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Assuming a civilization has the capacity to build space vessels designed to travel from one solar system to another, what is the technological difference between traveling at 50% light speed and traveling at 100% light speed (or near)? And then, what kind of technological leap is required to go beyond light speed? The idea is not to have "hyperjumps" but that there is a constant speed most ships can go. So traveling 4 light years takes 4 years at light speed. Takes 8 years at 50% light speed. you get the idea.

I am trying to decide how technologically advanced humans in my space-travel-based universe are. Would it make sense to say "We are only advanced enough to go x% of light speed"? Or is Light-speed the real barrier here? What are the limiting factors to going very fast (subluminal)? Assuming light speed is the real barrier, would anything really stop anyone going near light speed given enough fuel and distance to reach that speed?

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    $\begingroup$ You’re looking at this in small manageable numbers, but 50% light speed and 100% light speed are phenomenally different. Just take a look at the difference between going half the speed of sound vs breaking the sound barrier for example. $\endgroup$ – JustSnilloc Jan 27 '18 at 21:48
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    $\begingroup$ @JustSnilloc That's not a good analogy. There's nothing fundamental about travelling faster than sound in a particular medium: the difficulties with breaking the sound barrier are purely aerodynamic. Further, there's not a huge difference between travelling at half the speed of sound and travelling at, say, 90% of the speed of sound, which commercial airliners do all the time. $\endgroup$ – David Richerby Jan 28 '18 at 13:55
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    $\begingroup$ @PremierBromanov at near light speed the near vacuum of interstellar space is like standing in the beam of a particle accelerator. $\endgroup$ – Dan Neely Jan 28 '18 at 15:17
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    $\begingroup$ i must say that @JustSnilloc 's comment is very confusing and raises totally unrelated issues. (A) In fact, there's no difference whatsoever between a plane or car that can go 500 mph and 700 mph (it uses "more fuel" and you need "stronger windows"). If you put a huge engine in your Toyota Avalon it could trivially go over the sound barrier. (B) absolutely trivial engineering issues like "going fast in atmosphere" have just no connection at all to "faster than light?" physics issues. $\endgroup$ – Fattie Jan 28 '18 at 15:42
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    $\begingroup$ My point is that all the differences that you would find between half SoS and full SoS will be exponentially amplified when you consider the differences between half SoL and full SoL. More than “simply” going faster, there are a whole host of other things to consider. $\endgroup$ – JustSnilloc Jan 28 '18 at 17:29
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Assuming known physics, there's no way to go 100% of the speed of light ($c$), but (in principle) you can get as close to it as you want. So let's compare $0.5c$ (50% the speed of light) with $0.95c$ (95% the speed of light).

There are a couple of big differences between travelling at these speeds. The first is the amount of energy needed to reach them. In space it doesn't take energy to keep moving at speed - if you don't do anything you just keep coasting at whatever speed you're moving - but you need to use energy to speed up and slow down. Let's calculate how much energy it takes to move at the speeds mentioned above.

The kinetic energy of an object moving at relativistic speeds is

$$E_k = m\gamma c^2 - mc^2 = \frac{mc^2}{\sqrt{1 - v^2/c^2}} - mc^2$$

(from Wikipedia), where $m$ is the mass of the object and $v$ is its velocity. Let's use units where $c=1$ and let's assume $m=1$ as well for simplicity. Now an object travelling at $0.5c$ has a kinetic energy of about $0.15$, while an object at $0.95c$ has an energy of about $2.2$. This measures the amount of energy you need to get up to speed, assuming the mass of your spaceship doesn't change. You can see that getting up to $0.95c$ takes 14 times more energy than getting to $0.5c$.

However, it's likely to be much worse than that in reality. For most methods of propulsion you will need to take more fuel with you to get to a higher speed, and that means more mass, which means more energy. These feedbacks combine in an explosive way, so that travelling just a bit faster usually requires an exponentially larger amount of fuel. This is called the tyranny of the rocket equation, and is generally not your friend. Don't forget that it takes energy to slow down too, since you definitely don't want to be travelling near the speed of light when you reach your destination.

If you want to go even closer to $c$ you will have to spend even more energy. Travelling at $0.99c$ requires about $6.1$ energy units, and $0.999c$ requires $21$. As you get closer to $c$ you'll need more and more energy for smaller and smaller gains. Accelerating to $c$ itself would require an infinite amount of energy, which is why you can't do it.

The other big difference between $0.5c$ and $0.95c$ is collisions with space dust and other particles. Space is almost empty, but if you run into even a tiny piece of dust grain of sand at $0.5c$ it will hit like a nuclear bomb tonne of TNT.1 A larger object, with mass around 1kg, would be comparable to a nuclear bomb. At $0.95c$ it will hit with 14 times the energy, due once again to the higher kinetic energy. Such collisions are inevitable on a journey between stars, and so most serious concepts for interstellar travel have a huge bulky shield in front of them, to protect against this. The closer you get to c the more protection you need from collisions, which adds more mass, which again requires exponentially more fuel due to the rocket equation.

In conclusion, everything you say in your question is basically right. Nothing stops you from going as fast as you want given enough time, fuel and distance, but these practical considerations mean there's a huge difference in the amount of technology and cost between travelling between stars $0.5c$ and $0.95c$.

1My initial guess was way off, my apologies. Wolfram|alpha is a useful tool for doing these kinds of calculations, and I should have run it through that in the first place. Although the energies involved are smaller than I expected, colliding with dust grains at relativistic speeds will release a cascade of subatomic particles, and the radiation from this is probably more dangerous than the initial release of energy. I am not an expert on this stuff, though.

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  • $\begingroup$ Your calculation for the energy collision assumes the particle comes to a stop, and that ALL kinetic energy is released. $\endgroup$ – Justin Thyme Jan 28 '18 at 4:50
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    $\begingroup$ @JustinThyme that is correct. One would expect this to be the case. The only way it wouldn't be is if the particle passes all the way through the spacecraft and out the other side. One would hope the spacecraft is designed so that that wouldn't happen. $\endgroup$ – Nathaniel Jan 28 '18 at 4:58
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    $\begingroup$ @JustinThyme sure, that's what I'm doing: treat the spacecraft as if it were at rest, and the particle as if it were moving at 0.5c. The point is that even a tiny speck of dust moving at 0.5c would do a huge amount of damage - it definitely wouldn't pass through without doing any damage. See for example what-if.xkcd.com/1 for what happens when matter collides with matter at relativistic speeds. $\endgroup$ – Nathaniel Jan 28 '18 at 6:16
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    $\begingroup$ @JustinThyme "Also a particle traveling at you at a velocity equivalent to c would be showing the relativistic effects, not you" -- in the reference frame of the particle, yes, it's the starship that shows relativistic effects. This is the origin of the 'twin paradox'. $\endgroup$ – LSerni Jan 28 '18 at 21:33
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    $\begingroup$ @JustinThyme: "It is the assumption that all speeds are relative and not absolute that produces the paradox. If you throw out that assumption, there is no paradox." You're basically saying "if you stop saying that special relativity works, then special relativity doesn't work". Yes, that's true. But since special relativity has been observed and there is a multitude of evidence that it works, you can't just deny reality because you don't like where it leads. $\endgroup$ – Nicol Bolas Jan 28 '18 at 23:43
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What percent of the speed of light you go is not really a function of how "advanced" you are. So long as you have reaction mass for thrust (or whatever your particular method of acceleration is), you can get arbitrarily close to the speed of light. Obviously, you need some minimum tech level to be able to fly in space and navigate over long-distances at all.

The limit on how fast you go is therefore based primarily on your particular engine design, any external motive systems, and how much reaction mass you carry, all of which is relative to the overall mass of the ship you're using. But these elements of technology don't map to the practical speed of a ship.

So you can't look at a ship that travels 75% of the speed of light and judge anything about the tech level of the people who made it based solely on that. Maybe they had a stationary magnetic accelerator in their launch system and are relying on high-impulse propulsion to slow them down. That's not particularly higher of technology that someone who uses low-impulse propulsion over a long duration to achieve the same speed.

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    $\begingroup$ @PyRulez: My point is that you can't "really" know. If you see a ship going 0.75c, that alone tells you almost nothing about how they got it there, relative to if you see a ship going 0.25c. For all you know, the latter could be more advanced than the former, but the former was willing to use more brute-force/inefficient methods to do so. There are enough low-tech solutions to get high velocities that you cannot tell one way or the other just from its speed. $\endgroup$ – Nicol Bolas Jan 28 '18 at 3:17
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    $\begingroup$ In particular, if you can accelerate at 1g for a little under a year, you're travelling at the speed of light. $\endgroup$ – David Richerby Jan 28 '18 at 13:58
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    $\begingroup$ The original Voyager spacecraft were developed at a period of low technology compared to today, but they are going extremely fast compared to rockets launched from earth using current modern technology. Point taken. $\endgroup$ – Justin Thyme Jan 28 '18 at 16:32
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    $\begingroup$ @DavidRicherby False. $\endgroup$ – wizzwizz4 Jan 28 '18 at 18:22
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    $\begingroup$ If you are under a constant acceleration using the same technology, you will NEVER approach cee. The closer to cee you get, the more the acceleration you need to go faster. That is to say, the method and technology you use to accelerate at, say, 5 m/s/s if you are travelling at normal earthly velocities, will NOT accelerate you at 5 m/s/s if you are going at point 8 cee. At point 8 cee, if you add 5 m/s to your velocity, you are going considerably less than point 8 cee plus 5 m/s.Velocities are not purely additive at speeds approaching cee. $\endgroup$ – Justin Thyme Jan 28 '18 at 22:45
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The Wikipedia page on time dilation has a great chart.

When you add more energy with any thruster (assuming abundant reaction mass or bonkers Isp) as you get closer to light speed less energy is going into your relative velocity and more is bleeding over into time dilation effects. From the chart it looks like you start seeing some serious losses in Δv above 0.3c. Above 0.9c most of the energy from continued thrusting is going toward time dilation and not toward getting anywhere any faster - and then you'll have to decelerate which equates to a whole lot of wasted fuel.

So above 0.8-0.9c there's no advantage to trying to go any faster. Any limit below that is going to strictly be limited by the amount of fuel you can carry (or find, if you are going the ramscoop direction where you use a magnetic inlet to capture and fuse interstellar hydrogen), the efficiency of your engines, and the relationship between acceleration and distance between start and end points. For example, you could have very high efficiency but very low thrust engines for interstellar travel, so you may need several lightyears to get up to 0.8c. In this case you're average speed would be lower for "short" hops like from Sol to Alpha Centari, and approach the 0.8c cruising speed as you make very long journeys.

As a plot device, any sort of race in the 0.8-0.99c range where it's worth it to burn insane amounts of resources to gain a few days or hours on the competition could be interesting.

Faster than light is the big jump because with our current physics, no one knows how to do it. With any known propulsion method, we would just lose acceleration and speed to the time dilation effect. Any FTL method is going to have to abandon the Science and lean on the Fiction.

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    $\begingroup$ "less energy is going into your relative velocity and more is bleeding over into time dilation effects" The time dilation effects makes the trip shorter from your point of view though. For many applications, perceived time is what is important, not actual time. $\endgroup$ – PyRulez Jan 28 '18 at 2:48
  • $\begingroup$ @PyRulez Don't disagree at all. You get this fun situation where time is a resource and it enters the trade space with fuel consumption. You also get the interesting scenario where limiting the passage of perceived time is not really desirable - how much scifi has been written about the struggle associated with taking a few short trips and watching your loved ones age and die? $\endgroup$ – MParm Jan 28 '18 at 3:12
  • $\begingroup$ @PyRulez: The important question is what is the actual time? It's purely (if you'll excuse the pun) relative: to someone aboard the near-lightspeed ship, their time is every bit as real as the slowed-down time of the rest of the universe. $\endgroup$ – jamesqf Jan 28 '18 at 4:53
  • $\begingroup$ @jamesqf From the point of view of the ship, length contraction is happening, resulting in an overall shorter trip. Regardless of point of view, they will have "aged" the same (i.e., less than if they/the universe was moving slower). $\endgroup$ – PyRulez Jan 28 '18 at 4:57
  • $\begingroup$ @jamesqf For sure. Have you read Hyperion? - Very Highly recommend if you haven't. It's an anthology (but very well done, not usually a fan of anthologies) and the Consul's story has a lot to do with relativistic time effects and is a real tear jerker. $\endgroup$ – MParm Jan 28 '18 at 5:03
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I assume when you refer to speed, you mean relative to earth or some other planet, as all speed is relative. There is no huge difference between getting to different sub-light speeds, more thrust is simply required to go faster.

However, do keep in mind that going near light speed, the effects of time dilation get very noticeable. A journey of four light years might take a few years for the people on your ship, but centuries for everyone else on the planet from which they launched. Nothing can actually go faster than light, as this would mean going at a theoretically infinite speed and cause you to go back in time. You might however want to look into the Alcubierre drive, a theoretical warp drive which creates a bubble of spacetime, contracting space in front of it and expanding it behind. This means that the ship technically isn't moving at all, and would allow the it to travel at any speed with no time dilation. There are of course many problems with it, such as energy requirements and radiation, but it could work for your story.

Basically, the biggest technological difference is whether or not your civilization has discovered a way to go faster than light.

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You bet there's a difference

  • In 1804 the first steam rail locomotive could scream along at 5 mph.

  • Steam improved by 1830 when the Stephenson Rocket hit an earth shattering 30 mph.

  • In 1848 steam — or should I say, rail — had hit 60 mph. It took nearly 100 years to get to 100 mph. All this time, the technology to move the mail was changing and improving. Steam reached its peak in 1938 with 126 mph.

  • Then the technology changed and diesel was introduced. In 1936 diesel hit 127 mph. By 1980 it was up to 152 mph.

  • Then the technology changed again, and today we have mag-lev trains that top out at 375 mph.

My point is, there is a HUGE technological difference between 0.5c and 1.0c.

I'm ignoring completely today's understanding of physics. World history has proven over and over that "today's" understanding imposes few actual limits. Said limits tend to be overcome by "tomorrow's" understanding. Once humanity can build a ship that can reach 0.5c it's altogether likely that we'll have figured out the physics behind getting to 1.0c. Anyone who tells you "...can't be done, because..." is forgetting that people 100 years ago were saying the same thing about many of the technologies we enjoy today.

However, when you ask, "...what is the technological difference...," that's a question no one here can answer. You're asking us to postulate the operation of technology that doesn't exist in our wildest dreams, and then extrapolate from that ignorance whether or not light speed represents an insurmountable barrier.

Remember! Scientists actually thought the sound barrier was insurmountable until we figured out how to do it and Chuck Yeager actually did it. Today, we can't see how to overcome the light-speed barrier ... but we've walked across a barrier once before. I wouldn't be at all surprised that we do it again. It just takes a better understanding of the problem than we have today. Regrettably, it's the habit of science-oriented people to believe that what we understand today is all there is and all there will ever be. History has proven them wrong time and time again... but they believe it anyway.

So, you'll be inventing the "technology" that your story needs to accomodate space travel, but to answer your title question, yes! It makes reasonable sense to say, "that species can only reach 0.25c." as a reference to their general technology level. Indeed, this kind of reference has already been used in Star Trek where some species are only capable of "warp 4" while others are capable of "warp 7" and it's hands-off non-warp-capable species because Clarkian Magic would make you look like gods and that's considered poor sportsmanship.

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  • $\begingroup$ I have oft said 'If the physics book is thick enough. And we are doubling its thickness every decade.' Upvote for that. Proof in point, 150 years ago we didn't even have the technology to get into space. Constant acceleration does not cut it, as any acceleration we have today has a limitation in thrust and velocity, and once we reach that limit, greater acceleration is not possible. To go from point 5 cee to point 8 cee, it's not just a matter of a constant acceleration, but of an increasing acceleration. $\endgroup$ – Justin Thyme Jan 28 '18 at 18:29
  • $\begingroup$ ctd Velocities are not purely additive at speeds approaching cee. The closer to cee, the greater the acceleration needed to go 'faster'. It is this 'greater acceleration' that is the technological barrier. $\endgroup$ – Justin Thyme Jan 28 '18 at 18:32
  • $\begingroup$ @JustinThyme, that's absolutely true... according to how we understand the physics today. Most readers of Jules Verne's books were delighted with what they perceived as the pure fantasy of his stories. They couldn't imagine anything like what he described being possible. As with all fiction, most proved unobtainable, some proved wonderously possible. As we understand light speed today, we need an accelerating acceleration. But that's just a snapshot. Perhaps it will prove to be the end-all understanding, perhaps not. Cool, that. $\endgroup$ – JBH Jan 28 '18 at 19:06
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Assuming a civilization has the capacity to build space vessels designed to travel from one solar system to another, what is the technological difference between traveling at 50% light speed and traveling at 100% light speed (or near)?

I'd say, pretty significant. To achieve a speed of X, you need to gain a kinetic energy of mX2 and that energy, whatever your propulsion system, ultimately comes from fuel. But since you need to have the fuel with you, that's more mass that you need to have with you when you start. In the end, it's a matter of energy density.

Then, relativistic speeds offer two important challenges that your technology must overcome:

  • anything in space - dust, grit, stray protons, gas molecules, junk - in your trajectory becomes a projectile hitting at relativistic speeds. You need to be able to either locate such obstacles far enough, and maybe manoeuver fast enough, to avoid them, or survive the smaller impacts.

  • at relativistic speeds, your ship-clock time slows down. This means that you have even less time to detect obstacles, less time to react, less time to manoeuver.

At 99% c, you send out a pulse at the speed of light towards a half-kilo pebble floating one million kilometers in front of you. The pulse takes 3 seconds to reach the pebble; in those three seconds you've covered about 895,000 km and are at 105,000 km from the pebble. The pulse goes back, and you detect it when you're at less than 10,000 km from the pebble. To move a space of s = 50 meters off from your route, hold the relativistic slow-down, you have around t = 0.03 seconds. Given that $s = \frac{1}{2}at^2$, this gives $a=\frac{2s}{t^2}$ = nine thousand gravities.

So: you either have technology to survive accelerations two orders of magnitude above lethal, and detection technology capable of locating position and speed of a pebble one million kilometers away; or a detection range proportionately higher; or the capability to survive impact, and a half-kilo pebble at .99c has the same effect of a multimegaton-range fusion bomb.

And then, what kind of technological leap is required to go beyond light speed?

The impossible kind, for all that we know. It's a sort of Chinese Corridor race: every technological leap you do will halve the distance separating you from light speed. So you go from 50%c to 75%, to 87.5%, 93.75%... but you will never reach c (the Engineer's response in the joke is "Yeah, mate, but I only need to get close enough).

So traveling 4 light years takes 4 years at light speed.

Welllll... actually, 4 light years at light speed takes no time at all, if you're aboard the ship. Time contraction again. That might be an advantage.

Of course, reaching near enough the speed of light takes time.

Would it make sense to say "We are only advanced enough to go x% of light speed"?

Yes, it makes a lot of sense.

would anything really stop anyone going near light speed given enough fuel and distance to reach that speed?

At a certain point, exotic effects become observable and begin kicking in. The most relevant is probably the Doppler-Zatsepin effect, whereby you observe the ubiquitous microwave background blue-shifted towards higher energetic levels. In other words, wherever you look you see a gamma-ray laser firing at you point-blank with energy enough to photodisintegrate the ship. This phenomenon limits the distance traveled by a fast-enough particle to what is called the GZK limit. Accelerating further will expose you to a different but equally nasty effect: the temperature of the vacuum will appear to increase.

So, relativistic travel is hot, but wearing :-)

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There is one crucial term in your question that perhaps needs exploring. You do not ask in terms of 'anything' but in terms of 'anyone'. That is, can a HUMAN travel that fast?

We really have absolutely no data on how any biological process would function at that speed, let alone a human. The trick is, we have to ACCELERATE to that speed. We know that space flight has repercussions on the human body, and on biology. We DON'T know if these effects are cumulative.

As an analogy, consider a change in temperature. Frogs will freeze to death at a slow drop in temperature, without sensing it. Humans, on the other hand, show physiological reactions in order to maintain a specific body temperature. Could, somehow, constant acceleration to a faster and faster speed have a biological effect? We don't know. No human has yet accelerated to such a speed.

We know almost certainly that biology depends upon quantum effects. Quantum tunneling, for instance, in electrolyte transport through the cell, and in photosynthesis. Will the quantum effects be somehow altered?

So what happens to human biology, or biology in general, if the organism is subjected to a constant acceleration that results in a speed approaching that of a massless particle? Are humans adapted to operate optimally in an environment of an acceleration and velocity range typical of earth, and would we have extreme difficulty in adapting to any other environment?

So, in answer to your question, yes it is possible that humans (not things) might have limitations on going that fast, and these limitations would have to be addressed by technology beyond that which we currently have.

EDIT

I found the reference that, in part, addresses this.

Speed kills: Highly relativistic spaceflight would be fatal for passengers and instruments

Unfortunately, as spaceship velocities approach the speed of light, interstellar hydrogen H, although only present at a density of approximately 1.8 atoms/cm3, turns into intense radiation that would quickly kill passengers and destroy electronic instrumentation. In addition, the energy loss of ionizing radiation passing through the ship’s hull represents an increasing heat load that necessitates large expenditures of energy to cool the ship.

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    $\begingroup$ There were also back in the early 19th century people who said railway travelling was unhealty because the human body was not suitable for high speeds. $\endgroup$ – Karl Jan 28 '18 at 17:24
  • $\begingroup$ @Karl Point taken, until you ride a roller coaster. Some people can handle it, others can't. It's not just the pure g forces, it is the acceleration. $\endgroup$ – Justin Thyme Jan 28 '18 at 17:32
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    $\begingroup$ Äh, g force is acceleration. ;-) And if you're prepared to travel for decades, you can also take another half year to gain cruise speed. $\endgroup$ – Karl Jan 28 '18 at 17:51
  • $\begingroup$ @Karl Okay, more specifically, the CHANGE in acceleration, and the TYPE of acceleration. Car sickness is real, and it has its basis in our vestibular system. It has adapted to a constant centripetal acceleration as we rotate with the earth. We are always going around in circles. Slow, but constant centripetal acceleration. Yet we are unaware of it. Our body has adapted to it. Change that to faster or slower, and some of us are in trouble. Change that to constant linear vs constant centripetal, we haven't experienced that yet. Even our growth has adapted to centripetal acceleration. $\endgroup$ – Justin Thyme Jan 28 '18 at 18:18
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Assuming light speed is the real barrier, would anything really stop anyone going near light speed given enough fuel and distance to reach that speed?

I'm pretty sure the answer to the spirit of your question is very simply "no".

  1. Say you are going any speed, whatsoever. Any speed. To go faster, you simply attach a rocket at the back and light a match. Once again, no matter what speed you are going, to go faster you just fire a rocket. There is utterly no difference whatsoever, at all, in the fundamentals.

  2. Regarding travel at light speed, like a photon (or faster than light speed). This is simply utterly impossible, based on our current deepest understanding of mathematics.

Regarding point 1, of course - obviously - you might need staggeringly big rockets and other astounding engineering difficulties. (You may well need fusion! or anti-matter! engines to make huge amounts of electricity - whatever. You would surely need some sort of astounding laser technology to blast out of the way any micro-particles in front of you - etc etc.)

Once again, thanks Einstein - any speed at all, whatsoever, is identical to no speed at all. There is absolutely no difference between speed and no speed.

(Note that indeed our planet (indeed, our galactic group) is whipping along at an astounding speed; when we take off to the moon we just "add speed" - the "original" (staggering) speed of the planet means absolutely nothing.)

Speed and no-speed are the same.

In contrast - point 2 - traveling at light speed (or higher) is utterly and totally different, requiring utterly new base mathematical concepts, totally and completely unknown to us.

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    $\begingroup$ Your first point is not quite accurate. If you are accelerating from earth, and escaping gravity, then your rocket strapped to your back would also need enough thrust to allow you to reach escape velocity, otherwise you fall back to earth. Since gravity is everywhere, and everything is basically escaping from or being drawn to something under the effects of gravity, there is a minimum thrust required to overcome some gravitational effect. So you need to add 'CONSTANT unaccelerated' before speed. And maybe change 'speed' to 'velocity' (scalar to vector). There are advantages to inertia. $\endgroup$ – Justin Thyme Jan 28 '18 at 17:23
  • $\begingroup$ Hey @JustinThyme - lift off from Earth is uninvolved in this question. $\endgroup$ – Fattie Jan 28 '18 at 18:51

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