Would you ever notice relativistic speed?

[Talakeal]

So, all motion is relative, and there is no privileged frame of reference.

This means that, from many points of view, we are all moving at relativistic speed right now, correct?

If you were in a spaceship moving through a vacuum, and were constantly accelerating, would you ever notice a point where the efficiency of your engines went down? Would time and space aboard your ship ever become distorted? Would you have to stop at the speed of light?

Or, would time and space outside of your ship simply distort to account for your speed?

Like, I know that scientists have observed particles on Earth that were created in distant stars but only have a few minutes of radioactive decay, so clearly some combination of warped space and time allowed them to travel many lightyears in what, from their perspective, was only a few minutes.

In short, is relativity something that affects other people, but never one’s self?

[gomipile]

So, all motion is relative, and there is no privileged frame of reference.

This means that, from many points of view, we are all moving at relativistic speed right now, correct?

If you were in a spaceship moving through a vacuum, and were constantly accelerating, would you ever notice a point where the efficiency of your engines went down? Would time and space aboard your ship ever become distorted? Would you have to stop at the speed of light?

Or, would time and space outside of your ship simply distort to account for your speed?

Like, I know that scientists have observed particles on Earth that were created in distant stars but only have a few minutes of radioactive decay, so clearly some combination of warped space and time allowed them to travel many lightyears in what, from their perspective, was only a few minutes.

In short, is relativity something that affects other people, but never one’s self?

Relativistic effects only matter when you have a relative velocity/speed between two or more reference frames/objects.

If there's only one frame of reference, there's no relative motion.

Asking about what happens in relativity in a problem that only has one inertial reference frame is like asking about leverage with no fulcrum or a simple pulley system with no rope/cable. There just isn't enough context to begin to apply the method in such cases.

[NichG]

You wouldn't notice anything intrinsically in an empty universe. But in a universe with other things in it, you'd see red-shift and blue-shift, which would let you know those relative velocities. And if you were going very very fast relative to everything else, the blue-shift from stuff you're moving towards could be enough to make e.g. 3 kelvin black body radiation into stuff that would fry you, which would be pretty noticeable. But its noticeable because you're interacting with stuff moving at a different velocity than you, not just because the absolute value of your speed is large.

[Talakeal]

You wouldn't notice anything intrinsically in an empty universe. But in a universe with other things in it, you'd see red-shift and blue-shift, which would let you know those relative velocities. And if you were going very very fast relative to everything else, the blue-shift from stuff you're moving towards could be enough to make e.g. 3 kelvin black body radiation into stuff that would fry you, which would be pretty noticeable. But its noticeable because you're interacting with stuff moving at a different velocity than you, not just because the absolute value of your speed is large.

Ok. So building on this.

I am on a space ship with no windows heading towards a planet 30 light years away.

I have instruments that measure my acceleration. I continually accelerate toward the planet?

Would I ever notice that my continuous acceleration stops or becomes inefficient due to increasing mass?

If I added up all my acceleration, would I ever see that I am now moving toward my destination faster than light?

Now, assuming that is correct, say my average speed, from my perspective, was 3x the speed of light. When I arrive at my destination, is it correct that only 10 years will have passed from my perspective, but significantly more time will have passed for the people at both my destination and my point of departure?

[Manga Shoggoth]

Let's see...


This means that, from many points of view, we are all moving at relativistic speed right now, correct?

No. Relativistic speeds means speeds where the effects of Relativity start to become dominant (~75% the speed of light).


If you were in a spaceship moving through a vacuum, and were constantly accelerating, would you ever notice a point where the efficiency of your engines went down?

Yes, because you would be accelerating less, so your apparant gravity (as a result of that acceleration) would decrease. (In other words, things would weigh less)


Would time and space aboard your ship ever become distorted?

On board your ship, no. That will all be within your inertial frame of reference. Anything outside your ship, perhaps, depending on the relative velocity between them and you.


Would you have to stop at the speed of light?

Or, would time and space outside of your ship simply distort to account for your speed?

The second. Think of it this way: all measurements between frames of reference adjust so that the speed of light is always the same for all observers, no matter what reference frame they are in.


Like, I know that scientists have observed particles on Earth that were created in distant stars but only have a few minutes of radioactive decay, so clearly some combination of warped space and time allowed them to travel many lightyears in what, from their perspective, was only a few minutes.

I think you are getting confused here. This refers to muons created in the upper atmosphere created by cosmic rays hitting the atmosphere. The muons should mostly be decaying before they reach ground level, but we actually see far more of them than we should.

The reasons (somewhat simplified) are twofold:

From our point of view the muon is approaching at a speed close to light, so time runs slower for them, so they last longer and more of them reach the ground. This is called time dialation.

From the muon's point of view, they decay at the correct rate, but because they are moving so fast the distance they have to travel is shortened, so although they decay at the "proper rate", they don't have as far to go.

Both views are correct, because no reference frame has priority.


In short, is relativity something that affects other people, but never one’s self?

Yes and no.


Anyone and anything within your frame of reference will show no relativistic effects.
Anyone moving outside your frame of reference at non-relativistic speeds will show little to no relativistic effect, depending on how fast they are moving. The relativistic effects of a car driving past you will be unnoticable.
Anyone moving outside your frame of reference at relativistic speeds will show clear relativistic effects, like, for example, the aforementioned muons.



EDIT: A good explanation of the Muon bit can be found in this video (Is Earth Actually Flat? (https://www.youtube.com/watch?v=VNqNnUJVcVs)), starting around 06:53 (but the rest of the video is worth a look).

[Gnoman]

There's a lot to unpack here, but let us begin with the simplest. Measurable relativistic effects can be obtained at relatively low speeds, but "measurable" and "perceptible by humans" is not the same thing. At .5c, the effect is only 1.1547x. At .8c, it is 1.6666666666x. To get, for example, the 3x difference mentioned, you would have to be traveling at .942809c. For this question to even make sense, you're dealing with velocities that make silly putty out of conventional logic.

[NichG]

Ok. So building on this.

I am on a space ship with no windows heading towards a planet 30 light years away.


Just to be really explicit about this, you mean that even though you're heading towards the planet, you have no sensors on the ship that detect the planet?



I have instruments that measure my acceleration. I continually accelerate toward the planet?

Would I ever notice that my continuous acceleration stops or becomes inefficient due to increasing mass?


It sort of depends how you measure acceleration. From a purely inside-the-ship perspective you'd experience constant acceleration - that is, if you held a mass on a string, you'd feel it tug in the direction opposite to the acceleration and that force would be constant.

But if you did have external sensors and measured acceleration based on external reference points, it'd be a bit weird, because I think it depends on whether you're measuring how fast you're approaching something you're moving towards, versus how fast things are moving past you. Lets say that for some reason you were using two distant stars as reference points for how fast you were going. So look at what angle from 'straight ahead' star 1 and star 2 appear in your sensors, and you use that to figure out where you are, and from that figure out how fast you're going, and from that figure out if that keeps increasing.

What you'd find is that as you accelerated, you wouldn't just change where those stars were, but the apparent angular distance between those stars would also change, so you'd get inconsistent results when trying to infer your acceleration classically. Here's a page with some animations which do special relativistic raytracing to show the effect: http://www.didaktik.physik.uni-due.de/~backhaus/Relativity/startEnglishWWW.htm

Edit: This page also has some relativistic renders which are a bit easier to interpret: https://graphics.stanford.edu/courses/cs348b-competition/cs348b-04/relativistic/proposal.html Sadly, the originals seem to be offline, but there's a paper that explains some of the images: http://people.physics.anu.edu.au/~cms130/TEE/site/tee/learning/media/physicist.pdf

But if you took the original distance between your starting and end points, and ship's time, then you'd perceive that the journey to the far away planet took the same amount of time from your point of view as it would have classically. In order to explain why you can't just flip the role of the planet and the ship, you need general relativity (it's because the planet has not experienced acceleration, but the ship has, so it's not actually symmetric - the acceleration is what in the end accumulates the irreducible difference in passage of time when you bring everything back to rest relative to one-another).

In terms of the increasing mass, my intuition is that it has to work out that can't detect the gravitational effect due to changes in your own mass due to velocity without an external reference, but that seems like an interesting constraint (in the sense that it's hard enough to satisfy that you should be able to derive stuff from that constraint). So you shouldn't be able to collapse yourself into a black hole just by going fast, because if you could then that would imply a universal reference frame in which the gravitational effect of an object on itself is minimal.



If I added up all my acceleration, would I ever see that I am now moving toward my destination faster than light?

Now, assuming that is correct, say my average speed, from my perspective, was 3x the speed of light. When I arrive at my destination, is it correct that only 10 years will have passed from my perspective, but significantly more time will have passed for the people at both my destination and my point of departure?

Yes, if you just added up your acceleration as if it were classical, or looked at how long it appeared to take to arrive based on the initial distance and working it out classically, you'd conclude that you were going faster than light at some point. But you'd get the wrong answer for things like where other third reference points should appear in your view at stages along the way and things like that.

[Talakeal]

There's a lot to unpack here, but let us begin with the simplest. Measurable relativistic effects can be obtained at relatively low speeds, but "measurable" and "perceptible by humans" is not the same thing. At .5c, the effect is only 1.1547x. At .8c, it is 1.6666666666x. To get, for example, the 3x difference mentioned, you would have to be traveling at .942809c. For this question to even make sense, you're dealing with velocities that make silly putty out of conventional logic.

Perhaps, but these sorts of speeds crop up quite often in science fiction and with small particles in every day life.

For example, without warp drive, the USS enterprise-D is said to be able to travel at something like 25% the speed of light, and I am trying to figure out what that would actually mean in a setting with more realistic physics.


I think you are getting confused here. This refers to muons created in the upper atmosphere created by cosmic rays hitting the atmosphere. The muons should mostly be decaying before they reach ground level, but we actually see far more of them than we should.

The reasons (somewhat simplified) are twofold:

From our point of view the muon is approaching at a speed close to light, so time runs slower for them, so they last longer and more of them reach the ground. This is called time dialation.

From the muon's point of view, they decay at the correct rate, but because they are moving so fast the distance they have to travel is shortened, so although they decay at the "proper rate", they don't have as far to go.

EDIT: A good explanation of the Muon bit can be found in this video (Is Earth Actually Flat? (https://www.youtube.com/watch?v=VNqNnUJVcVs)), starting around 06:53 (but the rest of the video is worth a look).

Quite likely.

I am remembering something my physics professor said was proof that time dilation was real and not merely an optical illusion. This was ~15 years ago and I am likely misremembering the details. I will watch your video, thanks.


No. Relativistic speeds means speeds where the effects of Relativity start to become dominant (~75% the speed of light).

Right, but all motion is relative, and I am pretty certain that, from a great many points of reference points in this universe, you and I are moving at greater than .75C.


snip.

Ok, that's about what I thought. Thank you.

I have been trying to understand relativity in a way that makes sense to me without all of the short hand that people often use to explain it, and the idea of absolute speed limits, rest mass, all speed being relative, and no preferred frames of reference have always seemed contradictory to me.

[Manga Shoggoth]

Right, but all motion is relative, and I am pretty certain that, from a great many points of reference points in this universe, you and I are moving at greater than .75C.

Yes, but the term "relativistic" does not mean "relative".

"Relativistic " specifically refers to speeds where relativistic effects (as predicted by Special and General Relativity) are visible.

A car drives past me. That is relative motion, but not at a relativistic speed.

There are areas in the universe that are moving at relativistic speeds relative to us (we can measure the red and blue shifts of galaxies), but that does not mean all motion is relativistic, and most of the relative motion you will experience won't be.

[Talakeal]

Yes, but the term "relativistic" does not mean "relative".

"Relativistic " specifically refers to speeds where relativistic effects (as predicted by Special and General Relativity) are visible.

A car drives past me. That is relative motion, but not at a relativistic speed.

There are areas in the universe that are moving at relativistic speeds relative to us (we can measure the red and blue shifts of galaxies), but that does not mean all motion is relativistic, and most of the relative motion you will experience won't be.

But if they are moving at relativistic speeds relative to us, are we not also moving at relativistic speeds relative to them?

[Bohandas]

No. Relativistic speeds means speeds where the effects of Relativity start to become dominant (~75% the speed of light).

There are many objects moving at those speeds relative to us, mostly cosmic radiation particles


But if they are moving at relativistic speeds relative to us, are we not also moving at relativistic speeds relative to them?

That is correct

[Chronos]

Quoth Manga Shoggoth:

Yes, because you would be accelerating less, so your apparant gravity (as a result of that acceleration) would decrease. (In other words, things would weigh less)

If your engines are producing a constant thrust, then your proper acceleration (which is what you feel as apparent gravity) will remain constant. Why would it decrease? At the start of your journey, your velocity relative to yourself was zero. After you've been accelerating for years, your velocity relative to yourself is still zero. And so, aboard the ship, you'd experience all of the relativistic effects associated with zero velocity: That is to say, no effects at all.

[Manga Shoggoth]

If your engines are producing a constant thrust, then your proper acceleration (which is what you feel as apparent gravity) will remain constant. Why would it decrease? At the start of your journey, your velocity relative to yourself was zero. After you've been accelerating for years, your velocity relative to yourself is still zero. And so, aboard the ship, you'd experience all of the relativistic effects associated with zero velocity: That is to say, no effects at all.

The question was "If you were in a spaceship moving through a vacuum, and were constantly accelerating, would you ever notice a point where the efficiency of your engines went down?"

If the efficiency of your engine goes down either:


You will need more fuel to maintain the same acceleration, and you will see in increase in fuel usage
You will use the same amount of fuel and your acceleration (and hence weight) will decrease
You see a combination of the two


I described the second of those options.




There are many objects moving at those speeds relative to us, mostly cosmic radiation particles

I do not understand the point you are trying to make here. in the actual post you quoted from I stated that things do move at relativistic speeds to us and gave an example. The fact that there are other possible examples does not invalidate the point I was making, which was not all relative motion is relativistic.


But if they are moving at relativistic speeds relative to us, are we not also moving at relativistic speeds relative to them?

Yes indeed. There is no preferred reference frame. They will see you moving at relativistic speeds relative to them, you will see them at relativistic speeds relative to you.

It would be the same with non-relativistic speeds - it's just that the maths becomes an awful lot easier becase you don't have to add in the relativistic effects.

[Anymage]

In a properly realistic universe, an engine would have a hard time maintaining 1g acceleration because it would have to constantly be expending fuel. Having to account for fuel would limit a lot of sci fi trips and create a ton of math overhead, so it's okay to assume magic reactionless engines for all but the hardest sci fi. And assuming these engines, someone in a sealed off spaceship would experience a force practically indistinguishable from gravity, but would not experience that as motion any more than we perceive motion when we're standing so the floor pushing us up balances out the gravity pulling us down.

And to answer the base question, I'll repeat the point that all motion is relative. If I on earth think that your spaceship is going at 99.99% the speed of light, it isn't engine problems that will make me think that your engines won't give you as much more speed as they used to. I will see you as being more massive than your own scale would, but that only applies if I want to push you somehow. (If you're carrying your own fuel source the energy required to get you up to speed was already on your ship as fuel mass beforehand, and indeed you'll be lighter now due to spent fuel. Again, this is why outside of hard sci fi it's easiest to assume magic engines and not look too closely.) From my perspective your ship will also be contracted and your time will be going slower, and the apparent time slowing will be one of the big things that causes my relativistic measurements to disagree with the numbers I might get from a naive Newtonian assumption.

For that matter, if your ship were somehow programmed with Newtonian assumptions, it could count out that fuel was leaving at 1g and calculate your velocity from 10 meters per second per second. At that rate it would take ~10 years for the naive Newtonian computer to assume you were going faster than light. Any measurements of external objects would disagree with that assessment. (And no measurements/observations of external objects would quickly lead to a catastrophic crash.) So there's no reason not to program the ship's computers to do more accurate relativistic math.

[Tyndmyr]

We are not moving faster than lightspeed relative to any point in the observable universe.

We probably ARE moving FTL relative to points outside the observable universe. But given that we are departing from one another faster than the speed of light, we cannot possibly observe that, and vice versa.


Ok. So building on this.

I am on a space ship with no windows heading towards a planet 30 light years away.

I have instruments that measure my acceleration. I continually accelerate toward the planet?

Sure.


Would I ever notice that my continuous acceleration stops or becomes inefficient due to increasing mass?

Essentially every bit of additional acceleration has a constant effect compared to the difference between your speed and the speed of light. What I mean is that if x fuel takes you from stationary to half of light speed, expending another x fuel in the same way, would take you halfway from your current speed to lightspeed, or three quarters light speed.

This effect is continuous, and every bit of acceleration added will get you closer to light speed, but you will never reach it. There is no point at which acceleration stops accelerating.


If I added up all my acceleration, would I ever see that I am now moving toward my destination faster than light?

No.


Now, assuming that is correct, say my average speed, from my perspective, was 3x the speed of light. When I arrive at my destination, is it correct that only 10 years will have passed from my perspective, but significantly more time will have passed for the people at both my destination and my point of departure?

While you will not exceed the speed of light, even substantial fractions of light speed will introduce temporal effects. You will be substantially younger than stationary observers. These effects come into play, slightly, for GPS satellites orbiting earth, a speed that, while fast, is still quite far from light speed. Any probable interstellar trip is likely to have a much larger factor here on account of greater necessary speeds.

Actually approaching the speed of light isn't yet plausible with current engine technology, though.

[Talakeal]

snip

Ok, that is exactly how we were taught it in school.

But, AFAICT, this contradicts what we were also taught about all motion being relative and there being no preferred point of reference.

If we actually saw decreased acceleration due to relativity, wouldn't that apply to all acceleration, as any movement you make is at relativistic speed according to someone?

[Tyndmyr]

Ok, that is exactly how we were taught it in school.

But, AFAICT, this contradicts what we were also taught about all motion being relative and there being no preferred point of reference.

If we actually saw decreased acceleration due to relativity, wouldn't that apply to all acceleration, as any movement you make is at relativistic speed according to someone?

Oh, absolutely.

It's just that in most real world instances, the element of relativity is insanely small. Too tiny to really measure or reasonably use in any fashion, but it's still there.

"Relativistic speeds" are a pretty arbitrary label to slap on high speeds, the effects themselves just scale smoothly. All speeds are relativistic to some tiny degree.

[DavidSh]

One thing to keep in mind is that, under Special Relativity, while all observers in inertial frames will agree on who is accelerating and who isn't, they won't agree on how much acceleration anybody is undergoing. If you do something that will increase your speed from 0 to c/4 as measured in your starting frame, observers in other frames will not all agree that your speed is increasing by c/4.

[Anymage]

If we actually saw decreased acceleration due to relativity, wouldn't that apply to all acceleration, as any movement you make is at relativistic speed according to someone?

"We" meaning who? The people on earth? The people on your spaceship? The people on the destination planet? (Which is most likely to have a decent speed compared to earth's even if that speed is peanuts by relativistic comparisons.) The whole point is that everybody sees their own numbers, but that with a little math you can predict how they'll see each other and agree on the end results when they meet up.

An outside observer would see your effective acceleration slow down, because to them your time and distances would start getting wonky. Not due to any mechanical limits visible in the engines themselves. From your perspective you can keep going at the same acceleration forever (assuming you're powered by magic so you don't have to do mind fuel), and it's the rest of the universe that'll start to look weird if you look out the window. Not just that it's zooming by very fast. (Although that is happening too, so small bits of space junk all become energetic enough to become truly dangerous.) But that distances outside your ship appear to be warping too. From your perspective in the ship the journey will actually cover less distance than you'd get if you just laid a ruler from earth to the other planet.

Distance, time, and the very concept of simultaneity all warp in relativity. There's a reason most storytellers handwave most of it. Normal intuition and pop-sci analogies will only take you so far before you have to acknowledge and embrace the weirdness.

[Yora]

It looks to outside observers that your acceleration is decreasing as you get closer to the speed of light, because they also observe time on your ship slowing down. And it's length contracting.

Both inside and outside the ship, everyone will agree that the ship is accelerating by X m/s². But you'll be disagreeing how long a meter and a second are.

Where things get really funky is that not only will the observers on a planet see that the length of the ship is contracting, but because there is no preferred reference frame, people on the ship will see that the length of the planet is contracting. Not only do they disagree on how long a meter is, they will both claim that their meter is longer and the other one's meter is shorter.

The schoolbook version of "objects at relativistic speed experience time dilating and length contraction" only hints at something happening we don't notice every day, but it doesn't go into the actual strange weirdness that is going on.

When I noticed that "length contraction" and "no preferred reference frame" seem mutually exclusive, I spend a good portion of two or three days trying to find out what's going on. The explanation for it is in the "ladder and barn" example, or the now more popular "train and tunnel" example. That one really helped me make big leaps getting a better understanding of what relativity really is, and why space-time is not just space and time.

[NichG]

Essentially every bit of additional acceleration has a constant effect compared to the difference between your speed and the speed of light. What I mean is that if x fuel takes you from stationary to half of light speed, expending another x fuel in the same way, would take you halfway from your current speed to lightspeed, or three quarters light speed.

This effect is continuous, and every bit of acceleration added will get you closer to light speed, but you will never reach it. There is no point at which acceleration stops accelerating.


This is the description from an external inertial frame.

From the non-inertial frame of the ship, you can't know how fast you're going, so your acceleration does not appear to be any less effective. You are in effect always boosting from rest in your own frame.

For the specific calculation Talakeal asked about - measuring your acceleration locally without looking at the outside world, and then integrating over time - you will absolutely get a number faster than c after awhile. Its just that that number won't correspond to what an external observer in a fixed frame would get if they measured your speed.


Actually approaching the speed of light isn't yet plausible with current engine technology, though.

This is also a bit of an awkward phrasing in relativity. It would be better to say that we don't have engine technology that can achieve a relativistic delta-v from onboard fuel over the course of its trajectory. Since its not like 'near the speed of light' is a fixed thing - that's kind of the point, that all inertial frames are equal, so there isn't such a thing as absolute velocity.

[Yora]

For the specific calculation Talakeal asked about - measuring your acceleration locally without looking at the outside world, and then integrating over time - you will absolutely get a number faster than c after awhile. Its just that that number won't correspond to what an external observer in a fixed frame would get if they measured your speed.
If you set your speed meter on your ship to 0 as you start and then only look at your acceleration meter which keeps showing you an acceleration of 10 m/s², you would conclude that you have reached the speed of light after 30,000,000 seconds. And after another 7,500,000 seconds, you would conclude that you're moving at 125% the speed of light.

Obviously that's not actually what happens, but I have no clue what you'd see if you look out of a window.

[NichG]

If you set your speed meter on your ship to 0 as you start and then only look at your acceleration meter which keeps showing you an acceleration of 10 m/s², you would conclude that you have reached the speed of light after 30,000,000 seconds. And after another 7,500,000 seconds, you would conclude that you're moving at 125% the speed of light.

Obviously that's not actually what happens, but I have no clue what you'd see if you look out of a window.

Like with QM, a lot of what makes relativity counterintuitive is that it says that some things we thought of as fundamental properties that things have are in fact artifacts of how we measure them. So if you want to take relativity seriously, it says 'you can have a perfectly functional theory of physics in which velocity is not an intrinsic property of an object, but only relative velocities are real'.

So 'what speed are you going now?' is kind of a meaningless question in relativity - it doesn't have an answer that has any physical consequences, so you're free to set it arbitrarily.

What speed do you appear to be going from someone back at your starting point has an answer. It's a different answer then 'what speed do you appear to be going from a ship moving at constant velocity v relative to your starting point'.

'What will your clock show when you arrive' has an answer, and I think it's even the same answer that you'd get classically, just blithely integrating your acceleration as if it were additive (I should double check this though). Of course it's different than 'what will the clocks at your destination show?'

Maybe the overtly weird way to do it would be, if you took all your acceleration and applied it instantaneously at launch rather than continuously, your destination would immediately appear closer, as if looking through a lens (again, I probably should test this in a relativistic raytracer to be sure)

[DavidSh]

Obviously that's not actually what happens, but I have no clue what you'd see if you look out of a window.
There are two parts to the answer to that question.
The first is to use the relativistic velocity addition formula multiple times, maybe in the limit as your step size goes to zero, to compute the final velocity as measured in the frame of your initial velocity.
The second is what you see if you look out of the window. This involves blue- and red-shifting, and length contraction. One old science fiction writer wrote of a "starbow", the ring of stars that haven't been shifted out of visibility, but that may not be accurate.

[Talakeal]

'What will your clock show when you arrive' has an answer, and I think it's even the same answer that you'd get classically, just blithely integrating your acceleration as if it were additive (I should double check this though). Of course it's different than 'what will the clocks at your destination show?'

That was also the conclusion that I came to which prompted me to start this thread.

[Bohandas]

If I added up all my acceleration, would I ever see that I am now moving toward my destination faster than light?

No, but you'll see the space ahead of you contract

[NichG]

Huh, so it looks like you might actually get there faster in shipboard time than you would classically, because of the length contraction.

For example, accelerating at 1g to travel 30 ly takes about 4 years in ship time but would take 7.6 years classically: https://www.omnicalculator.com/physics/space-travel

So relativity actually makes space travel easier, not harder, at least for personal times.

[Bohandas]

Huh, so it looks like you might actually get there faster in shipboard time than you would classically, because of the length contraction.

For example, accelerating at 1g to travel 30 ly takes about 4 years in ship time but would take 7.6 years classically: https://www.omnicalculator.com/physics/space-travel

So relativity actually makes space travel easier, not harder, at least for personal times.

Yes. Although it's still a problem if you need to send a message or make a return trip.

EDIT:
Actually, now that I think of it it might be more of a complete wash for passengers than an actual help. I'm not sure the ship time would be any less than if you applied the same thrust in a pure newtonian setting. Can anyone answer this one way or another?

[NichG]

Yes. Although it's still a problem if you need to send a message or make a return trip.

EDIT:
Actually, now that I think of it it might be more of a complete wash for passengers than an actual help. I'm not sure the ship time would be any less than if you applied the same thrust in a pure newtonian setting. Can anyone answer this one way or another?

That calculator page says that the required fuel mass would be different for classical vs relativistic ships, but I admit to being a bit puzzled by that. They say something about '100% efficiency', but normally the fuel efficiency in the rocket equation comes from momentum limits rather than energy limits, so maybe its something to do with the fuel efficiency itself being different relativistically versus classically... I assume they're basically treating the fuel as a pure energy source and ignoring momentum entirely.

[asda fasda]

Yes. Although it's still a problem if you need to send a message or make a return trip.

EDIT:
Actually, now that I think of it it might be more of a complete wash for passengers than an actual help. I'm not sure the ship time would be any less than if you applied the same thrust in a pure newtonian setting. Can anyone answer this one way or another?

I'm not sure I understand question but wouldn't that be just the Twin paradox ?
Do yes due to relativity time of your travel seems shorter for you then to people outside of your reference frame

[Radar]

That calculator page says that the required fuel mass would be different for classical vs relativistic ships, but I admit to being a bit puzzled by that. They say something about '100% efficiency', but normally the fuel efficiency in the rocket equation comes from momentum limits rather than energy limits, so maybe its something to do with the fuel efficiency itself being different relativistically versus classically... I assume they're basically treating the fuel as a pure energy source and ignoring momentum entirely.
Can't say for sure, but the most efficient reaction drive (barring engineering problems) would be a photonic drive as it gives the best momentum to energy ratio. Maybe they assume that construction working with 100% efficiency?

As for what is actually more efficient (classical or relativistic), I have no idea and without examining the exact model that the calculator uses it is difficult to rely on the results it gives.

[NichG]

Can't say for sure, but the most efficient reaction drive (barring engineering problems) would be a photonic drive as it gives the best momentum to energy ratio. Maybe they assume that construction working with 100% efficiency?

As for what is actually more efficient (classical or relativistic), I have no idea and without examining the exact model that the calculator uses it is difficult to rely on the results it gives.

Yeah, that's fair. Can we reason whether the existence of a difference between classical and relativistic fuel consumption is compatible with relativity, and where that difference must lie? It seems like it must have to do with the transfer of momentum when boosting a packet of energy from rest to -c in the ship's frame being different classically versus relativistically, because otherwise you'd have an absolute way of knowing your current velocity relative to when you launched, which should not be possible.

[Yora]

Huh, so it looks like you might actually get there faster in shipboard time than you would classically, because of the length contraction.

For example, accelerating at 1g to travel 30 ly takes about 4 years in ship time but would take 7.6 years classically: https://www.omnicalculator.com/physics/space-travel

So relativity actually makes space travel easier, not harder, at least for personal times.

I once did a calculation for how much time would pass if you travel between stars if you could accelerate and decelerate at 1g for the entire journey. And it turned out that even with 2 light years of constant acceleration and 2 light years of constant deceleration, time dilation at the midpoint becomes so big that time almost stops completely on your ship.
Which means that any journey with 1g acceleration and 1g deceleration greater than 4 light years would basically feel the same length for people on the ship. The mid-part of the journey will be spend almost frozen in time, regardless of how long the distance is.

Edit: Turns out I was wrong, but the amount of additional time for multiplying a distance increases much slower than the distance.

1 ly = 2 years
5 ly = 4 years
10 ly = 5 years
50 ly = 8 years
100 ly = 9 years
500 ly = 12 years
1,000 ly = 13 years
10k ly = 18 years
100k ly = 22 years (across the whole Milky Way)
2.5m ly = 29 years (all the way to Andromeda)
100m ly = 35 years
1b ly = 40 years

[Radar]

Yeah, that's fair. Can we reason whether the existence of a difference between classical and relativistic fuel consumption is compatible with relativity, and where that difference must lie? It seems like it must have to do with the transfer of momentum when boosting a packet of energy from rest to -c in the ship's frame being different classically versus relativistically, because otherwise you'd have an absolute way of knowing your current velocity relative to when you launched, which should not be possible.
I think the easiest way to check that would be to calculate the flight time according to internal clocks in the classical and relativistic case on the assumption that through the whole trip a constant 1g acceleration is kept from the internal perspective - half time accelerating and half time decelerating. Since a constant thrust from internal perspective means constant fuel consumption, we could get efficiency just from the calculation of how much time the trip will take according to anyone onboard the rocket.

As it turns out, Yora provided exactly the kind of calculations we need:

I once did a calculation for how much time would pass if you travel between stars if you could accelerate and decelerate at 1g for the entire journey. And it turned out that even with 2 light years of constant acceleration and 2 light years of constant deceleration, time dilation at the midpoint becomes so big that time almost stops completely on your ship.
Which means that any journey with 1g acceleration and 1g deceleration greater than 4 light years would basically feel the same length for people on the ship. The mid-part of the journey will be spend almost frozen in time, regardless of how long the distance is.

Edit: Turns out I was wrong, but the amount of additional time for multiplying a distance increases much slower than the distance.

1 ly = 2 years
5 ly = 4 years
10 ly = 5 years
50 ly = 8 years
100 ly = 9 years
500 ly = 12 years
1,000 ly = 13 years
10k ly = 18 years
100k ly = 22 years (across the whole Milky Way)
2.5m ly = 29 years (all the way to Andromeda)
100m ly = 35 years
1b ly = 40 years
For comparison, the travel time under Newtonian physics would be:

1 ly -> 1.95 years (not sure how precise your numbers here are, so it might go either way here)
100 ly -> 19.5 years
1000 ly -> 195.0 years

Basically, under Newtonian mechanics and constant acceleration, travel time is a square root of the distance. Under special relativity it turns out that the intrinsic time in the same conditions increases far slower than than. Thus, it is indeed more fuel efficient to travel under relativistic physics rather than Newtonian. At least from the intrinsic time perspective. Rather funny conclusion to be honest, but there it is.

[Yora]

I just had a thought:

If I shine a beam of light in empty space, it goes in a straight line.
If I throw an object in empty space, it goes in a straight line.

If I throw an object on Earth, the gravity of the Earth curves space time to bend the straight line of the path into an arc.
If I shine a beam of light on Earth, the arc caused by the curving of space is so minute it's still pretty much a straight line.

Now if gravity would simply bend space, then the straight line path of an object and a beam of light would arc exactly the same degree. But they don't.

Is that were the difference between space and space-time becomes important?
Does the beam of light curve less because the photons are moving at relativistic speed and experience time dilation?
Is the slowing down of subjective time what reduces the curving of the path?

[NichG]

I just had a thought:

If I shine a beam of light in empty space, it goes in a straight line.
If I throw an object in empty space, it goes in a straight line.

If I throw an object on Earth, the gravity of the Earth curves space time to bend the straight line of the path into an arc.
If I shine a beam of light on Earth, the arc caused by the curving of space is so minute it's still pretty much a straight line.

Now if gravity would simply bend space, then the straight line path of an object and a beam of light would arc exactly the same degree. But they don't.

Is that were the difference between space and space-time becomes important?
Does the beam of light curve less because the photons are moving at relativistic speed and experience time dilation?
Is the slowing down of subjective time what reduces the curving of the path?

That's a place to start but I expect that thinking of it that way will lead to confusion later. Objects in relativity all move along geodesics (shortest paths) in 4D if not experiencing non-gravitational forces, and forces change which geodesic an object is on. The thing which indexes which geodesic you're on is your velocity. So different velocities = different paths. When spacetime is flat, curves corresponding to different speeds but same direction overlap when projected down to 3D (all the variation is in what value of the 4th coordinate you have when being at a particular point in the other 3). When spacetime is curved, they won't in general project down to overlapping curves in 3d anymore.

So the flatland analogy would be, imagine all the straight lines in a 3d space - you can always find sets of them which exactly lay on top of one another when viewing from some angle. Now instead think of the geodesics of a sphere projected down - in general they might intersect at points, but the curves all have different shapes and won't overlap exactly anymore.

[Rydiro]

To clarify some parts.
Inside the ship you experience accelleration as constant, only an outside observer sees you accellerating less to maintain the speed limit from her point of view.
You even see your travel path shortening (yay).
You can even get to a destination 100 light years away in less than 100 years ship-time, because for you the travel distance starts to shrink.
You still need more than 100 years, when you ask the outside observer.

Not to mention that this amount of accelleration would be unhealthy and technically difficult.

[DavidSh]

Not to mention that this amount of accelleration would be unhealthy and technically difficult.
Technically difficult I will grant you, but, for humans, 1G of acceleration (what we've been talking about) is more healthy than 0G.

[Khedrac]

If I throw an object on Earth, the gravity of the Earth curves space time to bend the straight line of the path into an arc.
If I shine a beam of light on Earth, the arc caused by the curving of space is so minute it's still pretty much a straight line.

Now if gravity would simply bend space, then the straight line path of an object and a beam of light would arc exactly the same degree. But they don't.
Is this part true? Surely the path of the object and the path of the beam of light would only be the same if the mass of the object was the same as the mass of the photon otherwise you are dealing with different amounts of mass.
(This also assumes no air "resistance" - the reason why hydrogen and helium travel up so quickly is at least in part because the heavier gas molecules displace them "pushing" them upward.)

And I rather suspect that if the object does have the mass of a photon then it will travel the same path as the beam of light.

(Note, we are not talking rest mass here.)

[Chronos]

Yora has it basically correct, here: The path of the baseball and the path of the photon are both "straight lines" (i.e., geodesics), but they're straight lines through spacetime, not just space.

Or to put it another way: If you want to get from RIGHT HERE to the opposite side of Earth's orbit, by the shortest path, that shortest path would go straight through the center of the Sun. If you want to get from RIGHT HERE, RIGHT NOW to the opposite side of Earth's orbit, 16 minutes from now, the shortest path would be very nearly straight through the center of the Sun, and is the path a photon would take. But if you want to get from RIGHT HERE, RIGHT NOW to the opposite side of Earth's orbit, 6 months from now, the shortest path would be along the orbit of the Earth. You might instead think of taking the photon's path to that location, and then stopping there and waiting, but if you actually calculate the total relativistic distance along that path, it's longer than the total distance along the orbit.

[Rydiro]

Technically difficult I will grant you, but, for humans, 1G of acceleration (what we've been talking about) is more healthy than 0G.
Yeah, it takes a really long time to get to relativistic speeds with just 1G. Can anyone do the math?

[NichG]

Yeah, it takes a really long time to get to relativistic speeds with just 1G. Can anyone do the math?

You hit 0.9c after accelerating for 1.4 years of shipboard time or 2 years of time passed at home.

[Rydiro]

You hit 0.9c after accelerating for 1.4 years of shipboard time or 2 years of time passed at home.Thats quicker than I thought. I mean, at least 30% travel time reduction after only 2 years? You can reach quite some stars within a shipboard decade (disregarding DEceleration).
EDIT: Math fail corrected.

[NichG]

Thats quicker than I thought. I mean, at least 30% travel time reduction after only 2 years? You can reach quite some stars within a shipboard decade (disregarding DEceleration).
EDIT: Math fail corrected.

Maintaining 1g for 2 years is pretty difficult if you have to carry your own fuel. I think the most feasible concept I've seen for this sort of thing is a laser sail (featured in Robert Forward's Rocheworld series) - basically you have a pair of mirrors on the ship, and you aim a beam at the ship from home. If you want to accelerate, you reflect it with one mirror; if you want to decelerate, you release the larger mirror to fly out ahead of you and reflect the base beam back, and you catch it with the secondary. You'd still have to deal with red shift as the ship accelerates (so it gets less efficient as you speed up relative to the beam source), but at least you can avoid the rocket equation.

[Radar]

Maintaining 1g for 2 years is pretty difficult if you have to carry your own fuel. I think the most feasible concept I've seen for this sort of thing is a laser sail (featured in Robert Forward's Rocheworld series) - basically you have a pair of mirrors on the ship, and you aim a beam at the ship from home. If you want to accelerate, you reflect it with one mirror; if you want to decelerate, you release the larger mirror to fly out ahead of you and reflect the base beam back, and you catch it with the secondary. You'd still have to deal with red shift as the ship accelerates (so it gets less efficient as you speed up relative to the beam source), but at least you can avoid the rocket equation.
Cool idea but it is not feasible at interstellar distances as you could not possibly focus the laser beam well enough to still such a high acceleration. Diffraction limit puts a hard stop to both laser assisted acceleration for interstellar ships as well as laser based space combat. The only way around it might be a network of beam collimation stations that you put along the way, but would it be practical at all considering how many you would need and how difficult it would be to maintain them?

My personal favorite design is actually Project Valkyrie (http://www.projectrho.com/public_html/rocket/slowerlight3.php#valkyrie) - basically a shoddy raft pulled by an oversized direct annihilation drive. True, antimatter is not exactly easy to get or store, but this does give the upper limit on mass to energy conversion. You could probably do a lot with the same design the nuclear fusion as well.

[gomipile]

Cool idea but it is not feasible at interstellar distances as you could not possibly focus the laser beam well enough to still such a high acceleration. Diffraction limit puts a hard stop to both laser assisted acceleration for interstellar ships as well as laser based space combat.

The diffraction limit puts a hard limit on the effectiveness of a particular piece of equipment. In some circumstances, you can design a better piece of equipment to get past the diffraction limit of a previous one.

Robert L. Forward was a professional physicist. I'm pretty sure he knew what he was doing. I don't have the figures he used in front of me, but IIRC, his system used an extremely large aperture focusing system at the Earth end.

The system he proposed might be so expensive as to be impractical, but I have little doubt that he got the principles correct.

And if you think this is an appeal to authority and therefore fallacious, I assure you that I am perfectly willing to accept mathematical proof that his system is categorically impossible as he laid it out. An engineer's level of mathematical rigor would be sufficient, if all the steps and premises are correct.

[Radar]

The diffraction limit puts a hard limit on the effectiveness of a particular piece of equipment. In some circumstances, you can design a better piece of equipment to get past the diffraction limit of a previous one.

Robert L. Forward was a professional physicist. I'm pretty sure he knew what he was doing. I don't have the figures he used in front of me, but IIRC, his system used an extremely large aperture focusing system at the Earth end.

The system he proposed might be so expensive as to be impractical, but I have little doubt that he got the principles correct.

And if you think this is an appeal to authority and therefore fallacious, I assure you that I am perfectly willing to accept mathematical proof that his system is categorically impossible as he laid it out. An engineer's level of mathematical rigor would be sufficient, if all the steps and premises are correct.
I was unaware of what kind of scale he was envisioning - his ideas are quite impressive. Still, the acceleration he estimated for such a system (taking into account mass and durability of used materials) would be just about 0.005 g. You might probably scale that up even higher (build lenses bigger than the 1000 km diameter he proposed), but for successively diminishing returns I think.

Diffraction limit is exactly why he proposed such a huge lens - scaling the size of the beam up is the only way around that limit. What would be also a problem is scattering of the beam on interplanetary and interstellar gas and dust. Not sure how it would affect the final effectiveness of this drive though.

[gomipile]

I was unaware of what kind of scale he was envisioning - his ideas are quite impressive. Still, the acceleration he estimated for such a system (taking into account mass and durability of used materials) would be just about 0.005 g. You might probably scale that up even higher (build lenses bigger than the 1000 km diameter he proposed), but for successively diminishing returns I think.

Diffraction limit is exactly why he proposed such a huge lens - scaling the size of the beam up is the only way around that limit. What would be also a problem is scattering of the beam on interplanetary and interstellar gas and dust. Not sure how it would affect the final effectiveness of this drive though.

It's almost certainly not practical on the scale of humanity's budget anytime soon, yeah.

Scattering on gas and dust. IIRC we've found that the interstellar medium is less dense than was thought in the 80s. I'm not sure how the density of gas and dust within the solar system compares to estimates from that time.

[Radar]

Scattering on gas and dust. IIRC we've found that the interstellar medium is less dense than was thought in the 80s. I'm not sure how the density of gas and dust within the solar system compares to estimates from that time.
Yeah, that killed the idea of Bussard ramjet (or its more refined versions), but ram augmented rockets are still a possibility.