Would it be a bad idea to travel the speed of light?

[K^2]

You either have to plug relativistic mass into the kinetic energy formula

Can't do that, either. You can use relativistic mass with mc² to get the total energy. And if you want kinetic energy, you can subtract mc² of the rest mass, but that will just give you the relativistic formula that you linked. Plugging relativistic formula into classical kinetic energy will give you wrong result, because classical formula is just a leading term of power series expansion of the relativistic one.

[architeuthis]

You cannot use the classical Kinetic Energy formula when calculating kinetic energy for objects moving with relativistic speeds. You either have to plug relativistic mass into the kinetic energy formula, or you have to use the relativistic kinetic energy formula.

Any object with any positive value of rest mass would have infinite kinetic energy if it was moving at 1c.

Good point, things with positive rest mass do not travel at the speed of light therefore it is an absurd scenario right off the bat. If we use the corrected version of the kinetic energy equation that you linked, with v being .99 c we get a KE of about 160 J which is about the same as a baseball going 100 miles per hour. Definitely not unsubstantial, but also not on the scale of a nuclear explosion either.

[peadar1987]

Ignorant question, but, if I understand correctly, if you're going close to the speed of light, time for you will pass slower than for an observer, right?

-Firstly, how does time "know" which one of you is the observer and which is the observee, surely which one of you is "moving" changes depending on which reference frame you use, so why is there a difference in situation between accelerating a spacecraft away from the earth, and accelerating the earth away from the spacecraft with a gigantic motor?

-Secondly, does the change in perception of time mean there is an optimum speed to travel? So if you're heading towards the edge of the galaxy, you don't want to travel too fast, because even though it will take less time from your perspective, to an external observer, it will seem to take a longer time? Or does it not work that way?

[Kulebron]

@peadar1987: the distance to the other side of galaxy is the same (about 100 000 ly IIRC), so you can arrive there not earlier than that by galactic clock.

[insylem]

You forgot relativity. A week passes for you, but millions if not billions of years may pass in "normal" time.

Um, that is part of what relativity is....

[Beowolf]

Ignorant question, but, if I understand correctly, if you're going close to the speed of light, time for you will pass slower than for an observer, right?

I'll take a swing at it, but please bear in-mind I'm only the father of a physicist, not one myself.

-Firstly, how does time "know" which one of you is the observer and which is the observee, surely which one of you is "moving" changes depending on which reference frame you use, so why is there a difference in situation between accelerating a spacecraft away from the earth, and accelerating the earth away from the spacecraft with a gigantic motor?

The universe doesn't know which is which. That's why Einstein called it "relativity": There is no "privileged" point-of-view and there can be no outside observer. The speed of everything in the universe must be measured relative to something else. If you're in a ship leaving Earth at 0.9 lightspeed, and I'm stuck on the planet (No fair!!!!) each of us will see our own clock running normally, and the other's clock as running slow.

Check this page http://en.wikipedia.org/wiki/Time_dilation and scroll down to the heading "Time dilation due to relative velocity symmetric between observers".

Now, 0.9c has a time dilation effect of around 2. Let's pretend our starship's magic drive requires no acceleration/deceleration time to simplify things. If you went 10 light years to your destination then sent a laser message home, I on Earth would observe your trip took 11.11 years (10 ly / 0.9c) so your msg would arrive 21.1 years after you left.

At your new colony, you would observe the trip took 5.6 years @ 0.9c, and the odometer in your starship says you've only travelled 5 ly even though you reached your destination.

-Secondly, does the change in perception of time mean there is an optimum speed to travel? So if you're heading towards the edge of the galaxy, you don't want to travel too fast, because even though it will take less time from your perspective, to an external observer, it will seem to take a longer time? Or does it not work that way?

Nope, just go as fast as you can go.

The thing where both clocks seem to slow down causes all sorts of bizarre paradoxes. See http://en.wikipedia.org/wiki/Ladder_paradox for some examples.

[jheriko]

Some things always bug me about these kinds of discussions - specifically the idea of a speed of light and the resulting discussions around time-dilation and relativity, coupled with not really knowing what anyone really means by a speed or time?

Personally I think calling it the 'speed' of light is confusing because what we think of as speed is a concept that breaks down massively at these extremes. Another way to look at the number c is a conversion factor between space and time - there are about 3x10^8 metres in a second. By remaining nearly at rest we cover almost c metres in the time-axis every second, but 0 in space, from the perspective of outside observers we may appear to be moving at any kind of speed dependent on their velocity - for one special set of observers that speed is zero. Light has the opposite experience, it travels 0 in the time-axis, but c metres through space and from the appearance of outside observers it appears that it is travelling at precisely c regardless of the observer's velocity - there are no observers who will see it move at zero speed - even other light. This strange seeming behaviour is an artefact of our looking on the 4 dimensional geometry of space-time in strange 3 dimensional slices - actually 2 dimensional projections of 3 dimensional slices as well... and coupling that with conceptualising time as an independent axis - which it is not.

Speed as you think about it day to day is a useful approximation at low speeds. Its not really the whole picture - like describing colours in terms of lightness or darkness with no thought for hue or saturation. So the question of if we can travel at the speed of light, or faster than it, neither of these really make much sense because speed doesn't make much sense in that context.

In the geometry of relativity going faster than the speed of light doesn't really make sense - its kind of a projective thing where infinity happens to be mapped to c. A different way to think of it is the classic analogy with the north pole - there is nothing further north of it because thats how north works... similarly there is nothing faster than the speed of light because that is how time works. Of course, assuming that special relativity is valid...

Of course we are still free to travel backwards in time, and if you ignore the complexities involved then that would look just like FTL travel in our natural interpretation.

I also think it would be a very interesting experiment to try - although the original question was about the speed of light I'd like to know what happens if I can go back and shoot my grandfather (well maybe not exactly that...) I feel that cosmic censorship hypotheses are a bit of a cop out. Hopefully that NASA guy builds a tiny experiment where this can be investigated whilst he is playing with warp drives...

[AngelLestat]

Nope. At 99,9% lightspeed, the Lorentz factor is still only about 22,4, which means that for each "week" passing for the people on the ship, the stationary universe around them ages about half a year. If you want to get to the edge of the galaxy, you'll have to go faster than that. At 99,9999% c it would just about be achievable within a human lifetime.

The impact energy of a single mote of space dust with relative velocity of 1c isn't so bad. A mote of space dust masses about the same as a bacterium; it would only have an kinetic energy of about 10J. Over time this would sandblast your hull, but otherwise it is not particularly devastating. It also means that the dust exerts a pressure on the hull not unlike aerodynamic drag in an atmosphere; therefore relativistic rockets, if they ever are built, will probably be streamlined, sleek designs.

But there would be some pretty extreme radiation hazards for near-light speed travel. At .99c visible light blueshifts into x-rays, which may not be a big problem if you are in the interstellar void but flying through a solar system at that speed would be a death sentence. Even worse is that interstellar gas and dust particles would have energy comparable to high energy cosmic rays, on the order of 100MeV up to 1-3GeV. In unshielded conditions this would equate to human radiation dosages in the tens- to hundreds of thousands of rems per second, which is similar to conditions inside the core of a nuclear reactor. Some of these particles are charged, so they could in principle be deflected with magnetic shields (of course then the problem would be cohabiting with 20 T magnetic fields). To deal with the neutral particles you would need a many meters thick radiation shield made out of water or titanium. Also our solar system is inside a bubble of abnormally low density interstellar medium. In other areas of our galaxy the radiation hazards might be even more extreme, therefore interstellar travel of the far future will probably have galactic navigation routes passing through low density corridors not unlike the hyperspace trade routes from starwars:)

Can't do that, either. You can use relativistic mass with mc² to get the total energy. And if you want kinetic energy, you can subtract mc² of the rest mass, but that will just give you the relativistic formula that you linked. Plugging relativistic formula into classical kinetic energy will give you wrong result, because classical formula is just a leading term of power series expansion of the relativistic one.

.

I just want to point the most important answers in my opinion.

Talking about kinetic energy, time dilation or energy require to get the speed of light. I guess all this questions are incomplete if we dont specific how close to C we are talking about..

There is a big difference between 99% and 99,9999999999999999999999999999999%

But well in case this crazy Cramer´s idea would be possible some time, then I guess is the best approach to exploit the speed of lights advatange.

http://www.analogsf.com/2012_05/altview.shtml

[TheGatesofLogic]

You forgot relativity. A week passes for you, but millions if not billions of years may pass in "normal" time.

Umm, relativity isn't exactly a two way street the way your describing it man. If i travel .99999c i will certainly only experience a weeks worth of time crossing the galaxy (let's not think about the fact that I would be exposed to more cosmic radiation than would be needed to kill the planet 6 times over due to blueshift) but from the earth's point of view I will not "slow down" OR "speed up" I'll just be observed to be moving at .99999c. and so i would cross a 100,000 lightyear wide galaxy in 99,999 according to what people from earth will see, though these are totally arbitrary and uncalculated numbers.

Edited January 3, 2014 by TheGatesofLogic

[K^2]

Umm, relativity isn't exactly a two way street the way your describing it man. If i travel .99999c i will certainly only experience a weeks worth of time crossing the galaxy (let's not think about the fact that I would be exposed to more cosmic radiation than would be needed to kill the planet 6 times over due to blueshift) but from the earth's point of view I will not "slow down" OR "speed up" I'll just be observed to be moving at .99999c. and so i would cross a 100,000 lightyear wide galaxy in 99,999 according to what people from earth will see, though these are totally arbitrary and uncalculated numbers.

First of all, at 0.99999c, your proper velocity^* is only 223.6c. So it would take you well over 400 years to cross 100kly. And you got your math backwards in map frame. At that speed, you'd traverse 99,999ly in 100,000 years. Finally, I think that's what SargeRho was talking about. He just didn't bother to verify any of the numbers.

^* Proper velocity is defined as distance of map time traveled per unit of proper time. In other words, how far you travel through the galaxy in a given amount of ship's time. This speed can exceed speed of light due to structure of Minkowski Space.

There is a big difference between 99% and 99,9999999999999999999999999999999%

Which is another reason to think about it in terms of proper velocity. It gives you a good idea of how much dilation the ship will experience, how long it takes to cross a certain distance, and how much energy and momentum the ship has. A ship traveling at 400c proper velocity will cross a certain distance in the same time as a ship traveling at 200c proper velocity, because both are basically going at nearly the speed of light, but the former will age half as much as the later. And that's useful information here.

Edited January 3, 2014 by K^2

[TheGatesofLogic]

yeah, i actually made the mistake of posting at 2 am and didn't even notice that there were more pages to the thread so i posted arbitrary numbers and broken reference times without bothering to check, so i never saw that what i said was really a repetition of the same thing other people had said and yes, i know all of the nice bits under the asterisk, and the difference in relativistic speeds is certainly important, but not necessarily relevant from a conceptual standpoint once the IDEA is explained sufficiently to incentivize the statement of argument which was more along the point i was making

[AngelLestat]

I dint knew that kind of notation. Seems usefull.

So how do you calculate? you just multiply by the lorenzt factor or what do you do?

This mean that we can have a proper acceleration? This is what Carl Sagan was talking about when he said that we can reach the center of the galaxy in X time (i dont remember) with a constant acceletarion of 1g?

[K^2]

So how do you calculate? you just multiply by the lorenzt factor or what do you do?

Calculate proper velocity? Yes. Proper velocity is equal to coordinate velocity multiplied by Lorentz factor.

This mean that we can have a proper acceleration? This is what Carl Sagan was talking about when he said that we can reach the center of the galaxy in X time (i dont remember) with a constant acceletarion of 1g?

Probably. Proper acceleration is the actual acceleration that the crew is going to experience, yes, so 1G proper acceleration would be quite comfortable. And yes, it also scales in a crazy way, so that it lets you have a round-trip to Andromeda Galaxy in under 60 years of ship time. Of course, it'd still be millions of years on Earth.

Unfortunately, even with a photon drive, maintaining 1G proper acceleration for that long requires an unobtainable amount of fuel.

(Edit: Note, proper acceleration scales differently from proper velocity. It is defined as rate of change of proper velocity with respect to map time. The actual factor depends on direction of acceleration with respect to velocity. But if you are accelerating/decelerating in direction you are traveling, then the proper acceleration is greater than coordinate acceleration by a factor of Lorentz factor cubed.)

Edited January 6, 2014 by K^2

[TheGatesofLogic]

In all honesty, star-trek was wrong, space is most certainly not the final frontier. In reality, it is time that is the ultimate boundary.

[K^2]

In all honesty, star-trek was wrong, space is most certainly not the final frontier. In reality, it is time that is the ultimate boundary.

What's the difference?

[Moon Goddess]

Nothing Space and Time are the same thing, relatively speaking.

[victory143]

It's not advisable to do either, since at that kind of speeds, a grain of dust hits with the force of a large nuclear device.

One day on Apollo-58, Luke the captain is about to go in to light speed travel.

"Engines ready captain. Countdown has started." shouted Jeff.

"Hey Luke, have you done the EVA cleaning duties yet? Y'know, like making sure there is no dust outside?" asked Tom.

"Oh Sh-"

Apollo-58: First spacecraft to be annihilated by dust

[TheGatesofLogic]

they most definitely are not the same thing, even speaking relatively. Yes they are intertwined, but that does not make them the same thing. time and space can be considered to be one thing, but in that case it is more of a juxtaposition rather than a superposition and so it is still incorrect.

[K^2]

they most definitely are not the same thing, even speaking relatively. Yes they are intertwined, but that does not make them the same thing.

They actually are the same thing. Distinction is about the same as that between direction "North" and direction "Up". Yes, given a location on the planet, I can say that one is strictly vertical and the other is strictly horizontal, because we have a direction of gravity. But at another place on the planet, these directions are going to be different. We live in a four-dimensional manifold. Because the metric happens to be non-positive definite, making it a pseudo-Reimannian manifold, once you chose a coordinate system, you can separate directions into strictly time and strictly spacial directions. But in a different coordinate system, the direction of time will be different. So it will naturally pick up a spacial component from your original coordinate system.

[TheGatesofLogic]

They actually are the same thing. Distinction is about the same as that between direction "North" and direction "Up". Yes, given a location on the planet, I can say that one is strictly vertical and the other is strictly horizontal, because we have a direction of gravity. But at another place on the planet, these directions are going to be different. We live in a four-dimensional manifold. Because the metric happens to be non-positive definite, making it a pseudo-Reimannian manifold, once you chose a coordinate system, you can separate directions into strictly time and strictly spacial directions. But in a different coordinate system, the direction of time will be different. So it will naturally pick up a spacial component from your original coordinate system.

on the contrary, their substituent natures are intertwined, however this does not mean that they are the same thing always, certainly north and up convey this exact piece of information, though in a less meaningful way. They are in essence composed of the same conceptual manifestation, but their corresponding effects on our perception of passage are totally different. on the basis that any difference indicates a separation between concepts it is irrefutable. though certainly they are exactly the same in many ways. it really depends on exactly where and how you are looking at it.

in this case what i truly meant is that from any real person's point of view north is not necessarily up on a fixed coordinate plane and as such time is not necessarily space, though the difference is only really arbitrary and they do align. I could go into detail about how we can't actually say something like that without admitting that we consider ourselves inhuman and thus incorrect, but this isn't a philosophy thread. like i said, the difference is between juxtaposition and superposition.

also, i hate the english language

Edited January 7, 2014 by TheGatesofLogic

[Guest Brody_Peffley]

Didn't you guys ever hear of a nasa scientist who made a theory of using negative mass to not got faster than the speed of light but to bring things closer to it.

My theory is that suns create negative mass when there about to turn into a black hole. Which is why black holes are dark and deflect light because the negative mass is messing with mass itself. Since even light has mass. Whats happening is its like air pressure on a spaceship. If theres a leak or a large hole. Everything would be pulled in. Which is how the warp drive would use negative mass to pull things towards itself.

[Godot]

Yes, if you want to keep your weight, it may be a bad idea

[K^2]

I could go into detail about how we can't actually say something like that without admitting that we consider ourselves inhuman and thus incorrect, but this isn't a philosophy thread.

It's not. Which is why how you feel about these concepts is pretty irrelevant. The physics are exactly the same. The labels simply mean different directions. The fact that you, as a human, are stuck on this ball of rock, and have never experienced time as anything other than this rock's proper time is your own personal problem, and has nothing to do with the physics of it.

Didn't you guys ever hear of a nasa scientist who made a theory of using negative mass to not got faster than the speed of light but to bring things closer to it.

I wonder what people were saying back when the Wright Brothers managed to get off the ground. "Didn't you guys ever hear of some American bicyclists who made a theory of using dead dinosaurs to get themselves not into the skies, but close to it?"

The theory you are thinking of is called the Alcubierre Drive. Also known as the warp drive. It was actually developed by a Mexican physicist Miguel Alcubierre. The theory does involve negative energy densities, which can be interpreted as negative mass, but probably not the way you are thinking of it. And the NASA scientist you are thinking of is Harold White, who developed an improved version of the warp drive, significantly reducing amount of energy required, and further developed a proof of concept experiment that has been conducted at NASA.

Warp drive does allow exceeding speed of light, but it also makes sub-light travel significantly easier.

My theory is that suns create negative mass when there about to turn into a black hole. Which is why black holes are dark and deflect light because the negative mass is messing with mass itself. Since even light has mass. Whats happening is its like air pressure on a spaceship. If theres a leak or a large hole. Everything would be pulled in. Which is how the warp drive would use negative mass to pull things towards itself.

Stop, just stop. Please. This is total nonsense. Not only is the "theory" portion of this a total fantasy, but even the facts are completely wrong. Black holes do not reflect light. Gravity always affects light. And light only has an inertial mass, while lacking invariant mass, which is what people usually mean by the word "mass".

It's good that you are interested in this, but you really need to do a lot more reading, and probably learn a lot of math, before trying to get into a discussion on the topic.

[AngelLestat]

Probably. Proper acceleration is the actual acceleration that the crew is going to experience, yes, so 1G proper acceleration would be quite comfortable. And yes, it also scales in a crazy way, so that it lets you have a round-trip to Andromeda Galaxy in under 60 years of ship time. Of course, it'd still be millions of years on Earth.

Unfortunately, even with a photon drive, maintaining 1G proper acceleration for that long requires an unobtainable amount of fuel.

Thanks for the info.

About how to maintain that acceleration, When Carl Sagan mention this, was in the time when Bussard Ramjet concept seems feasible. But some years later this was prove it wrong due to drag.

But I find hard to imagine how this constant acceleration would work meanwhile you are close to the light speed. What is mean mantain constant acceleration if your ship is more heavier each second. So now with this way to see it, I understand.

And the NASA scientist you are thinking of is Harold White, who developed an improved version of the warp drive, significantly reducing amount of energy required, and further developed a proof of concept experiment that has been conducted at NASA.

Warp drive does allow exceeding speed of light, but it also makes sub-light travel significantly easier.

Easier? Dont tell me that you really believe that we are close to discover how to make an Alcubierre Drive transport..

Here is Harold´s paper , it seems less seriuos than any farie tale story.

I can not prove it.. But this is going nowhere.

[Bobnova]

You have to read the energy values.

Assuming 1:1 mass:energy conversion, the first warp drive design needed roughly the mass of the universe (or was it just a galaxy? I don't remember) for fuel. Not useful.

This new version would only require Jupiter.

Significant reduction! But still a bit much.