Question about Accelerating to Nearly the Speed of Light

[Kuroneko II]

Well, yes and no - the story would have two frames of reference, after all, that aboard ship and that back on the home planet.

I'm not sure what you're replying to here.

Even without a time lag (say, a relativistic-speed ship passing close to a planet - not this story but a different one) the planet-based "stationary"* group would perceive any real-time communication with the passing ship as slowed-down. Anyone on the passing ship would perceive real-time communications from the planet as speeded-up. You could have text or video messages passing between the two groups and play them back.

Not quite. The situation is symmetric: either they both perceive each other as sped up or both perceive each other as slowed down. Which it is depends on whether they're moving toward or away each other. The perceived speed-up occurs when they're closing distance and the perceived slow-down when they're separating. The relativistic Doppler factor gives the amount by which this occurs, in this case about 6.2.

N.B. What is measured is not necessarily what is seen or perceived. The Doppler shift is a combination of both time dilation and the distance-caused signal delay.

Those on the ship might perceive any replies as instantaneous or nearly so, whereas on the planet even an immediate reply might have a noticeable time lag.

No, they both have a time lag in their replies. How much time it takes for a signal to reach them and for the reply to travel back is determined by their distance apart, as they're communicating with signals with finite speed. How fast the reply gets there is not the same thing as how much sped-up or slowed-down the reply itself is.

I can't figure out if real-time communications sound would be dopplered up or down. If they are, then I have to wonder if the lighting/color of a video feed would also show doppler effects, which may or may not be particularly noticeable to a human eye.

It depends entirely on the encoding, but for most sensible encoding schemes, there will be no color differences--the video feed would just be sped-up or slowed-down, which is something that can be compensated for through buffering. Of course, if they just looked at each other through a telescope, that image would be very Doppler-shifted.

As as simple example, say they're communicating a digital signal by sending pulses of red light, flash for bit 1 and lack of flash for bit 0 or whatever (for simplicity), with the bitrate 1 Mbps. An Doppler factor of about ~2 would mean that the pulses arrive blue instead of red and that the bitrate is ~2 Mbps instead (i.e., the time between flashes/lack-of-flashes is shorter). But in this scheme, the information the signal carries is completely unaffected.

In this case, if communications are at lightspeed there would be both time distortion effects and a time lag due to distance.

Right. Note for 'hard' ansibles (i.e., neglecting the fact that any ansible exists in the first place), communication is instantaneous in only one inertial frame, while every other frame has to have a finite though superluminal signal speed. The reason is that it's the only kind of ansible compatible with special relativity in the sense of not breaking causality.

[Jerry the Vampire]

The equation Jerry the Vampire posted is actually wrong.

http://en.wikipedia.org/wiki/Relativist ... nics#Force

The correct derivation introduces the mass correction in the equation F = dp/dt.

The basic conclusion is that your question is not correctly formulated. The acceleration produced by a given force reduces at relativistic speeds. So are you talking about a constant force, or a constant acceleration? The two are only directly proportional in Newtonian mechanics, so it's meaningless to speak about "g forces" in special relativity.

Jerry the Vampire's statement that it takes a year to reach c at 1g acceleration is, if not wrong, at least misleading. The force required to produce a finite positive acceleration asymptotes to infinity at c, so you can never acclerate a massive object to c.

Two points firstly I only gave the equations for the factor time is dilated and how apparent mass changes so I wasn't speaking of force. Do you understand what's going on or is it all learnt from wikipedia.


Obviously I meant approximately as the equations I posted prove you can't reach the speed of light.

[Jerry the Vampire]

Also what do you mean treated it as a Newtonian problem? I have not once used any Newtonian equations or thought processes. As I SPECIFICALLY mentioned that after 50% C Newtonian equations of motion can't be used hence the only equations I have mentioned were relativistic. Also if you read the thread we discussed, albeit briefly the relativistic rocket equation but neither I nor Simon_Jester wanted to do the maths but the link is there.

[Simon_Jester]

The equation Jerry the Vampire posted is actually wrong.

http://en.wikipedia.org/wiki/Relativist ... nics#Force

The correct derivation introduces the mass correction in the equation F = dp/dt.

The basic conclusion is that your question is not correctly formulated. The acceleration produced by a given force reduces at relativistic speeds. So are you talking about a constant force, or a constant acceleration? The two are only directly proportional in Newtonian mechanics, so it's meaningless to speak about "g forces" in special relativity.

No, it is not- the g-force experienced by the ship remains a meaningful concept in special relativity, and that's the context in which it's being discussed. See Kuroneko's remarks for more technical accuracy.

I would expect that Broomstick's rocket would be throttled to allow constant acceleration.

Jerry the Vampire's statement that it takes a year to reach c at 1g acceleration is, if not wrong, at least misleading. The force required to produce a finite positive acceleration asymptotes to infinity at c, so you can never acclerate a massive object to c.

It is not misleading if you have the common sense to assume that this is known, and are using "c" as a short-hand for "highly relativistic speeds," which is a fair assumption about everyone participating in the debate so far. If you ask me, anyway.

This is purely a request, but I think it a wise one:

Please resist the impulse to name-drop facts about relativity into the discussion and tell people they're wrong, unless you are (at least in principle) competent to do the relevant integrals and derive the relevant equations yourself.

Jerry appears to be, Kuroneko is, I can (my credential is an M.S. and I don't have the time for this sort of thing I'd like, but it's enough for special relativity).

Are you?

If the target velocity is held fixed, then yes, the time it takes to reach it from rest is inversely proportional to acceleration, for both proper time (ship) and coordinate time (rest frame). The nonlinearity is in how the velocity is related to either acceleration or time. See previous page for formulae.

To avoid any ambiguity- you are saying that, for example, doubling the acceleration will halve the time needed to reach the target speed? Even under special relativity?

What energiewende was talking about was the coordinate acceleration, i.e., what some observer in the stationary frame would measure. Which is not wrong as such, but it's not what anyone on the rocket would experience, so its relevance is quite dubious here.

It is relevant from the point of view of an observer in the rest frame, and might matter from the perspective of follow-up tanker craft whose job it is to refuel the antimatter "catcher" so that it can get home with the cargo.

Well, yes and no - the story would have two frames of reference, after all, that aboard ship and that back on the home planet. That's one of the appeals of attempting to write such a story, it would highlight the relativistic effects.

Aboard the ship you measure "proper" time and such (Kuroneko uses these terms frequently)

I'm assuming that past a certain point real-time communications would first become awkward, then impractical due both the time lag and the different perceptions of time.

They become 'awkward' before you pass the orbit of Mars. They become impossible, or at least useless, after that, because the light speed time delay is longer than the time required for any crisis the rocket might run into to resolve itself.

If the rocket has onboard AI, and control of its own transmitters and receivers, it can compensate for relativistic effects. For instance, it can deliberately shift its own transmitter frequency, to make up for the fact that its radio signals appear Doppler-shifted for an observer on the homeworld. It can also 'speak faster' or slower, as appropriate.

I can't figure out if real-time communications sound would be dopplered up or down. If they are, then I have to wonder if the lighting/color of a video feed would also show doppler effects, which may or may not be particularly noticeable to a human eye.

Competent computer use would fix the problem. Digital signals would not be affected at all; the real problem would be data transmission rates (I am sending data at one kilobyte per second in my frame, but you receive only 500 bytes per second in yours), and communication frequencies.

In this case, if communications are at lightspeed there would be both time distortion effects and a time lag due to distance. If I decide to inflict instantaneous/ansible** communications on my 'verse there would be no lag due to distance but there would still be issues with time dilation. It's an important consideration, though, as it would add additional complications to any needed coordination between fetch-ship and base.

Also, ansibles plus relativistic objects approaching each other equal causality paradoxes, because there will exist a frame of reference in which the ansible message is sent after it arrives.

In this case, if communications are at lightspeed there would be both time distortion effects and a time lag due to distance.

Right. Note for 'hard' ansibles (i.e., neglecting the fact that any ansible exists in the first place), communication is instantaneous in only one inertial frame, while every other frame has to have a finite though superluminal signal speed. The reason is that it's the only kind of ansible compatible with special relativity in the sense of not breaking causality.

Yes, I've wondered about trying to calculate what FTL communication speed is possible without breaking causality, as a function of relative velocity between the inertial frames. As you say, it is not infinite.

[energiewende]

The equation Jerry the Vampire posted is actually wrong.

http://en.wikipedia.org/wiki/Relativist ... nics#Force

The correct derivation introduces the mass correction in the equation F = dp/dt.

Introducing a mass correction, particularly in the form of in that link, is almost to create more confusion than is remotely worthwhile.

This isn't a good way to approach the problem. However, Jerry the Vampire appeared to have stated that in special relativity the force is given by F=ma after applying a Lorentz factor correction to the rest mass (here) which is simply wrong regardless of approach.

Reading this again I think you are right that he simply treated it as a Newtonian problem, and this post is referring to something else.

The basic conclusion is that your question is not correctly formulated. The acceleration produced by a given force reduces at relativistic speeds. So are you talking about a constant force, or a constant acceleration? The two are only directly proportional in Newtonian mechanics, so it's meaningless to speak about "g forces" in special relativity.

You're mistaken. A g-force is measured with an accelerometer, so it has very direct experimental meaning, and is obviously what's relevant in the context of the original question because it would be directly proportional to the weight experienced by an humans aboard.

Hence, context makes it the only sensible interpretation of 'acceleration' as proper acceleration, corresponding to the the proper time τ measured by the ship. In the follow-up, the rocket thrust has F = dp/dτ, which is relativistically correct and requires no mass corrections. Moreover, even without the context of the OP, it's quite typical to interpret an unqualified 'acceleration' and 'force' as proper acceleration and proper force, respectively. That's because in addition to being experimentally direct, those quantities have fundamental, Lorentz-variant meaning, and further conceptual significance, e.g., through the equivalence principle.

People on the ship will measure a constant acceleration with an accelerometer while feeling a constant force (since an accelerometer is really just measuring proper force), but they will not observe the rate at which the universe recedes increasing at a constant rate, which is the common understanding of what acceleration is. That is the point I was making. I agree with you that an engineer designing such a ship would be interested in the proper acceleration since that is what would determine structural requirements, but I wouldn't necessarily assume that of a fiction writer who does not seem to have studied special relativity.

I agree with everything you have written in this post.

[Simon_Jester]

If I may translate from the questions I've actually heard her ask...

Broomstick has expressed concern about g-forces felt by the ship (proper acceleration, even if she has never heard that term in her life), and also about the time it takes to reach a certain velocity "relative to the fixed stars," to the more-or-less shared inertial frame of reference occupied by low-speed objects like stars and planets.

Therefore, with reason, she is concerning herself BOTH with the proper acceleration of the ship, AND with the acceleration as measured in outside frames of reference.

[Broomstick]

If I may translate from the questions I've actually heard her ask...

Broomstick has expressed concern about g-forces felt by the ship (proper acceleration, even if she has never heard that term in her life), and also about the time it takes to reach a certain velocity "relative to the fixed stars," to the more-or-less shared inertial frame of reference occupied by low-speed objects like stars and planets.

Therefore, with reason, she is concerning herself BOTH with the proper acceleration of the ship, AND with the acceleration as measured in outside frames of reference.

^ This. There is more than one frame of reference here and I'm interested in all of them.

I must say, I'm rather pleased that this has stimulated a polite discussion of the implications of the scenario.

Anyhow, let's step back a minute and review. The basic sequence of events are:

1) Mysterious Object discovered moving at some arbitrary percentage of c. I'd actually like to move that down to 70% of c because (correct me if I'm wrong) relativistic effects will be apparent at that speed but getting up to that speed isn't quite the miraculous effort it would be to reach 95% of c.
2) Some Agency wants to retrieve the MO and gets together the necessary resources, including an AI equipped spaceship to fetch it.
3) The fetch ship accelerates at approximately 5g's proper (limited by both engine capability and structural limits) to catch up with the MO and bring it aboard.
4) The fetch ship plus cargo decelerates/returns to home planet, probably at a lower proper acceleration (and thank you for that term, as it save many words).

As a side note, the story will have scenes both on the fetch ship and back at the home planet. Time will be moving at a difference pace in the two reference frames though, of course, to people in a particular frame everything things to be moving along as usual.

Questions I would like to have a value for are as follows:

- Assume the ship weighs 20,000 kg when empty of fuel but containing all other equipment and supplies needed for the trip. With that in mind, how much fuel (assuming some highly efficient way to convert mass to thrust) is required to de-accelerate from 70% of c back down to zero. (Trust me, there is a reason for figuring this out first).

- How much fuel will be required to accelerate the non-fuel mass plus half the necessary return fuel mass up to 70% c? (I'm declaring, via Author's Privilege, that they first time the fetch ship will be able to meet up with a fuel resupply drone will be halfway back to base)

- Assuming a 5g proper acceleration all the way outbound, how long does the outbound trip take from the point of view of A) the AI aboard the ship and B) the home base?

- Assuming a 1.5 g proper return acceleration all the way back, how long does the inbound trip take from the point of view of A) the Ai aboard the ship and B) the home base?

Additional question which may or may not become relevant to the tale:

- IF they have an ansible on both ends, what sort of communication distortions can be expected? Assume both parties are speaking at what a human would consider a normal conversational speed within their own frame of reference. Would the AI seemed slowed down to the planet? Would the planet group seem speeded up to the AI? What is the difference in perceived time rates? At the peak speed of the fetch ship/MO how many planetary minutes would pass for each ship minute, as an example.

Keep in mind these figures do not need to be exact, I'm looking for ballpark figures so nothing seems too out of whack to anyone bothering to do the math. No one in the story is going to say "accelerating at 5.26314982 g proper acceleration", they're going to say "accelerating about 5g's". Not even the AI. This is a story, not a math test.

[Darmalus]

How big is the Mysterious Object? You need to decelerate both the ship and it's cargo after pickup.

[Broomstick]

Oooo! Good question!

200 kg mass for the Mysterious Object.

[Simon_Jester]

In other words, negligible compared to the mass of the ship. OK.

[Broomstick]

Maybe not negligible for such a flight though, given how much energy is required to propel any amount of matter at such speeds.

[Simon_Jester]

What I mean is, the mass of the payload affects the detailed calculations of fuel consumption by the mission planners, but does not affect the approximate calculations we might make here. We can rough out a mission profile from your specifications, at least in theory, even if we assume that the payload has zero mass.