How does this not get me traveling to another star FTL?

[Scott444]

Hi, Please not too many sighs but I'm stuck with this my miracle realisation - the scenario is -
I'm in a rocket (tons of fuel ) - I blast away (from Earth say) - accelerate hard for ages and by my special onboard inertial calculator I have got to 100 000km/s (with respect to earth). Switch the engines off - coast along do some experiements and see that all as it should be (given I'm in just another frame of reference in a universe that has no absolute frame of reference etc) ..maybe look at the Earth and see slow clocks. Take a nap - and do it again - and again - and again - and then so by my reckoning I'm doing 400 000km/s (and there is no great hand of god slowing me at this speed as he says no mister not allowed ...right?) and then repeat it all ten times so I'm doing 4 000 000km/s - stay at that speed for some years (50 say).
And then slow down to the speed of some conveniently moving star - planet system - Eta Carinae shall we say, and get out.
Now have I not then got myself some many light years away from Earth faster than light? There must be some dumb trap here I'm not seeing but I can't see it. Surely it's not about the fuel or something? Since it seems otherwise we're not stuck at less than light speed at all. I mean it may be that by the time that folks on Earth see me arrive at Eta Carinae - a long time has passed on Earth - but that doesn't matter to me.
Thanks very much for any help. :)
Scott.

ps this seem to make the Fermi paradox much worse - why aren't they scooting about then.

 

[PeterDonis]

ake a nap - and do it again - and again - and again - and then so by my reckoning I'm doing 400 000km/s

No, you're not. Velocities don't add in relativity the way you are assuming they do. See here:

https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

 

[Mister T]

Take a nap - and do it again - and again - and again - and then so by my reckoning I'm doing 400 000km/s

Your reckoning doesn't match what's actually been observed to happen when people do the very same thing to particles. Just to expand on what @PeterDonis said, let's say one of your rocket firings raises your speed to 100 000 km/s relative to Earth, but before you do your second firing you release a buoy in such a way that it's at rest relative to you and therefore also moving at 100 000 km/s relative to Earth. Now you perform your second rocket firing and when you're done your speed relative to the buoy is 100 000 km/s. But your speed relative to Earth will be about 180 000 km/s.

So, you are right in thinking your coasting ship's rest frame is just as valid as Earth's, but so is the buoy's. Your ship moving at a speed of 100 000 km/s relative to the buoy is just the same as the buoy moving at a speed of 100 000 km/s relative to Earth. What's not valid is the way you combine those two speeds to get the speed of the ship relative to Earth. When you combine them you don't add the speeds, you instead combine them in a different way.

This is analogous to combining slopes. If you have two wedges, each with a slope of 0.1, and you stack one on top of the other to form a wedge that has a steeper slope, that slope is not 0.2. That's not the correct way to combine slopes. Sure, if the slopes are small, like say 0.001, then adding them together gives an answer that's close enough. Likewise, if the speeds are small enough you can add them and get a result that's close. But it only works if the speeds are small compared to the speed of light, like is the case for even the fastest rockets people have ever flown. But it's not the case for particles that people routinely speed up.

 

[m4r35n357]

Your boosts are each with respect to a different (co-moving with you on each occasion) frame, not the earth's, so what you are adding is called rapidity. You are right though about your shortened elapsed time, this phenomenon is explained in the relativistic rocket.

 

[Scott444]

Thank you MisterT and PeterDonis, seems my imagined rocket trip was sunk by an annoyingly odd universe however, and if I'm reading things right, and using the well established scientific principle of confirmation bias as my guide, it seems that the idea of the relativistic rocket linked by m4r35' has my rocket travel plan verified.
It seems to at least ..doesn't it?

I guess I'm not sure of the veracity of the web page info and the variables names are perhaps ever so slightly ambiguous but it does say
"So in theory you can travel across the galaxy in just 12 years of your own time."
haha so we're done. :)

And we haven't contrivened say the 'can't communicate at more than light speed' rule since the time used in that case is time as measured from earth. (and there are very large time dilation effects).
So we can, if not for practical reasons yet, fly to Andromeda. ...yes?
Further thoughts would be greatly appreciated.

 

[PeterDonis]

it seems that the idea of the relativistic rocket linked by m4r35' has my rocket travel plan verified.

No, it doesn't. You are confusing the time the trip takes according to the crew of the rocket, with the time the trip takes according to the rest frame of the origin or destination (we're assuming that those two places, e.g., Earth and Eta Carinae, are at rest relative to each other). The crew of the rocket can experience a shorter time for the trip, but remember that to them, the distance between the origin and destination is length contracted, so they still appear to themselves to be traveling slower than light.

The best way to really investigate the question of whether the ship travels faster than light is to actually compare its travel with that of a light ray. In other words, imagine a light ray emitted from Earth at the same time as the ship departs. That light ray will always arrive at the destination before the ship does--regardless of how the ship accelerates. This is easily shown using either spacetime diagrams or simple math.

we can, if not for practical reasons yet, fly to Andromeda. ...yes?

In principle, yes, you could fly to Andromeda in less than a human lifetime according to the crew of the ship. But you would not get there before a light ray emitted from your starting point at the same time that you left.

 

[Scott444]

Thanks again PeterDonis, I guess this threads title is asking whether my trip is in effect faster than light - which it is not (from Earth's or my destination's perspective) but the corollary is that to those on the trip - it is FTL - given their distance measurements taken before they start, and even if they can't measure their speed as FTL on the trip.

If one can say I wish to travel 1000 light years away and we CAN do it in 20 say ..I mean is it not a matter of ones perspective as to whether one really did or didn't do it. Sure all those watching will say you took forever ..but heck why not take the perspective of those who actually made the trip as, if not the preeminent one, an equivalent one.

Anyhow it seems I have forever misunderstood the FTL limit - surely there is angst about we are stuck on Earth because of the enormous difficulty of getting to other planets and stars and the literal eons it takes to get anywhere ..when it all isn't necessarilly true.

Or at least it doesn't matter much if the need for such travel was about saving humanity from some variety of destruction of earth. It appears then quite feasible that humans could get themselves - not their 50th generation of decendant - to far away places in our galaxy at least.

 

[PeterDonis]

to those on the trip - it is FTL - given their distance measurements taken before they start

No, that's not the case, because "FTL" does not mean "divide distance by time"--it means "compare your motion to the motion of a light ray that starts out at the same time you do". And we've already seen that a light ray that starts out with the ship will reach the destination before the ship does. That's true regardless of whether you take the viewpoint of someone at rest at the starting point or destination, or the viewpoint of the crew of the ship.

It is true that the trip time as experienced by the crew can be shorter than the time, according to someone at rest at the origin or destination, that it takes light to travel between them. But the term for that is not "FTL"; it's "time dilation".

urely there is angst about we are stuck on Earth because of the enormous difficulty of getting to other planets and stars and the literal eons it takes to get anywhere

It's not the trip time in itself that's the problem; it's the difficulty of getting up to a speed fast enough, relative to the origin and destination, that the trip time becomes manageably short. For that you need, first, rocket technology far in excess of what we currently have; second, a huge amount of fuel and reaction mass, because of the rocket equation; and third, a way of shielding the ship against extremely hard radiation, since at the velocities you will need, every stray atom of hydrogen in interstellar space becomes a highly energetic cosmic ray.

 

[Ibix]

Anyhow it seems I have forever misunderstood the FTL limit - surely there is angst about we are stuck on Earth because of the enormous difficulty of getting to other planets and stars and the literal eons it takes to get anywhere ..when it all isn't necessarilly true.

One other thing to note is that, if the implausible rocket technology Peter mentions were possible, you could get to Eta Carinae in twenty years by your watch. And if you sent a postcard home the mailman would only age twenty years on the return trip. But even if all this were possible, around 15,000 years would have passed for Earth by the time the postcard arrived. No point writing "wish you were here" since anyone you might want to write it to will have been dead for millenia.

 

[mfb]

because "FTL" does not mean "divide distance by time"

Especially not "divide distance as seen by Earth by time as seen by the spacecraft ".

Our super powerful rocket will see a much shorter distance to Eta Carinae.

 

[rkyeun]

"maybe look at the Earth and see slow clocks. Take a nap - and do it again - and again - and again - and then so by my reckoning I'm doing 400 000km/s (and there is no great hand of god slowing me at this speed as he says no mister not allowed ...right?)"

There is a great hand of god slowing you down. As your velocity increases towards the speed of light, you gain relativistic mass. Your spaceship appears to weigh more than it did before. You fire up your engine again and again, yet it pushes you less and less than before because your mass has become so great. You will run out of fuel before you reach infinite mass at the speed of light. Nothing can push you that fast.
As you go at sufficiently large velocities, your clocks, including the one judging how fast you are thinking, will slow down. You will see the future flash by quickly, and your clock may say you have spent only hours traveling to a star many light years away. Looking back behind you, the Earth will also seem only a few hours older. But the planet in front of you is older by the many years, and when you turn to go home the Earth will also age by many years. You cannot beat the beam of light there and back. For the beam of light, the trip is instant, because light's clock is stopped entirely. As far as light is concerned, the two places are touching.

 

[mfb]

As your velocity increases towards the speed of light, you gain relativistic mass.

The concept of relativistic mass is not used any more in science.

Your spaceship appears to weigh more than it did before.

No it does not. This misconception is one of the reasons the concept of a relativistic mass got abandoned.

You fire up your engine again and again, yet it pushes you less and less than before

This is wrong as well - in the spacecraft you still feel the same acceleration.

As you go at sufficiently large velocities, your clocks, including the one judging how fast you are thinking, will slow down.

Only as seen by external observers.

For the beam of light, the trip is instant, because light's clock is stopped entirely.

There is no such clock.

As far as light is concerned, the two places are touching.

That doesn't make sense.

 

[Ibix]

There is a great hand of god slowing you down.

Nothing is slowing down here.

As your velocity increases towards the speed of light, you gain relativistic mass.

As mfb notes, relativistic mass isn't used much any more, largely because it causes more confusion than it clears up.

Your spaceship appears to weigh more than it did before.

This is confusingly written. Do you actually mean "weigh"? In that case, the ship is moving inertially and weighs nothing. If you are simply repeating your comment on relativistic mass then you shouldn't use the word "weigh". You should also make clear that the relativistic mass increase is only detected by the Earth frame - someone in the ship detects no change in the mass, relativistic or otherwise.

You fire up your engine again and again, yet it pushes you less and less than before because your mass has become so great.

Again, this is only true as observed from the Earth frame. In the ship frame, you will always feel the same acceleration (neglecting the effects of burning fuel decreasing your invariant mass). Local measurements will always show the same acceleration. It's only your coordinate acceleration that decreases.

You will run out of fuel before you reach infinite mass at the speed of light.

The relativistic mass of something with non-zero invariant mass moving at the speed of light is undefined, since such a thing traveling at the speed of light is self-contradictory.

As you go at sufficiently large velocities, your clocks, including the one judging how fast you are thinking, will slow down.

Again, this is not an absolute statement. It is true in the rest frame of the Earth, but a person in the ship will notice nothing out of the ordinary.

You will see the future flash by quickly, and your clock may say you have spent only hours traveling to a star many light years away. Looking back behind you, the Earth will also seem only a few hours older. But the planet in front of you is older by the many years, and when you turn to go home the Earth will also age by many years.

The last two sentences are true, but refer to your own direct observations rather than your deductions after correcting for the travel time of light (and aren't true in the frame of the Earth, which is the frame you appear to have been working in up to now). This is not the same thing as time dilation. The first sentence doesn't really make sense, as far as I can tell.

For the beam of light, the trip is instant, because light's clock is stopped entirely.

Light does not have, and cannot even theoretically have, a clock. Talking about the behaviour of a thing that it is impossible to define precisely is never going to make sense.

As far as light is concerned, the two places are touching.

Here, again, you are talking about the "perspective of light", which is a contradiction in terms.

 

[Scott444]

rkyeun, Ibix and mfb thank you for your responses, this matter does seem to engender endless sense of 'but what if's ...' which seem impossible to resolve in the absence of a very thorough and complete understanding.
haha and now in that vein a question please ...and then a comment of sorts.

My question is about the nature of the space and or time distortion - would mfb or ibix or anyone be able to aid in or offer any intuitable sense of that distortion - seems such a profound thing - an odd and strange thing - what is happening to time or space that has it so skewed - how could it be that Einstein sees 'it' in his maths and then thinks yes that's more likely than an aether - or whatever. And this thing is evident, although tiny in effect, even in earthly speed and distance - what is ? - what is interjecting itself in a given speed or distance measure to warp it? I take it the warping is not done, by something, 'to' it but is, in itself, its character ...? It's not about the measuring is it ..it's the actual stuff of space and time varying as I stare it in the face. How could distance possibly be not Newtonian, so to speak. Is it intuiatable? If I get down to quantum (plank) distance does it add or subtract little bits or shrink ..or ..thanks for any aid in this regard. [edit ..it's not even linear ...and if the answer is geometry ..I'm done.lol]

lastly just a muse ..the thing that bothers me is the idea of the classic startrek ftl spaceship or most any scifi portrayal of intergalactic travel, since in fact there is nothing to stop a suitably powered ship going (by their reckoning) above 300 000km/s. And given the problem then about locally measured superluminal 'lms' travel :) (...since the ftl thing I have been assured here is not a possible thing) - is not centred on the ship but other frames of reference. That is, the problem to be solved in getting about the universe at a great pace (while keeping those not traveling alive) is that most everything else, from the speedy ship's perspective, is warped in time and distance - which I can't imagine has any solution - ..and I'd be intrigued to read even a scifi account of how that may be imagined to be resolved.

 

[mfb]

what is interjecting itself in a given speed or distance measure to warp it? I take it the warping is not done, by something, 'to' it but is, in itself, its character ...?

This sounds like philosophy.

If you require that the laws of physics are the same in every inertial reference frame, and that light doesn't have infinite speed, relativity is the only option. Spacetime has to be like that.
Newtonian physics is another self-consistent theory. It wouldn't work with particle physics, and we don't live in a universe with Newtonian physics, but that is a different topic.

 

[Ibix]

this matter does seem to engender endless sense of 'but what if's ...' which seem impossible to resolve in the absence of a very thorough and complete understanding.

Special relativity isn't actually that complicated. It's just rather different from our everyday experience, and you have to let go of some assumptions you're probably not even aware you are making. That last bit can be tricky.

My question is about the nature of the space and or time distortion

Nothing is being distorted here. The simplest explanation is that it turns out that a clock is to spacetime as your car's odometer is to space. The odometer measures the distance your car has traveled through space. A clock measures the "distance" the clock has traveled through spacetime. Then the reason for the different times is utterly prosaic: the clocks on Earth and the clocks on the rocket did not take the same route through spacetime from the moment the rocket left Earth to the moment it returned. The routes have different "lengths" so the clocks show different elapsed times - just as two cars that leave the same factory with zero mileage need not have the same mileage the next time they meet.

how could it be that Einstein sees 'it' in his maths and then thinks yes that's more likely than an aether - or whatever

James Clerk Maxwell published equations describing electromagnetism in the 1860s. They worked really well in some senses and were utterly incomprehensible in other senses. And various experiments testing Maxwell's equations (Michelson and Morley, Fizeau, others) kept producing unexpected results. One of the sillier predictions of Maxwell's equations was that that speed of light was always the same in all inertial frames. Einstein decided to take that prediction at face value and see where it led him; the result was special relativity. And with it, Einstein resolved the problems with Maxwell's equations and explained forty-odd years of confusing experimental results. No ether theory except Lorentz's could do the same, and Lorentz's ether theory is just special relativity plus an ether that doesn't actually do anything.

Regarding your SF question, there is no known way to travel faster than light, so a realistic description of what would happen if you did isn't possible. Basically, you are asking "what do the laws of physics say would happen if they didn't apply", which is nonsensical. SF uses faster than light travel as a vehicle to tell stories, and Bellisario's Maxim should be born in mind.

 

[pervect]

The main comment I have for Scott is that he seems to be basically assuming that there is some sort of "warping" (his words) that changes his pre-existing ideas of how space and time work.

If one tries to view relativity as some sort of "warping" of Newtonian and Gallilean mechanics, it's always going to seem more complicated and strange, because one is assuming that things really are Gallilean/Newtonian, and then trying to fit additional effects on top of that basis to understand Relativity.

Not only is this view more complicated, in the end it will turn out not to work, because a key feature of relativity, the relativity of simultaneity, just isn't compatible with Newton's "absolute time". Unfortunately, this is a notorioulsy tricky point to get across - my conclusion is that criticizing the words "absolute time" just doesn't get through to many readers, for various reasons.

The amount of math needed to understand special relativity isn't very great it's basically just high school algebra. Perhaps this is "too much math" for some readers, I'm afraid I don't have a solution without it. Without the math, I find it too slippery to try to communicate the needed points in just words. Certainly though there are a lot of attempts to do so, if math simply isn't an option, one can try reading various popularizations that don't use it and hope for the best. I can't really make any suggestions along this line though.

With a modest amount of math, I find the Bondi approach , in his book "Relativity and Common Sense", <<amazon link>> to be worthwhile. There is one key distinction about time that I think I can try to make that can be helpful in this short post. That is the fundamental notion of what we call "proper time" as the basis on which other, more advanced concepts of time, can be built with some extra additions. The concept of proper time says simply that if we have two properly functioning clock (possibly with different constructions, it doesn't matter whether they use gears, atoms, quartz crystals, dripping water, or pendulii,k or whatever - though atoms tend to be the most accurate in practice) and these clocks follow identical paths through space-time, then they will both read the same value.

Is this different than the traditional notion of "absolute time"? Yes, it definitely is, and a simple example will demonstrate this. Suppose one clock is left "at home", which could be on Earth, but to avoid gravity we'll set it out far in space. And another clock is put on a rocketship which accelerates away from home, turns around, and comes back. When the two clocks re-unite, they won't read the same time. This can be seen as a core necessity in how time works in understanding special relativity, and it's something that's not directly compatible with absolute time.

People sometimes try to imagine that there is still some sort of master "absolute time", and that the clock on the rocketship is "distorted" by it's motion, but this turns out in the end not to work very well. All the clocks are actually going what they're supposed to, and there just isn't any sort of universal, "master" clock, there are just a bunch of different clocks that one can construct (or imagine). Understanding relativity in the end winds up as understanding how these clocks behave, and downplaying the role of any sort of universally applicable time. One can set up a convention that one particular clock will be the "reference" clock, and one can define (through the exchange of light signals) other clocks that are at rest with respect to the reference clock, and use these to set up a particular notion of time. But it turns out that this notion of time is not and cannot be universal - other observers moving relative to the first will come up with different schemes.

 

[nikkkom]

My question is about the nature of the space and or time distortion - would mfb or ibix or anyone be able to aid in or offer any intuitable sense of that distortion - seems such a profound thing - an odd and strange thing - what is happening to time or space that has it so skewed.

It's not odd. It is in fact not that difficult to understand. It's "simply" a rotation.

For a "normal space", Euclidean space where distance between points is d^2 = x^2 + y^2 + z^2, rotation of coordinates looks like you expect:

http://mathworld.wolfram.com/images/eps-gif/RotationMatrixAxes_1000.gif

However, we are not living in Euclidean space: one coordinate in our space is special, not like the others: time coordinate. It is special in the way that it enters distance formula with an opposite sign: d^2 = x^2 + y^2 + z^2 - t^2. Note the minus. Let's drop y and z and draw a "rotation" for a two-dimensional space with distance rule of d^2 = x^2 - t^2:

https://commons.wikimedia.org/wiki/File:Animated_Lorentz_Transformation.gif

This "rotation" preserves "distances" (in the sense d^2 = x^2 - t^2) between all points. And this "rotation" is exactly what happens when you accelerate in a rocket in a direction of x-axis - you "rotate" your t axis into the direction of x axis.

Think of it this way: when you are using a coordinate system where your rocket is at rest, it is not really at rest. It is still moving - into the future. It has a velocity vector which completely and only points into the t direction.

When you accelerate your rocket, you in fact is applying a "sideways" push (say, into x direction) to an object which is moving in the t direction. Hence, rocket velocity vector "rotates".

Because of the minus, this makes x-axis move towards t axis, not away from it as happens for Euclidean rotation. In a graph, this turns rectangular coordinate grid into rombs. You can relatively easily see both time dilation and length contraction in this picture.

 

[Scott444]

Thank you all for your guidance. I have come across a sufficiently simple, and hopefully too, a fair representation of time dilation on the web.

This scenario I think is akin to an observer watching the operation of a moving bouncing photon (mirror) clock. In the vid the 'moving' reference frame actually just shoots a photon and sees it speed off a distance ct. In that same time the 'stationary' observer reference frame sees it traverse a greater distance (conveniently the hypotenuse of the triangle) - and of course, (or begrudgingly accepting) that said photon must traverse the longer path (ct') ..i.e without beating c - so the only thing able to vary in that case is t'. The observer then sees t' as t dilated. Solving the triangle lengths with pythagoras gets lorentz transform.

So that's great, ...now similar scenario two observers in space/vacumn, one with a pea shooter on a slowish (space)-train - same thing only in this scenario t' doesn't have to dilate because the intuitive vector addition of velocities just allows for a greater observed velocity of the pea, by the observer not on the train. So I see how constraining the velocity of c for all observers is, or has great consequence. ...but...
..but, and while I have made progress it's the resolving of these two scenarios as essentially versions of the first ( i.e one just where v << c) ...or appreciating how they dissolve into one ...well I'm not there yet.

- a frustration - other derivations of the lorentz transforms I've seen (which may offer the maths for the generic solution of all velocities) often feel like they ramn the 'ct' in as replacement for distance ..arbitrarilly - bit like no one in their right mind would do that unless they had desperate need to hack a result...cough I mean show how breakthrough intuitions are supported in maths. lol (and yes I'm sure I'm failing to get something :) )

But to make myself feel better I'm going to look up experiemental support for SR. facts is facts and I presume I will be wearing them.
Thanks again for responses.