Light Speed?

[duncan1297]

I was just thinking about this today. i remembered from a video (I think Vsauce but i'm not sure) the event horizon is the point where orbital velocity is the speed of light.

so if you are orbiting a black hole and you lower your perigee to beneath the event horizon, but keep your apogee above it, at your perigee will you be traveling faster than the speed of light?

like this

red circle is the event horizon

green is circular orbit

blue is altered orbit

[Steel]

Unfortunately not, because it's not the orbital velocity that is the speed of light at the event horizon, but the escape velocity.

One big rule in Physics, you cannot got faster than the speed of light

[NGTOne]

Unfortunately not, because it's not the orbital velocity that is the speed of light at the event horizon, but the escape velocity.

One big rule in Physics, you cannot got faster than the speed of light

Newtonian/Einsteinian physics.

It's theorized that you can exceed lightspeed (from the PoV of a stationary observer outside the bubble) by bending spacetime around your spacecraft - effectively, space moves and carries your ship with it, while the ship itself remains stationary (from the PoV of someone inside the bubble).

[MoonHeadJohn]

This wouldn't be possible. Anything that falls into the event horizon of a black hole cannot escape as any and all possible paths lead further into it.

[Pugspaceprogram]

Theoretically, shouldn't we be able to travel faster than light? It is finite after all.

[WestAir]

Here is another way to think of lightspeed acceleration. It takes time to accelerate. Because the universe contracts as you go faster, it is completely possible from the perspective of the spaceship crew to travel the entire universe in zero time at C. However, it takes finite time to accelerate. If you accelerate to C, it would take longer than the age of the universe to hit C, or from the crews perspective, you would escape the "edge" of the universe before you reached lightspeed.

Because neither is possible, reaching c certainly is not possible.

Edited August 14, 2013 by WestAir

[MoonHeadJohn]

...you would escape the "edge" of the universe before you reached lightspeed.

This wouldn't be possible. The universe expands faster than the speed of light, so you would never reach the edge.

[WestAir]

This wouldn't be possible...

Which is why I stated:

Because neither is possible...

Edited August 15, 2013 by WestAir

[MoonHeadJohn]

Yep, jumped in there, but at least it expands a bit on why it's not possible.

Also, surely it wouldn't take a finite amount of time but rather an infinite amount of time and more fuel than there is matter in the universe?

[Diche Bach]

What if you extend that blue ellipse just a bit 'south' and also widen it so it is more of a circle: basically orbit the black hole, just a couple meters or perhaps even millimeters on the outside of the event horizon.

I suppose you'd get very close to the speed of light, and if you combined that with a perigee burn . . . well the ultimate gravity assist?

My simple understanding of the principle was that, when an object achieves very high velocities, say 25 or 50% of c, the energy required to accelerate increases in some exponential function. So according to one interpretation it is impossible for an object under its own propulsion to get even very close to the speed of light, because at some point, it requires virtually infinite energy to accelerate a tiny bit, even if the mass of the object is quite small.

However, maybe using a black hole for a gravity assist could somehow sidestep that constraint?

Edited August 15, 2013 by Diche Bach

[Person012345]

Theoretically, shouldn't we be able to travel faster than light? It is finite after all.

No, due to the relationship between mass and energy and inertia and so on.

[NGTOne]

However, maybe using a black hole for a gravity assist could somehow sidestep that constraint?

From what I understand, you'd still need to burn the near-infinite amount of propellant to approach C any closer. While grav-assist from a black hole would put you very near C, and fling you out to wherever you wanted to go at what is likely a very appreciable fraction, you'd still be dealing with relativistic values. Infinity is, after all, a very big number.

[Person012345]

However, maybe using a black hole for a gravity assist could somehow sidestep that constraint?

No.

And OP, your orbit goes inside the event horizon of the black hole which is impossible because it will never escape. We don't actually know -what- happens beyond the event horizon of a black hole because infinities don't translate into reality very well.

[Diche Bach]

Yeah good point I suppose. Even if the gravity assist itself did accelerate you substantially more than a perigee burn around a less massive object, it wouldn't accelerate you to c unless you crossed the event horizon, in which case, you ain't coming back. Whatever remainder of speed you were shy of c would I'm sure, as you point out, still be subject to the relativistic effects, i.e., require infinite energy to accelerate any more.

This actually raises a question for me though. Would it work in 'retrograde' fashion too?

Meaning, if the mass of the black hole were used with a gravity assist to accelerate the craft far closer to c than it would ever be able to accelerate under only its own propulsion, would it then be stuck at that high speed because it would not be able to muster sufficient retrograde Delta-V to slow down?

You'd have to find another black hole around which to perform a braking maneuver! LOL

Fun stuff to play with.

[Nuke]

i have a feeling the energy (not even sure delta-v is the relevant term in this case) required to get out of that few inches form the event horizon orbit will be quite significant. you are orbiting at a very high percentage of c, and since you cant go c, you would have a lot of trouble doing a prograde burn to get out of it. you would have to burn along the orbital radius, with a little bit of retrograde to allow some leeway to perform an orbit raising maneuver, which will of course cause your orbit to temporarily intersect the event horizon. lets just say it would be a really bad time to have an engine failure.

Edited August 15, 2013 by Nuke

[NGTOne]

Whatever remainder of speed you were shy of c would I'm sure, as you point out, still be subject to the relativistic effects, i.e., require infinite energy to accelerate any more.

Near-infinite. The closer you get to c, the more you need to get even closer. Getting to 0.9c from 0 is actually easier than getting to 0.99 from 0.9, if I remember my physics right.

This actually raises a question for me though. Would it work in 'retrograde' fashion too?

Meaning, if the mass of the black hole were used with a gravity assist to accelerate the craft far closer to c than it would ever be able to accelerate under only its own propulsion, would it then be stuck at that high speed because it would not be able to muster sufficient retrograde Delta-V to slow down?

You'd have to find another black hole around which to perform a braking maneuver! LOL

Fun stuff to play with.

I think you've hit the nail on the head - you'd need a black hole (or other sufficiently dense object - neutron stars come to mind) to slow yourself back down. Of course, whether or not you WANTED to slow down would depend a bit on your mission objectives, but I digress.

i have a feeling the energy (not even sure delta-v is the relevant term in this case) required to get out of that few inches form the event horizon orbit will be quite significant. you are orbiting at a very high percentage of c, and since you cant go c, you would have a lot of trouble doing a prograde burn to get out of it. you would have to burn along the orbital radius, with a little bit of retrograde to allow some leeway to perform an orbit raising maneuver, which will of course cause your orbit to temporarily intersect the event horizon. lets just say it would be a really bad time to have an engine failure.

Damn right it would take a lot of energy, but we're dealing with something that is improbable on a number of levels (for instance, the tidal forces that close to the event horizon would shred your spaceship like it was made of wet tissue paper), so a few key assumptions have to be made (indestructible spaceship, some means to make these maneuvers possible, etc). And, yes, it would be a bad time to have an engine failure. Though methinks you might end up shaking hands with Jeb on the other side of the event horizon

Edited August 15, 2013 by NGTOne

[KOCOUR]

From what i remember from school, and IF i remember it right, than the closer you are to C the heavier you are, the shorter you are and your time flows slower. so at C you have infinite mass, zero length, and your time stops. So even if you have some magical propulsion that can compensate for your increasing mass you will have zero length at C so in my opinnion you just cease to exist, or you at least will not be able to further controll your ship as you will be frozen in time. Or you will collapse entire universe, as you will have infinite mass.

But i can be wrong. its Some time iam out of school.

[K^2]

I was just thinking about this today. i remembered from a video (I think Vsauce but i'm not sure) the event horizon is the point where orbital velocity is the speed of light.

so if you are orbiting a black hole and you lower your perigee to beneath the event horizon, but keep your apogee above it, at your perigee will you be traveling faster than the speed of light?

like this

red circle is the event horizon

green is circular orbit

blue is altered orbit

Won't work. Basically, when you get really close to the black hole, Kepler's Laws break down. In particular, you no longer follow an elliptic trajectory. Once you cross event horizon, you'll just keep falling in towards the singularity at the center of the BH.

There are coordinate systems in which the object bellow the event horizon is traveling faster than the speed of light, but in GR this is a very loose statement. Yes, you are traveling faster than light relative to remote observer if you draw the coordinates a certain way. But it doesn't really have any physical meaning. What's important about the speed of light limit is that it's a true limit locally. That means you can't be moving faster than light past something. And that's still going to be true even after you deep bellow the event horizon.

[Mephane]

From what i remember from school, and IF i remember it right, than the closer you are to C the heavier you are [...] so at C you have infinite mass

This alone makes it impossible to reach c. Infinite mass translates into infinite kinetic energy, or if you want to approach it the other way round, infinite kinetic energy translates into infinite mass.

I think what a lot of people don't realize about relativity, especially the famous equation e=mc², is that it has to be taken absolutely literally. Mass is energy, energy is mass. When something accelerates towards c, the very kinetic energy it thus gains itself is mass, which has to be accelerated, too. This leads us to the rocket equation on steroids, not only do you need exponentially more energy (i.e. fuel) to accelerate both the payload and all that additional fuel, but you also need to accelerate the mass of the kinetic energy itself.

[KOCOUR]

This alone makes it impossible to reach c. Infinite mass translates into infinite kinetic energy, or if you want to approach it the other way round, infinite kinetic energy translates into infinite mass.

Well thats wha iam talking about magical propulsion. :-)

[jwenting]

the speed of light it not a speed limit, it's a speed bump.

Theory does not say you can't go faster than light, it only says you can't go AT light speed.

So if you could derive a way to accelerate to a speed >c without ever being at c, you could travel ftl.

Of course the same goes for slowing down.

[K^2]

I think what a lot of people don't realize about relativity, especially the famous equation e=mc², is that it has to be taken absolutely literally. Mass is energy, energy is mass.

This requires clarification. Technically speaking, E = mc² is wrong. The correct equation is E² = p²c² + (mc²)². The reason for that is that the symbol 'm' is reserved for rest mass which is invariant for an object. However, inertial (and therefore gravitational) mass remains proportional to total energy. Since inertial mass of an object is equal to γm, it is also entirely fair to write E = γmc². Gamma is, of course, Lorentz Boost factor and it satisfies 1/γ² = 1 - v²/c². Since p = γmv, the two expressions for energy are equivalent.

Your point is entirely valid, however, since it is the inertial mass of the object that determines the force required to accelerate it.

As for relativistic rocket formula, something very interesting happens. While from perspective of the outside observer the ship accelerates less and less, requiring more and more fuel to get closer to speed of light at alarmingly faster rate than classical rocket formula would suggest, it's not actually as bad as it seems. Due to space contraction, it becomes increasingly faster for the ship to cover distance as measured by ship's clock. If instead of looking at speed relative to various objects you consider proper velocity of the rocket, which is how far you get in certain amount of ship time, eventually the equivalent "rocket formula" becomes linear. That is, to go twice as fast, you need twice as big a fuel fraction. And that actually makes it possible to go really, really far, provided you have good fuel.

Unfortunately, this doesn't let you break the light speed barrier. You can get insanely far on reasonable amount of fuel and within life time of the crew, but on Earth many, many years will pass.

the speed of light it not a speed limit, it's a speed bump.

Theory does not say you can't go faster than light, it only says you can't go AT light speed.

So if you could derive a way to accelerate to a speed >c without ever being at c, you could travel ftl.

Of course the same goes for slowing down.

That isn't actually true. It's a common misconception arising from poor understanding of special relativity, but there is no self-consistent theory that allows for faster than light travel without warping space-time.

[NGTOne]

That isn't actually true. It's a common misconception arising from poor understanding of special relativity, but there is no self-consistent theory that allows for faster than light travel without warping space-time.

This.

As far as I'm aware, the only mathematically consistent theories we have about FTL travel require some bending or warping of spacetime around the object in question - in effect, the object remains still relative to local spacetime, and spacetime instead moves around it (think of a surfer riding a wave - he's moving, but from the PoV of the wave, he's stationary). To an observer outside the bubble, the ship is faster than light. To an observer inside the bubble, the ship is completely stationary (I use the term "bubble" here because warp field geometry [and, yes, there are people - real scientists - who do research into warp field geometries, which is, in a word, AWESOME] is still highly theoretical and nothing is known experimentally, and this is unlikely to change for some time barring a few changes in our current understanding of how the universe is put together that would make it possible for us to construct an FTL drive system - if I recall, current equations call for a particle with negative mass to exist, though I have no idea how it works - I'm not a physicist. As far as I'm aware, the current general consensus is, "there is no way for us to currently generate a warp field where one does not already exist").

c, under classical/Einsteinian physics, is an immutable barrier. It is a natural constant, and CANNOT be reached by classical physical means (see bending spacetime, above), including any sort of rocket, INCLUDING such exotic propulsion sources as antimatter. It's only when we start messing with the underpinnings of physics itself that we can do any differently.

Edited August 16, 2013 by NGTOne

[Monkeh]

E = γmc²

My head saw this as:

Einstein =

[Person012345]

the speed of light it not a speed limit, it's a speed bump.

Theory does not say you can't go faster than light, it only says you can't go AT light speed.

So if you could derive a way to accelerate to a speed >c without ever being at c, you could travel ftl.

Of course the same goes for slowing down.

To accelerate faster than light conventionally would require more than infinite energy. Which doesn't make sense.