Archive for August, 2013

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.

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.

Time Cards in a Time Travel Industry

Posted in science fiction on August 4, 2013 by Alex

The Blog form of Space Madness may be over, but I assure my dedicated fan(s) that I am hard at work editing and revising and adding to the story, preparing it for publication as a novel. I have no idea how long this will take, as I have never written a novel before. It will probably be somewhere between two weeks and a decade before it is ready.

In the meantime, to tide you over, here is an excerpt from another writing project of mine, which I began way back in November as part of National Novel Writing Month. The story itself is titled “The Causeway,” and is mostly about the goings on of a company that uses time travel to generate profit in revolutionary ways.

The company, called “CTC Industries,” is not a perfectly run company by any means, but the use of time travel on a daily basis gives it an overwhelming advantage over all competitors. (CTC stands for “Closed Timelike Curve.”) Here is a sneak peek inside the company with this recently recovered internal memo regarding the reporting of hours worked. Enjoy!

 

To: Accounting Department, CTC Industries.

Subject: Questions about my timecard

 

I have a few concerns regarding the reporting of hours worked through our new online timekeeping system. It seems that the nature of my duties here at CTC Industries does not fit well with an all-purpose time card. Such systems were originally designed for ordinary 9-5 jobs where the employee stays within the office the entire time.

Some of my duties require me to go off site for much of my work day. I would like to know if I should include travel time between sites on my timecard. Also, the policy on overtime is a little unclear, as I am often required to put in a lot of work at home and some extra hours in the office just to get the day’s work done. If you could send me a document laying out these policies in detail, as well as instructions on how to enter them into the automated system; that would be great.

In addition, I often find myself leaving work slightly before I arrived, so as not to cause any embarrassment by having an awkward conversation with my past self. The system seems to have some problems when I enter the “time in” and “time out” fields on days like this. I assure you, that in my own personal timeline, I am careful to keep it to 8 hours a “day” in the office. No more and no less.

There are some days, especially when a deadline is approaching, that I need to interact with my past self in order to get a job done as efficiently as possible. This involves the younger me carefully executing instructions from the older me and retaining as much as possible so that I can properly explain what needs to be done to myself later on. Does this situation count as two days worked, or just one?

Another thing, regarding field work in the past: I received a per diem of $500 for expenditures and meals for a two day excursion in 1987, which will occur next week. Is that $500 in today’s dollars or 1987 dollars? I have been instructed to report my hours to a carpet cleaning company in Sand City and the details will be sorted out by payroll as of last week. Will a pre-paid credit card from today function in 1987, or will I have to bring cash? If I need a rental car, should I get a driver’s license from the appropriate year made up for me? I realize some of these questions may not be in your purview, but I was hoping for some helpful information about these issues from someone. I have asked around, and those who do seem to know something about these things refuse to tell me for fear of creating temporal paradoxes.

I appreciate any time you take in answering these questions. I have heard the new temporal payroll dept. has its hands full at the moment distributing paychecks from future accounts, and I wish you all the best.

Yours,

Leonard Schmidt

Lead Project Engineer, CTC Industries

Department of Causal Loop Construction

Mail Code 6645558