How Would You Navigate After Using a Warp Drive?

[SpaceTiger]

Alright, so here's my long-delayed response to the question of warp drive. Again, for easier consumption, I'm going to split it into multiple posts. Also, I know that many of the people here won't need such a pedagogical treatment, but this subject is of great interest to amateurs as well, so I'll keep it in simple terms.

It's true that I'm not an expert on the topic and had to do a little research today to put the wormhole stuff together, but the things I've stated previously in this thread were rushed responses repeated from several people in whose judgement I have a great deal of trust, so I don't think I was in error stating them.

Anyway, here's the situation. We want to get across the galaxy in less than a person's lifetime. There are several things in modern physics that we'll call possible possibilities. I'll try now to determine whether or not they're real possibilities.

1) Near-light speed travel.

This is perfectly workable, but I would not say that it constitutes what we normally understand to be warp drive. The idea behind it is that if we travel near light speed, there will be time dilation/length contraction effects which allow us to quickly traverse large distances in the rest frame of the galaxy. It can be understood entirely with special relativity. In the Earth's rest frame, the minimum time with which anything can cross the galaxy (d~15 kiloparsecs) will be roughly:

\Delta t=\frac{d}{c}\sim50,000\ years

There is no escaping this. No matter how close you get to the speed of light, the people on Earth will have to wait that long for you to reach your destination (and the same time for you to communicate back). From the traveler's point of view, however, time is dilated:

\Delta t'=\sqrt{1-\frac{v^2}{c^2}}\Delta t

We want to know the speed requirement to shorten the trip, so let's solve for v:

v=c\sqrt{1-(\frac{\Delta t'}{\Delta t}})^2}

If we want to cross the galaxy (\Delta t=50,000\ years) and want the trip to take a human lifetime (\Delta t'=100\ years), this equation says that you must travel at v \sim 0.999998c. In general, it's convenient to put relativistic equations in terms of the gamma factor:

\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}

Now, we'll just solve for \gamma instead of velocity because it can be easily converted to velocity and because it has more physical meaning. With this, the above equation takes the form:

\Delta t'=\frac{1}{\gamma} \Delta t

and we find that \gamma \sim 500 is needed to allow a person to live for the entire trip. For shorter trips, you just multiply this number by the factor by which you want it to be shortened (e.g. \gamma\sim 2000 for a 25 year trip).

To explore the practical issues surrounding this problem, however, we want to look at it from a different point of view -- that is, we'd like to know how much energy we need to give the ship in order to make the trip. The relativistic equation for kinetic energy is:

E_k=(\gamma-1)mc^2 \sim \gamma mc^2

if \gamma >> 1. For a 1000 kg ship and the factor calculated above, this gives an energy of \sim 5 \times 10^{22}\ Joules. This is about a hundred times the total annual energy use of the United States. A steep cost, but certainly not impossible.

Another issue that JesseM briefly addressed was that of acceleration. If we try to accelerate too fast, then our bodies won't be able to take it (as any fighter pilot can attest to). This means that we can't build a ship that will jump immediately to the speed quoted above -- we have to take into account the extra time it takes to accelerate. JesseM gives the time assuming an acceleration of 1 g, an acceleration we're perfectly capable of handling.

So what's wrong with all this? Well, it depends on what you want. If you want to create an intergalactic civilization, the above means of transportation is completely useless. As I already said, even though the traveler makes the trip in a short amount of time, the earthbound folks will have to wait 100,000 years to hear back from them. If everybody lived on ships of this sort and spent most of their time traveling near the speed of light, then I suppose we could create a star-hopping civilization, but it seems like costs of something like that would far outweigh the benefits. This means of interstellar travel seems like it would be better as a means of escape if something nasty was going on in the solar system (like the sun dying).

So that's the simplest possibility. I'll address wormholes in the next post.

 

[SpaceTiger]

I've had many people ask me why we're so sure that we can't travel faster than the speed of light; after all, Einstein could be wrong at some limit. Maybe in the future we'll create a machine that will actually break the speed of light barrier and penetrate into new physical realms.

This might happen, of course, and I'm never one to completely exclude possibilities, but it should be understood that the theoretical problems surrounding faster-than-light travel (FTL) go far beyond a simple mechanical limit (like the sound barrier). Rather, the existence of FTL would require a complete shift in our current understanding of the way the universe works. According to Einstein's theory, an object that moved faster than the speed of light would, in some reference frames, be traveling back in time, and any time you introduce the possibility of time travel, you run into all sorts of paradoxes.

The most common and easily understood paradox is called the "grandfather paradox". Basically, it says that if you could travel back in time, you could kill your grandfather when he was young and render your own birth impossible. Since it was you that killed your grandfather, your non-existence wouldn't make a whole lot of sense. If you ask me, this simple argument should be enough to suggest that we need new physics (or, at least, a better understanding of the existing physics) to fully deduce the theoretical possibilities of any means of time travel (including wormholes). However, we'll put that aside for the moment.

What are wormholes? Well, they can be thought of as a sort of "tunnel" in spacetime. In Dr. Gott's book on time travel, he gave a great analogy that went something like the following (I don't have the book with me at the moment). If you have two ants on opposite sides of a table, what's the quickest way for them to reach each other? Well, they can take the long route in which they crawl all the way to the edge of the table and then around to the other side. This is analogous to traveling at sublight speeds to the other end of the galaxy. There is a quicker way, however. Given a suitable amount of strength/energy, the ants can break right through the table and create a tunnel that brings them to their destination in a much shorter time. This is analogous to a wormhole. You just need to bend spacetime enough to get where you want to go. This does not technically constitute FTL travel, but it does lead to the same time travel paradoxes.

There are many other problems with this picture. The first is that, in the conventional ideas surrounding warp drive, you would need both ants to break through the table. In other words, you would need someone to "open up" the wormhole at your destination as well as at your point of origin. Unless the opening was already in place, this would require someone to travel to your destination and the only other way to do this is at sublight speeds. Another problem is that Stephen Hawking's recent work seems to suggest that quantum fluctuations would prevent the wormhole from even opening. This is part of his "Chronology Protection Conjecture", which basically asserts that the laws of physics conspire to prevent the possibility of time travel.

Thus, I would say that both Dave and I were wrong. Our current understanding of physics does not suggest that warp drive is possible, nor does it suggest that it's impossible. Rather, we're still unsure whether the mainstream theories of physics predict its possibility.

As for my comment about the "galaxy of energy", I was indeed referring to the "Gott loop". Since the possibilities of time travel and warp drive are intimately connected and this is the time travel theory that is experiencing the least opposition, then I assume it is what he was referring to in his quote to me.

 

[mapper]

For the galaxy worth of energy poster.
http://www.nasa.gov/centers/glenn/research/warp/possible.html

"Zero Point Energy"
Zero Point Energy (ZPE), or vacuum fluctuation energy are terms used to describe the random electromagnetic oscillations that are left in a vacuum after all other energy has been removed. If you remove all the energy from a space, take out all the matter, all the heat, all the light... everything -- you will find that there is still some energy left. One way to explain this is from the uncertainty principle from quantum physics that implies that it is impossible to have an absolutely zero energy condition.

For light waves in space, the same condition holds. For every possible color of light, that includes the ones we can’t see, there is a non-zero amount of that light. Add up the energy for all those different frequencies of light and the amount of energy in a given space is enormous, even mind boggling, ranging from 10^36 to 10^70 Joules/m3.

In simplistic terms it has been said that there is enough energy in the volume the size of a coffee cup to boil away Earth’s oceans. - that’s one strong cup of coffee! For a while a lot of physics thought that concept was too hard to swallow. This vacuum energy is more widely accepted today.

What evidence shows that it exists?

First predicted in 1948, the vacuum energy has been linked to a number of experimental observations. Examples include the Casimir effect, Van der Waal forces, the Lamb-Retherford Shift, explanations of the Planck blackbody radiation spectrum, the stability of the ground state of the hydrogen atom from radiative collapse, and the effect of cavities to inhibit or enhance the spontaneous emission from excited atoms.
The Casimir Effect:

The most straight-forward evidence for vacuum energy is the Casimir effect. Get two metal plates close enough together and this vacuum energy will push them together. This is because the plates block out the light waves that are too big to fit between the plates. Eventually you have more waves bouncing on the outside than from the inside, the plates will get pushed together from this difference in light pressure. This effect has been experimentally demonstrated.

Can we tap into this energy?

It is doubtful that this can be tapped, and if it could be tapped, it is unknown what the secondary consequences would be. Remember that this is our lowest energy point. To get energy out, you presumably need to be at a lower energy state. Theoretical methods have been suggested to take advantage of the Casimir effect to extract energy (let the plates collapse and do work in the process) since the region inside the Casimir cavity can be interpreted as being at a lower energy state. Such concepts are only at the point of theoretical exercises at this point.

With such large amount of energy, why is it so hard to notice?

Imagine, for example, if you lived on a large plateau, so large that you didn’t know you were 1000 ft up. From your point of view, your ground is at zero height. As long as your not near the edge of your 1000 ft plateau, you won’t fall off, and you will never know that your zero is really 1000. It’s kind of the same way with this vacuum energy. It is essentially our zero reference point.

What about propulsion implications?

The vacuum fluctuations have also been theorized by Haisch, Rueda, and Puthoff to cause gravity and inertia. Those particular gravity theories are still up for debate. Even if the theories are correct, in their present form they do not provide a means to use electromagnetic means to induce propulsive forces. It has also been suggested by Millis that any asymmetric interactions with the vacuum energy might provide a propulsion effect.

 

[ohwilleke]

Against wormholes:

http://www.arxiv.org/abs/gr-qc/0503097

Date (revised v3): Fri, 8 Apr 2005 19:54:25 GMT (6kb)

Wormholes and Time Travel? Not Likely
Authors: Leonard Susskind
Comments: 5 pages, remark added about time delay in identification. Reference added

Wormholes have been advanced as both a method for circumventing the limitations of the speed of light as well as a means for building a time machine (to travel to the past). Thus it is argued that General Relativity may allow both of these possibilities. In this note I argue that traversable wormholes connecting otherwise causally disconnected regions, violate two of the most fundamental principles physics, namely local energy conservation and the energy-time uncertainty principle.

 

[ohwilleke]

[W]e find that \gamma \sim 500 is needed to allow a person to live for the entire trip. For shorter trips, you just multiply this number by the factor by which you want it to be shortened (e.g. \gamma\sim 2000 for a 25 year trip).

To explore the practical issues surrounding this problem, however, we want to look at it from a different point of view -- that is, we'd like to know how much energy we need to give the ship in order to make the trip. The relativistic equation for kinetic energy is:

E_k=(\gamma-1)mc^2 \sim \gamma mc^2

if \gamma >> 1. For a 1000 kg ship and the factor calculated above, this gives an energy of \sim 5 \times 10^{22}\ Joules. This is about a hundred times the total annual energy use of the United States. A steep cost, but certainly not impossible.

There is one more step you have to take to really get a good handle on the energy costs. This is the problem of how you get your ship to go so fast.

If you accellerate with carried fuel, then E_k is proportional to your fuel requirements or worse, and twice that much if you want to both speed up and then slow down when you arrive at your destination. The theoretical limit on the amount of energy that can be extracted from carried fuel is E=mc^2 (i.e. an anti-matter drive). But, of course, no system can be 100% efficient in converting matter to energy.

Of course, the problem is that E_k is also proportional to the mass of the object you are trying to move, and if you want to travel at \gamma \sim 500, you are going to find that a very large proportion of your ship's entire mass needs to be fuel.

In particle accellerators, we can get particles to close to the velocity c, by using a device to accellerate the particle which it outside and hence doesn't add mass to the particle itself. But, if you are to have a viable, conventional relativity starship, you need to either have massively huge ships with very small payloads, or find some way to not carry your own fuel, or to carry your fuel it in a form that has energy and not matter (e.g. photons swirling at high density in a nearly perfectly optically transparent ring).

 

[SpaceTiger]

But, of course, no system can be 100% efficient in converting matter to energy.

You're absolutely right and I should have included a little remark about that. In a hypothetical futuristic warp drive, however, we can probably consider this factor to be of order unity (i.e. less than an order of magnitude from 100%).

 

[ohwilleke]

A variant on a warp drive which poses considerably fewer engineering challenges would be essentialy an extremely powerful slingshot. You would put your payload in some sort of large ring and slowly power them up to nearly "c" with an external power source, and you would use gravitational braking (and perhaps space dust and interstellar radiation) to bring the amount of energy you need to carry as fuel to slow down to considerably less than E_k for the payload, which would still be predominantly fuel, but perhaps not nearly so impossible as a ship that needed to speed itself up and slow itself down.

Of course, once the first crew gets to the destination, they then build the starship equivalent of an aircraft carrier tail hook system to move as much as possible of the braking energy off the ship as possible (e.g. with a series of targetted electromagnetic beams directed in such a way as to decellerate the ship at a tolerable rate). A shift from a 2E_k carried energy requirement to a 0.8E_k energy requirement dramatically reduces the engineering challenges involved.

Naturally, the first crew also has to build its own slingshot to return, and when they return, they find the planet they left is 100,000+ years older.

Also, given the immense energy cost you are paying to shorten the ride for the passengers with special relativity, it would probably be more likely that any such ship would either rely on some form of biostasis (essentially hibernating the people on board for a very long time), or would be multi-generational carrying a community in which the original crew's descendants, perhaps many generations later, are the ones who actually arrive at their destination.

 

[matt.o]

SpaceTiger, I too have had the problem of people asking about special relativity and why you can't travel faster than the speed of light. I have found that if you explain that the constancy of the speed of light was observed experimentally by the Michelson-Morley experiment, then normally this is enough.

I think a common misconception with the general public (and some physicists) is the belief that Einstein came up with SR and GR out of no where (complete with a light bulb above his head!), when in fact he was just attempting to explain some observed phenomena.

 

[AcEY]

FTL travel would surely be possible if we found a way to create a weightless material. Unfortunatly that's impossible (although if i believed quantum mechanics then if i kept trying eventually it may happen). I was thinking, maybe we could create some kind of bubble that would make us weightless, but in technology terms its far into the future for something like that. And Dave on the making worm holes into a time machine, i believe that you somehow connect one end to your ship and fly at sub-light speeds (but close to light speed) so that time dilation occurs and one end is older than the other - like the "Twin Paradox" (Being that if one twin went on a ship and flew at close to light speed then came back, due to length contraction - not time dilation as both twins would age the same amount - be different ages). But some theorise that when you bring the end of the wormhole back together with the other end (to have them close enough to be a wormhole) a light feed back loop would occur (light would go in one end and come out the other, because one end is in the past the light could then go back in at the same time as it originally went in and keep doubling up) until it exploded.

 

[SpaceTiger]

FTL travel would surely be possible if we found a way to create a weightless material.

Actually, a massless object would move at the speed of light.

 

[AcEY]

hrm ok, well anyway. If we found a way to travel faster than the speed of light, I am guessing at this point we would also find a way to get from FTL to sub-light which is apparently impossible as well, and you didnt travel into the past then we could level journeys out so that when we arrived it would be the same time as we left, imagine never having to leave 30 mins before work starts, you could just be there when you leave.

sorry i meant to point out that traveling into the past would be more useful, but would probably be illegal due to paradoxes.

 

[JesseM]

Against wormholes:

http://www.arxiv.org/abs/gr-qc/0503097

Date (revised v3): Fri, 8 Apr 2005 19:54:25 GMT (6kb)

Wormholes and Time Travel? Not Likely
Authors: Leonard Susskind
Comments: 5 pages, remark added about time delay in identification. Reference added

Wormholes have been advanced as both a method for circumventing the limitations of the speed of light as well as a means for building a time machine (to travel to the past). Thus it is argued that General Relativity may allow both of these possibilities. In this note I argue that traversable wormholes connecting otherwise causally disconnected regions, violate two of the most fundamental principles physics, namely local energy conservation and the energy-time uncertainty principle.

Susskind later realized that that paper contained some elementary errors and basically retracted the whole argument:

http://www.arxiv.org/abs/gr-qc/0504039

Rebuttal to a Paper on Wormholes
Authors: Leonard Susskind

In a recent paper on wormholes (gr-qc/0503097), the author of that paper demonstrated that he didn't know what he was talking about. In this paper I correct the author's naive erroneous misconceptions.

 

[ohwilleke]

Susskind later realized that that paper contained some elementary errors and basically retracted the whole argument:

http://www.arxiv.org/abs/gr-qc/0504039

I'd seen the pair, but hadn't caught the sweet irony that the reply and the original were by the same person.