Ok, I played around in Matlab , and came up with interesting conclusions

I tried to figure out how would one reach speeds near high speed using Newtonian rockets (any kind of machine that uses force to accelerate)

First I started of with kinetic energy of a body in light of special relativity theory which is

Ek= 1/ sqrt [1/(1-V^2)] * m * c^2

before anyone jumps V here is expressed as a FRACTION of c , that's why it's not written as v^2/c^2

this kind of function gives a rapidly increasing energy requirements to change speed as speed increases, because
mass also increases into infinity as it reaches speed of light

For easier use, I inverted this to be a function of Ek instead of function of V, so that
you have a rapidly decreasing acceleration with added energy increasing in a linear fashion

But since we are talking about huge amounts of energy, we have to consider fuel mass, because it will probably
take a large portion of total mass of ship.

but that fuel mass decreases as added EK energy increases, which is why I have chosen the function to be expressed
through EK (so that we are observing a linear increase in EK, and therefore a linear decrease in fuel mass as it is being converted into energy)

The only way to get mass completely converted into energy is by using matter-antimatter annihilation, and ASSUMING
that all of the generated energy is converted into kinetic energy of the ship, which again is impossible, but
that's another story

So the fuel mass of m being both antimatter plus matter counterpart together,
gives E=m*c^2 energy, which is presumably converted into kinetic energy.

As this mass is "burned" so does ships mass decreases, so
we have to express the mentioned function with m being a variable expressed through Ek

When you put that back into the equation, and sort it all out, you get a much simpler fuction:

V=sqrt ( EK/ m*c^2 )

where m is innitial mass of the ship, and EK is the input of the function (energy from "burned" fuel) , and V is the reached fraction of c


this is the top speed of a ship of decreasing mass m in which you convert a fraction of its mass into EK, this speed is reached
when EK is given to the ship through fuel.

If you replace EK with mass of fuel times c^2
you get that

in order to reach V , a fraction of C, you need to convert V^2 of fraction of ships mass into energy

For example, to reach 0.5 speed of light, you need to
"burn" 0.25 of its mass into energy, meaning 25% of ships mass has to be matter+antimatter fuel, because that's the only known way
of converting nearly all mass into energy.

So, what's the point.

Well, as you reach speeds of say, 90% speed of light, you need 81% of the ship to be fuel,
which is hard, because half od that 81% mass has to be antimatter, which is hard to store

Why?

Well, today, we have penning traps which hold anti matter, which contain tiny fractions of a milligram of antimatter in
a heavy machine millions of times more heavy than its contents.
So imagine having to store huge amounts of antimatter in a machine that weights many times less than its contents.

So if you wanted to reach 0.99 speed of light, with a 200 000 kg ship,
you would have to have 196 020 kg of it to be fuel, and out of that 98 010 kg to be antimatter,

and you would only have 3980 mass left to be used as machinery to contain antimatter, matter, to control the craft,
include passengers, cargo and the ship itself.
Which is about the mass of a small truck

Now imagine having 196 020 kg of fuel stored in a 4 ton truck

Pretty difficult.

I played around some more with numbers, and tried to figure out how
does slowing down affect this, because once you reach some speed you also have to you also need energy/fuel to slow down to your original speed (relative zero)

So for reaching a V fraction of light speed AND decelerating back to full stop, the fraction of mass of your ship that is taken by your fuel has to be :

f= 2* V^2 - V^4

And here is how this function looks like:




X axis is desired fraction of light speed to reach

Y axis is required fraction of ships mass to be fuel to reach that speed AND decelerate

When compared to one way fuel requirements ( V^2) , it takes more fuel of course,
but not as much as one might assume at first

Your calculations look pretty good to me. I'm assuming these are just rough numbers and for discussion purposes.

What is interesting is that why would anyone want to go to .7 or .9 of c? It is so much easier (relatively) to get to .2 or .3 and you would only need twice or three times as much time for a trip.

The trip will still be so long to get to any other star that the difference compared to using conventional (chemical rockets) engines would be miniscule.

Such speeds are really only possible if we are able to mass produce anti-matter, harness gravity or zero point energy.

The numbers are non realistic because you can hardly ever convert all of the reaction energy into motion.
First of all, some of it would go into heat, either waste heat, or some heat based electrical power system,
second, there are no known ways to reflect every product of antimatter-matter annihilation, so
I guess in order for this to be realistic one would have to come up with some kind of efficiency factor for this type of drive,
which is basically a "beam core" antimatter rocket.

But if you DO consider all the energy to go into motion, then, it is accurate, like any function would be.

Why go to such speeds?

Because of time dilation. Of course these speeds mean nothing to someone in "mission control" on earth waiting for the trip to happen, but they mean everything to the crew.

As you approach the speed of light , viewed from a certain reference system, so does time actually slow down,
towards zero.

So in theory, if you had enough fuel, to accelerate into say 0.999999999etc. of speed of light, you could travel
millions of years (as viewed from earth), and have the trip seem like days, meaning you can travel to the end
of observable space (as viewed from earth) in one life time.
But if you got back, you would find that in your life time sun had already swallowed the earth and exhausted its fuel

Now, this is the extreme case, but
in a more practical model, you can shorten your trip by say 10 times, which is considerable.

It's not hard to wait 10 years for earth, because they go about their everyday life, the real problem is having
astronauts live on a ship for 10 years, so if you could shorten that time from their perspective to 1 year
that would be great.

There would also be no need for example to have so called generation ships, when traveling to nearest
star systems, because it could be done in a couple of years from ships perspective.

If you travel at say 0.2 or 0.3 c , the effects would be minor, and of no benefit , but
if you can reach 0.8, 0.9 and more, then you would have real benefit from time dilation

Back in the '90s, JPL had a website covering numerous aspects surrounding this issue- with the exception of relativistic effects. They spelled out every reasonable rocket engine design and its capabilities for deep-space travel.
Including the various constraints, both engineering and economic.

Your posts have pointed out, among other things, what may lead to the twins paradox. Always interesting.

Almost forgot- Burkhard Heim, et al., were covered by the press a few years ago. Supposedly, the issue regarding his unification theory was to be tested by the Z-machine (which normally tests nuclear weapons design).

There was a flurry of speculation about its real-world value, and if it could assist spacecraft propulsion. Needless to say, it is another of numerous such GUT theories. I have not read but a few press releases a few years ago.

http://en.wikipedia.org/wiki/Heim_theory

Well if you could get the twin "paradox" (it's not a real paradox though, anymore than the Achilles and the Tortoise paradox, when you think about it, in fact these two paradoxes are related) , then that would be great, because it would shorten the suffering for astronauts.
It wouldn't be a problem to make a kind of a software clock which would adjust time ever few seconds, based on
Lorentz transformations.

Regarding other propulsions, sadly, non of them can get you anywhere near light speed, because mass/energy ratio is way to low.
For example, if you used D-T fusion, and had a way to convert that spare neutron into pure kinetic energy (which again is impossible), you would
get 20% of fuel mass converted into energy.
So the math would go something like this, if your ship was 99% made of fuel, you could in theory reach little over 40% of light speed.
But this is impossible in reality. At least not without some future technology of plasma containment that is indistinguishable from pure magic to our current scientific knowledge.
You would have to have a fusion reactor and fuel containers to take less than 1% of mass of your ship, while 99% of mass being fuel.
And all that even considering that you would actually shoot out hydrogen4 as waste (to reduce mass)
All that to reach 40% of light speed.

With antimatter, you could reach same speed with just 20% of your ships mass being fuel, and not even have to eject anything out.

with fusion being almost useless for relativistic travel, we don't even have to consider fission


But, of course for the kind of traveling NASA is doing today, both fusion and fission would be an enormous leap

Here is another interesting math game..


Interstellar (much less interplanetary) space is not empty, there are particles all around in different densities.

Now if you use the density for interstellar (which is a rough estimate that I found) space to be
between 1 atom of hydrogen per cm3, and 1000 atoms of hydrogen per cm3, then by using speed that you are traveling with, and
mass of hydrogen atoms, you can get a rough estimate of how much mass you are encountering in some time interval
per area of your "windshield" surface.

I used one second and one square meter for reference,
and the mass encountered at half of light speed (0.5c) that I got was

between 9.9628 * 10^-13 kg

per second per square meter

and 9.9628 * 10^-7 kg per second per square meter

that's not a lot of mass

BUT

you are moving at 0.5c, so in reference to your point of view, each of these particles is moving at
0.5c towards you, having a huge amount of kinetic energy from your point of view (or from your point of view, your own energy being used against you through reaction).

Now, when you calculate that energy (using relativistic kinetic energy equation),
you get energy per second, which is power, and the power turns out to be from 13 852 Watts to 13 852 MegaWatts pers square meter.

Now, things get serious, this is a LOT of energy on your windshield

Now, luckily for the astronaut, most of this energy remains in the particle (as it receives kinetic energy from the massive ship), so you don't actually receive megawatts of heat into your hull, otherwise your ship would fall apart.

But since, I don't know what amount of energy is converted into heat, I wanted to
at least see what would be the equivalent encounter of mass/energy if this was a plane, and you were moving
through air.

And I got this:

The energy encountered on your "windshield" , would be equal to that from 546.9 km/h to 546 996 km/h
traveling in air of density of 1.2 kg/m^3 if you ignore actual temperature of the air (say its zero)


Now, obviously from practice we can observe that at 546.9 there isn't that much heat energy absorbed that would damage
the plane, but at 546 996, I'm sure any plane would burn up, meaning a lot of heat is absorbed.

Since the first number is for lower density interstellar space (1 atom per cm3),
and second number is for a molecular cloud of 1000 atoms per cm3

my guess is you would be getting considerable amounts of heat on the front of your ship as soon as you entered
a molecular cloud, possibly those close to what you would be getting on the hull of a plane in air
at mentioned speed.

All this is just oversimplified math, but I think it shows that there IS a problem of some sort
regarding encounter of low density matter at extreme speeds.

If anything, once you reach near light speed, any particle that hits you would be a lot like
driving around in the middle of a particle accelerator

Doesn't the Ramjet type design add considerably to the ability of atomic, ion and fusion based engines to go to percentages of c? Since the craft would be scooping up a significate percentage of what it is throwing out the back from intersteller space. The trip would be many times longer then the proposed anti-matter engine above, but is feasable. And the time available to colonize space would seem to be measured in billions of years. Perhaps time enough to get to other galaxies.

The problem with reaching any kind of considerable percentage of c is not so much in thruster technology, but it's in energy sources.

If you did have a 100% efficient thruster, you could only speed up so much, until you exhaust your fuel, even if it is a fusion reactor.

In trying to reach even 0.5 c, no matter how much your fuel mass/ship mass is large (even approaching 0.999999etc.) you
would simply run out of fuel (be it fusion, fission or chemical energy) before you got to that speed.

Imagine then how much energy is required if you exhaust a small sun trying to get to that speed

If you did have unlimited amount of energy, you could eventually reach near-c even with going outside and pushing the craft, so
thruster technology can only be as good as theoretical limit of energy that runs through it.

Very interesting thread. I never thought about these kinds of issues. Now that you drew my attention to it I found that Wikipedia even has an article on relativistic rockets.

Since you're already dealing with unrealistic assumptions I wonder if you'd like to extend your considerations to relativistic gravity assist maneuvers.

Surely we can't hope for black holes shooting by at relativistic speeds so we could use them to hitchhike.
But what I'm thinking of is even more unrealistic. If we could somehow manage to build a highly eccentric binary system of two equal masses--which sould be very massive and dense, probably black holes--this system can be used as a kind of catapult, accelerating and expelling a particle if we drop it into the center of our binary just at the right moment. The kinetic energy for the expelled particle is drawn from the binaries orbital energy. Look up "Sitnikov problem" if you want to learn more about this.

In newtonian physics and with point masses the energy transferred can be made arbitrarily large if we make the occuring near triple collision close enough.
I'm not really versant with relativistic mechanics. What is instantly clear is that this technique can not result in velocities larger than c.
Also the distance for close encounters must be larger than twice the Schwarzschild radius of the binary. A larger lower bound for the distance could be derived from the requirement that our space craft should not be disrupted by tidal forces. Do you see how a better upper bound for the final velocity would be calculated from that?

Interesting idea. I haven't really investigated such ideas and concepts.

But we are dealing with a relatively short force impulse here, and in order to reach high speeds, you either need
a really strong force, that would kill any living thing inside or have a lower force over a larger period of time (which is what we need).

In order to use this kind of system to speed up to say half of light speed, imagine the distance from which you would have to start accelerating.

No matter what kind of force you are using to accelerate the ship, that force is limited by how much acceleration the astronauts can endure. So whatever you use to accelerate, the acceleration has to last for at least several months or weeks.

Perhaps I'm missing the point of this theory, but I don't see a way to have a steady acceleration for weeks using this method.

You can't just shoot out a ship with living beings, because they can only take so much gravity.

Of course, this could work for probes, for which there is much more freedom regarding the nature of the impulse
(you can use more force and less time)

Ah, anti-matter and all.

I prefer Warp drive. AKA Alcubierre drive.


Or other such modes of travel in which you are only travelling 0.2c in "your" dimension but from a third person perspective your travelling 0.9c.


Always interesting with those theories. I think they are our best chance as well and very possible looking at what our worl has turned into from what people imagined in 1800's.

Isn't science great? There are people on it already!
see Warp when?

speaking of "virtual" speeds, I made a nice graph showing what kind of virtual/effective speed you get when going with a certain speed.

It's not real speed (otherwise it would brake laws of physics), it's just a measure of how much distance did you travel
after "synchronization" with the speed of the destination (planet speed, in other words stopping)
in how much time from your perspective

Real speed would be a speed in one inertial frame, which can never go to c or above,
but this speed would be a kind of a cross-reference-frame speed, or totals of your trip after decelerating

In fact, this virtual speed goes to infinity, meaning if you reach 0.999999999 of light speed, you can
travel to the end of the universe in one life time, because of time dilation

here is the graph:



X axis shows real physical speed which can never go over speed of light

Y axis shows "virtual" speed (distance traveled AFTER returning to earth's reference frame, divided by time spent on ship)


As you can see, you can virtually travel at 3 times speed of light if you physically travel at 0.95c, and
if you go to 0.97c, you are virtually traveling at 4 time speed of light.
As you can see, there is an explosion from there on into infinity.

At 0.99999999999 etc. of speed of light, you are traveling at more than 100 times speed of light

Depending on how close you come to light speed, your effective trip speed (virtual) can reach
million times light speed or more

Seems like, whoever designed the universe, while putting a limit on speed ©, gave a neat little
trick which allows anyone who doesn't mind outliving their own planet, to travel anywhere in the universe lol

But the point is that when using gravitation the space ship would be in free fall. So acceleration would not be a problem.
Tidal forces would be dangerous in gravitational fields as strong as one would need to reach relativistic speeds.
Maybe passing through a sequence of exactly aligned and timed binaries could accelerate a space ship more cautiously.

But still this would require extremely massive objects which would inevitably gather a thick cloud of gas around them. As you've pointed out this would be a real problem at relativistic speeds. And since this method makes the ship reach its maximum velocity right in the center of the catapult, yeah, I see, that would not work.

That's interesting, interstellar highway made of singularities

But it wouldn't last long, because the gravities would affect both the stars around it, and each other. And the highways would soon fall apart.

And either way, you would have to develop a near c ship to go and plant these things.

Now, I'm only in gr 10 so please don't laugh if i say something stupid. I was reading your post about reaching 0.999999c and how you would be going four times the speed of light. And I just could not stop myself from asking this. If time is slowing down so your moving 4 times the speed of light why does light travel at c which is faster than 0.99c? If we would be going 4 times its speed how the hell is c more than the speed of light. Basically what I'm saying is how can we travel faster than light by going slower?

Shouldn't light also have time dilation as well?
And if you say that photons have no mass, then why are they particles? If we say they are an electromagnetic wavelength and all, shouldn't it not exist since it has no mass? And then why does it exist? And most importantly, the double slit experiment.


Sorry for asking all these questions, I would greatly appreciate it if someone explained these things to me!!!!

travel is a wrong word perhaps

You are not traveling faster than light.

think of it this way: you travel at 0.999999c and measure how much time has passed from start to end of your trip, then you stop at your destination, and ask the locals, how far is it from your home planet , and they say X light years.
When you divide this distance by time you have spent on your trip, you are dividing distance from one inertial frame ("static" one), by time from the other inertial frame (the ships travel frame) , and you get a kind of a hybrid effective trip speed, which would end up being more than C.
So you are not moving faster than C, but you get there AS IF you were traveling faster than C

That's what I mean by "virtual" speed.

You ask how can we go faster than light by going slower than light.
I'll try not to be too confusing, but the question itself contains the answer, the "faster" and "slower" words
you are using are all from the same inertial frame (the frame in which you and I are, more or less)
But faster and slower lose their initial meanings once you accelerate to relativistic speeds


Yes, from "perspective of light" time is infinite (or is still, not moving, slowed down to zero, one tick is infinite), so yes, time dilation applies to light too, but I'd rather call it time eradication , because time stops being a dimension at C and is actually equalized with space, so time and space are the same axis, the faster you go the more time affects space and vice versa, until they become one at C.
That means if you were a light beam you would feel like traveling the universe at an infinite speed ("speed o thought" if you will) being from any destination to any source at the same time.
You see at C space contracts into 2D by eliminating the dimension you are moving in.
For example if there is x, y, and z axis of space, and you are traveling in direction of z, at C speed, z is contracted into zero, and you have 2D space meaning you are everywhere at the same time in that direction, therefore your speed is infinite.

Why is photon a particle if it doesn't have mass?
Simply because it sometimes behaves like a particles, so it's considered one.

Of course not, if you are confused at first it means you are able to start your process of understanding special relativity.

If you haven't studied it yet, but find it common sense, then that's a problem because obviously you missed something.
After studying the math behind it, then it actually does become common sense, because it makes sense

So being confused is the first step

regarding the original topic of the thread. I haven't thought of it yet, but you could save even more fuel (and thus reach higher percentage of C), by throwing out portions of machinery that contained and distributed spent fuel.
For example instead of storing tons of antimatter in one penning trap, they could store it in sections, for example having the ship have a repetitive structure of modules containing antimatter and matter fuel containment and distribution machinery, and getting rid of module by module as its fuel is wasted, which would allow reaching even higher speeds, or at least same speeds with less fuel.

So if you had say 99% of ships mass to be fuel, then 0.1% to be crew equipment and thrusters, and 0.9% be fuel containment technology, you could not only get rid of 99% of mass through fuel but additional 0.9% that held the fuel and distributed energy to common thrusters.

Oh... thanks mate. That explained a lot of it.


I'm not sure if this is a good comparison, but is that like Einstein's point of view theories (forgot what they are called already)???

What I mean by that is that one person may experience a certain speed/movement and a different person from a different position will see it differently.

This IS Einstein's special theory of relativity.

Ah... so I'm basically a tad slow. Oh well, at least I understand.

Not remembering the name of some theory doesn't make you slow.

Lol, just that I remember printing something out about that not a while back and I just couldn't recall the name. Must be that heavy metal I listen too

Sounds like a rail gun. I wonder what kind of speeds would be possible with modified rail gun technology?
In other words, if the gates thru which the ship passes only powered up upon approach of the craft and
powered down after it had gone thru, so that gravities would not persist long enough to effect the
material (gasses, dust, etc...) around it for a while (not that we have the technology to create sufficient
energies to do that). I'm just curious.