Faster than Slower than Light



In the last article on Tachyon Rocketry, it appears that even a rocket propelled by tachyons is limited by the lightspeed barrier.

The problem is that our bodies (and our starship) are made of electrons, quarks, and other particles with real, non-zero mass. In the context of faster-than-light tachyons, such particles are known as bradyons or tardyons, and are always constrained to travel slower than light.

What if we got rid of the starship altogether? Instead of traveling the galaxy the slow way, what if we could just transmit ourselves to our destination? Sort of like Star Trek’s transporter technology?

Beam Me Up

The Star Trek transporter may be a bad example, because it’s said to break you down into subatomic particles, transmit those particles to your destination, and then reassemble them –er — you. Those subatomic particles are still constrained to travel slower-than-light.

However, if all we need to transmit is information, then we can speed you to your destination at the speed of light, encoded into a radio transmission. (How do we convert that radio transmission back into you? We’ll probably need a receiving station at the destination to do that dirty work. Presumably it traveled there slower than light.)

Is it feasible to transmit data about an entire human body? How much data would we need to transmit? The maximum amount of information that can be contained in a volume is given by the Bekenstein bound, which is:

I \leq \frac{2 \pi R E}{\hbar c ln(2)}

This works out to 2.577 \times 10^{43} m R bits, where m is the total mass of the system in kg, and R is its radius in meters. Assuming a sphere with a radius of 1m, encapsulating 100kg, this works out to 2.6 \times 10^{45} bits. There’s not an SI prefix for numbers remotely this big: it’s roughly 3 \times 10^{20} yottabytes.

At present, the fastest wireless transmissions can hit 100 Gbps, which means that transmitting the data for an entire human body would take 2.577 \times 10^{32} seconds. That’s about 8 \times 10^{24} years: many orders of magnitude longer than the current age of the universe.

Heck with that. I’ll take the starship, thank you very much.

Compression

Of course, sending an uncompressed stream of bits would be foolish. Most traffic on the internet is compressed to conserve bandwidth. Compression algorithms such as DEFLATE can achieve compression ratios of up to 1032:1. Of course, that’s an ideal compression, where the bit stream contains no data at all, and even that level of compression wouldn’t put a significant dent in our transmission time.

What if we only send your brain? It’s a lot smaller than your whole body, after all. Sure, the receiving station won’t know anything about what your old body looked like. They may end up downloading your brain into the cloned body of a gorilla or a bikini model.

Unfortunately, the Wikipedia article has already worked out the Bekenstein bound of the human brain, and it’s only one order of magnitude smaller than the whole body. Still not a lot of savings.

Then again… the Bekenstein bound is a maximum limit. Most physical systems can be described with much less information than this maximum. For example, this Slate article suggests that the information content of the human brain may only be on the order of 10 – 100 terabytes.

Now we’re getting somewhere. 100 terabytes is easily within the range of some RAID backup systems. Our 100 Gbps wireless network can transmit that amount of data in just a few hours. Likewise, if you still insist on keeping your body, we can probably find ways of significantly compressing the necessary information.

You wouldn’t be aware of this passage of time. First, because we’re transmitting a snapshot of the state of your brain at the instant we scanned it. Second, because particles traveling at the speed of light experience zero time. From your perspective, you would step into the scanner on Earth, and step out of the reassembly device on Omicron Persei 8 an instant later, unaware of the passage of a thousand years of travel time.

Faster?

In the last article, we built a tachyon-propelled rocket. Assuming the existence of tachyons, couldn’t we transmit the data stream via tachyons rather than ordinary radio waves, and get to our destination even faster?

I didn’t go into any detail in that article, but FTL, relativity, and causality are mutually inconsistent. The existence of any two immediately rules out the third.

Causality, the principle that cause precedes effect, is practically a founding principle of physics. Without causality, it becomes impossible to predict the outcome of an interaction. This would render physics useless, since its purpose is to create predictive models of the universe, so physicists are understandably reluctant to let it go.

Relativity has been well-tested in the past century, and has always been upheld by experiment. It’s not an exaggeration to say that half of modern physics is relativity.

FTL, in contrast, has never been observed. If it exists, which of the above do we throw away: relativity or causality?

If relativity is wrong, then there’s nothing special about FTL. We can get you to your destination as quickly as you like. The physicists will probably spend another century scratching their heads and wondering why relativity looked correct.

If causality is wrong, then we’ve opened the door to time travel, and all sorts of temporal paradoxes. You can arrive at your destination before you leave your origin. On your return trip, you can meet up with yourself for lunch before your original departure.

Isn’t FTL fun?

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