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Do you think there is an element or compound out there in space that contains the energy or means to propel us faster than the speed of light / allow time travel?

Or materials that can contain a sustain nuclear fusion without melting down?

Or do you think we can figure it out with what we have on earth?

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The key to FTL travel won't be a material, it will be energy.

Fusion is possible now using magnetic containment - the problem is getting an energy-positive sustainable reaction.

Elements are arranged by atomic number - if we were missing one, we'd know.   Unknown compounds, sure - but we have reached the end of finding naturally occuring elements.

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Mass = energy





I'm talking about heavy elements beyond our periodic table.  OR compounds that are not possible on earth due to gravity or other earthly limits.

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Heavy elements are unstable.  Some of the heavier one's don't actually exist in any quantity...we just know we've made them (in extremily minute quantities) by their decay products.  Fusion will be driven by technology, not discoveries of a new fuel source (most likely).

 

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faster than light... no  Not unless we find a naturally occurring wormhole.  Besides relativistic effects are cool and allow you to build a ship that makes a 1000 year trip with only 10 years of supplies and have the crew be just fine.



Elements... no not really we pretty much know all the stable elements.  But you know Neutron Stars?  Their density is about the same as the nucleous of an atom... you could think of them as giant atoms...  I don't think at that size scale there is much of a difference between atomic number googleplex and atomic number googleplex +- 100,000
Compounds sure we're discovering new compounds all the time right here on earth.  And discovering new and novel ways of combining things.





Particles... the LHC is working on that... but then that's right here on earth too...



Energy... Dark energy is one of the biggest unknowns in physics right now but again if we're right it is permeating everything around us right now... same for dark matter.
So to put it shortly... about the only thing we'd need to leave the planet to find are compounds.

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Errr.... http://en.wikipedia.org/wiki/Neutron_star



 

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So to put it shortly... about the only thing we'd need to leave the planet to find are compounds.

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I choose to believe my astrophysics professor who specializes in neutron stars...
 

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the problem is your use of the word density when you likely mean volume.

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True, we may discover compounds that we hadn't imagined, but as computer technology continues to progress, we'll just simulate every possible chemical/biological combination possible, and then synthesize the ones that look promising.

And the act of synthesizing a compound is trivial in terms of energy and cost vs. interstellar travel. Any species capable of interstellar travel is so powerful they can pretty much make whatever they want at home already.

Exploration, and colonization (getting humanity's eggs out of one basket) will be the reasons to go.

Although I don't think humans will have bodies by the time we get leaving the Solar System. We'll probably leave as data, recorded personalities, or AI's, because the differences between all three might be academic at that point. You could put millions... billions of "people" into something the size of a beer can and fire it off at another star with a big coil-gun made from asteroids here in out solar system. And they won't grow old, get impatient, or go hungry etc. Or the same thing, but using a light-sail and a launch laser.

Nanobots in the probe can start mining and setting up a new "human" civilization (file servers?) when it reaches asteroids or a planet in the target star system, then one day send out probes of it's own. Eventually covering the galaxy faster and faster at an exponential rate.

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Elements, no. We've found all the naturally-occuring ones and are adding many of the ones that don't last longer than a tiny fraction of a second. Some even theorize that elements beyond 137 may not be able to exist due to relativistic effects. Strange things might happen if we could, say, alter the shape of the nucleus (I believe it's considered to exist as a series of shells, much like electrons, but I could be wrong), but that's probably not possible without changing the laws of physics.

Compounds, unlikely. Though we're always developing new molecules so it's no stretch to think there's many we don't know about, using them to extract energy would require input of energy during their creation, and anything that's going to provide the shitton of energy necessary for interstellar travel is most likely going to have broken down to a lower energy state as it is. Try looking into compounds like selenium tetra-azide. Sure, it'll release a lot of energy when it breaks down (usually violently and with the sound of shattering labware), but it'll do that as soon as you look at it funny. It's not stable, it doesn't last.

The problem with nuclear fusion IIRC is not that it puts out too much heat, but that it's too hard to convert the energy to a useful form. There are fusion reactors on a scale of anything from a basement hobby device to large research reactors, but there's just no way yet to get more energy out than we use powering the device.

Useful interstellar travel will almost certainly depend on some way to suspend and preserve people, or provide support for a limited population with continued breeding and have a colony descended from your original astronauts, but the problem with the latter is without a ship for thousands upon thousands, you're looking at the mother of all founder effects in your population. Think inbreeding causes problems on earth, try a hundred generations out from a population of a few dozen.

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According to the link YOU provided, he is correct.  Density similar to a nucleus, mass comparable to several suns, diameter of 10's of kilometers.  That's pretty big atomic nucleus.  
 

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I like it!  The human race as a pestilence upon the galaxy!

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The problem is that in the hundreds of millions... billions of years that stars with planets that could support life, only ONE other technological species that did not go extinct or destroy itself would have to have survived, or they'd have done it by now, and we'd have seen evidence of them.

So if Humanity is not some unbelievable fluke, I think any species that gets the ability to go interstellar, they "move on" to ways of existing, ways of thinking, or whatever that we don't understand, and don't do the exponential Von Neuman spread across the galaxy-thing.

Sci-Fi analogies fail at some point, but at our current rate of progress, assuming there's not some fundamental limit to it, give us just 100-500 years without destroying ourselves, and we'd be way higher than any human or alien civilization ever imagined on screen, and in most Sci-Fi books too. We'll be more like the "Q" from Star Trek, or the monolith makers of 2001.

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I think your timeline may be a little compressed (as in, I don't think 100-500 years is enough,) but I get what you are saying.

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There's a concept called the technological singularity. If you think of our technological progress as an exponential graph, at some point it basically would turn more vertical than horizontal, i.e. progress occurs much, much faster than before. That point is the singularity, and it would basically be impossible for a pre-singularity group to predict post-singularity developments. It is, of course, just a wild guess, as most future predictions further than a few years tend to be.



I wonder if it's more likely that technology might develop more along the lines of a sigmoidal curve. As in, it starts growing faster and faster, but at some point it becomes impossible to make significant developments due to physical limits (e.g. it's probably not possible to make a transistor smaller than an atom) and growth begins to slow.

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At some point we'll figure out the brain and how to connect computers to it.  Once we do that we'll be able to wirelessly communicate with each other and machines.  The speed at which we exchange ideas and thus advance will be increased tremendously... if we don't all kill each other first.