals are then sent to your brain which then interpret what type of object the photons came from, as well as some rough information about how big it is, and what it is made of. Successive bursts of photons hitting the back of your eye can give you more information about your oncoming doom. You can now determine how fast it is moving, whether or not it is slowing down, whether it is coming right at you or is beginning to veer away.

Your eyes (and the part of your brain that processes the incoming information constantly streaming into them) are a fantastically complex and effective bit of measurement and interpretation machinery. They are not, however, perfect. They only have so much resolving power (limited by how many photons can be shoehorned into your eyeball at any given time,) they can only see photons of specific wavelengths, and they require time to process the information input. Much information is thrown out by your brain, leaving you with a highly stylized picture of what is bearing down on you.

In principle, we could make better measuring devices. (And in practice, as well. There are telescopes with much greater resolving power than our eyes, which can see different parts of the electromagnetic spectrum, and can interpret the data they receive into cool, three dimensional false color graphs. See the images taken by the Hubble Telescope, for example.) But every measuring device works essentially the same way. The object being observed sends out “messenger particles” that travel the distance to the measuring device, and the measuring device then measures some properties of these particles: their wavelengths (or equivalently, their energy), the direction it came from, how that direction and energy relates to the direction and energy of all the other messenger particles hitting it, etc…

All we ever really see are the messengers.