If Traveling At Light Speed Towards a Planet...

[DrowElfMorwen]

This is my first post as I have a serious but "heavy" question regarding the recent news from NASA about TRAPPIST-1's planets.

I posted on Facebook, to my friends, the following:

"This particular system is 40 light years away, meaning even if we could travel at light speed it would take 40 years to reach it. However, realize that as you began your journey and say, for example, you can see it from Earth or your space ship telescope--you're looking at a planet 40 years in the past. As you travel toward the planet and periodically look at it again, do you know how how much time would have passed on that planet, say, ten years into your journey? Well, ten years would pass, but are you SEEING it ten years older? How much older would the planet be by the time you arrive?"

Wondering on my own questions, I want to know if I'm on the right track. The planet will not have an 40 nor an 80 years difference of age, but somewhere in between, as the distance of space between yourself and the planet would be getting smaller and smaller. But does anyone have an idea of how I could figure out the exact age of the planet by the time our hypothetical traveler arrives? What equation(s) would be used in this physics question?

 

[YNM]

Traveling at light speed means no time at all.

[HebaruSan]

Distance = Speed * Time works in your destination's reference frame. For the planet, 40 years pass.

Time dilation makes the time shorter in the traveler's reference frame. As YNM says, if you travel at light speed, no time passes at all for you (and you are a photon).

[Shpaget]

The planet woul look as many years in the past as the number of light years you are away from it.

For a planet 40 ly away, after traveling for 10 years at light speed it would appear as it was 30 years ago, but as previous posters said, the travelers would not perceive those 10 years of travel. It would be instantaneous for them.

[Green Baron]

For an outside observer it would take 40 years. For the fictitious traveler at light speed the whole time of the universe would just be a flash. That is relativity.

But note that anything that has a mass cannot reach light speed. The mass increases with speed and would become infinite when reaching light speed.

Edit: this relatively incorrect ...

Edited February 23, 2017 by Green Baron

[Piscator]

To answer the actual question: The planet would look 80 years older when you arrive. The planet would be 40 years older and stop looking 40 years younger due to distance giving you a total of 80 years.

[Green Baron]

Actually no. If the traveler was a photon at the speed of light from here to there it would travel an infinite short way in an infinite short time, from it's view. But that does not matter as the space contracts in flight direction and the distance between objects becomes infinitely short, as seen from the photon.

On the other hand, in the same manner as the space for the traveler contracts, the time for the outside observer stretches. He would actually measure an infinitely long time for the journey, the universe together with the planet had just gone when the traveler arrives.

But luckily we don't have to stress our brains over that because anything that has a mass cannot reach light speed.

Edit: if the photon had a very little mass and speed of light was not the limiting speed but the limiting speed was just a bit higher than c, then ... i don't know, trying to summon @K^2 ?

Edited February 23, 2017 by Green Baron

[munlander1]

What would happen if we were able to travel at or above the speed of light?

[Green Baron]

Poetically: at the speed of light you are, from your point af view, everywhere in no time.

Above is left to your fantasy.

Contraction of space: ll = sqrt( 1-v²/c² ) * l where ll = length in moving system, v is your speed, c is c and l is lenght without relative motion. Now set v = c and you get ... 0.

Dilatation of time: tt = 1 / sqrt( 1-v²/c² ) * t. Set v = c and you get an undefined value.

Edit: if only a physicist could take a look at this ...

Edited February 23, 2017 by Green Baron

[p1t1o]

13 minutes ago, munlander1 said:

What would happen if we were able to travel at or above the speed of light?

RealTalk^TM? Nobody knows. Mainly because theory forbids this from happening to anything with mass. Its like asking "What happens if you divide a large prime number by 3 and get an integer?" nobody knows because none of the rules that we know to work make any sense under these conditions. There are no mathematical models that describe  a large prime that is divisible by 3.

Extrapolating from well known theory (skipping past the parts of the theory that says this is impossible) says things like you travel backwards in time, or collapse into a singularity as your mass goes to infinity, things like this. Infinites come up quite a lot in the maths which describes our physical theories, but they are generally accepted not to be 100% literal. It is perfectly acceptable for a mathematical model not to work under extreme conditions, and maths spitting out infinites is a good sign that this is what is happening.

Eg: the singularity at the centre of a black hole is described as being infinitely small and infinitely dense. It is assumed that in reality, it is "merely" extremely small and extremely dense.

So when theory tells us that you would become a black hole shooting back in time, that might not be literally true in reality.

That might make a good sig

If you dont ignore the parts of theory that forbids this, the answer becomes: as you put more kinetic energy into an object, it approaches 1c asymptotically. As in, you get closer and closer but every joule of kinetic energy you add gives less and less raw velocity. Even if you poured the entire energy of the universe's rest-mass into your kinetic energy, all you get is closer to 1c, you never reach it. Your relativistic mass (which is real and measureable, although not quite the same as regular mass) also asymptotes to infinity, but of course never reaches it. It is concievable within physical law, to accelerate a grain of sand so fast that its mass become so great that if it passed through our system it could tear it apart. Whether there is enough energy in the universe to get something that fast is another question, but it is allowed. Going faster than 1c, or reaching it at all, is not.

At least as far as we know. (Which is quite far actually, but we are scientists and rarely deal in absolutes)

Edited February 23, 2017 by p1t1o

[KerikBalm]

44 minutes ago, munlander1 said:

What would happen if we were able to travel at or above the speed of light?

You could travel back in time:

http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-time-travel

Anyway, anything with mas cannot reach light speed, but it can get infinitely close.

So lets just say 0.99999999999999999999999 c.

Many people are aware of time dilation, but not length contraction:

https://en.wikipedia.org/wiki/Length_contraction

Not only is time perceived differently, but so is distance. To an observer on Earth, the traveller spends just over 40 years travelling 40 light years. To the traveller, while travelling, (s)he spends a miniscule amount of time traversing a miniscule distance. Earth looks about the same as when the traveller left because light is reaching the destination from about the same time the traveller left the destination. The destination appears 80 years older: the destination aged 40 years while the traveller was travelling, and the light from the destination as seen from earth was already 40 years old

[Green Baron]

A, well, i get for an observer observing a traveler at 0.99c for 40 years in the travelers reference system "spending 40 years" a relative time of ~283.5 years. Travelling at 0.9999c i get ~2828.5 years, 0.99999999999999999999999c will be a relatively "long time, brother" :-)

What am i doing wrong ?

Edited February 23, 2017 by Green Baron

[p1t1o]

1 hour ago, p1t1o said:

So when theory tells us that you would become a black hole shooting back in time, that might not be literally true in reality.

That might make a good sig

Quoting myself - narcissistic?

Daydreaming about this concept -

What does a mass that collapses into a black hole whilst travelling backwards in time look like? Well it looks like a black hole that explodes. What does an exploding black hole look like? It looks like a large splash of hard radiation [probably]. And look at that, everything that was massive in your body is now travelling at 1.0c!

If you put enough EM energy into a small enough space, part of it can convert to mass. You need two photons, without 2 object there can be no interaction and no effect (or some really complex maths that says roughly that) 2 very high energy photons can interact to produce a spray of massive particles and a single (or multiple?) lower energy photon(s). So light with enough energy can convert to mass.

In our thought experiment we have a mass exceeding the speed of light and converting to EM radiation ("light"), which is the same as the physical example above but backwards in time!

A meaningless thought experiment, but what the hey

 

7 minutes ago, Green Baron said:

A, well, i get for an observer observing a traveler at 0.99c for 40 years in his reference system "spending 40 years" a relative time of ~283.5 years. Travelling at 0,9999c i get ~2828,5years, 0.99999999999999999999999c busts my computherium ... :-)

What am i doing wrong ?

Your calculations are slightly askew: 283.5 years is how much time a stationary observer would experience if you specify 40 years of "ship time" if travelling at 0.99c. I think. So if you're on a ship travelling 0.99c and count off 40 years on your clock, when you stop, 283.5 years will have passed. And you will have traveled 0.99*283.5 light years.

Edited February 23, 2017 by p1t1o

[KerikBalm]

14 minutes ago, Green Baron said:

A, well, i get for an observer observing a traveler at 0.99c for 40 years in the travelers reference system "spending 40 years" a relative time of ~283.5 years. Travelling at 0.9999c i get ~2828.5 years, 0.99999999999999999999999c will be a relatively "long time, brother" :-)

What am i doing wrong ?

What are you doing wrong? assuming that the traveller thinks the trip takes 40 years... the traveller thinks the trip was nearly instant.

You may think its impossible for the traveller to think they cross 40 light years in less than 40 years of their relative time - but that ignores length contraction. To the traveller going at 0.9999999... c the distance appears to be far less than 40 light years.

In fact, to a photo, the relative distance to anywhere is zero, and from a photons point of view, it gets to anywhere in the universe instantly - its not FTL, its just that everything has 0 relative distance.

[Hannu2]

1 hour ago, munlander1 said:

What would happen if we were able to travel at or above the speed of light?

This is not well defined question. Natural laws we know predicts that any massive thing can not move faster than light (or at light speed). If you put such numbers in equations all results are nonsense. Infinite or imaginary values which have no physical meaning.

[Green Baron]

12 minutes ago, p1t1o said:

Your calculations are slightly askew: 283.5 years is how much time a stationary observer would experience if you specify 40 years of "ship time" if travelling at 0.99c. I think. So if you're on a ship travelling 0.99c and count off 40 years on your clock, when you stop, 283.5 years will have passed. And you will have traveled 0.99*283.5 light years.

 

8 minutes ago, KerikBalm said:

What are you doing wrong? assuming that the traveller thinks the trip takes 40 years... the traveller thinks the trip was nearly instant.

Sure, thinking before writing might help :-) Thanks for the correction !

[p1t1o]

@KerikBalm @Green Baron

To travel 40ly @0.99c, the traveller experiences:

For an observer moving with the object the travel last 5 years(s) 234 day(s) 14 hour(s) 10.341897338629 second(s)

To travel 40ly @0.999c, the traveller experiences:

For an observer moving with the object the travel last 1 years(s) 287 day(s) 18 hour(s) 26 minute(s) 46.699442148209 second(s)

To travel 40ly @0.9999c, the traveller experiences:

For an observer moving with the object the travel last 206 day(s) 11 hour(s) 16 minute(s) 49.569235172123 second(s)

...0.99999c:

For an observer moving with the object the travel last 65 day(s) 7 hour(s) 1 minute(s) 57.075729092583 second(s)

Calculator breaks at 0.999999c

http://www.dcode.fr/time-dilation

 

for Relativistic mass-energy (basically kinetic energy corrected for relativistic effects):

A 1ton mass travelling at 0.99c: 6.6*10¹⁴ MJ

A 1ton mass travelling at 0.999c: 3.6*10¹⁵ MJ

http://keisan.casio.com/exec/system/1224060366

And I couldn't find a calculator that didn't give "NaN" for 0.9999 and above

What that shows is that to accelerate 1ton from 0.99c to 0.999c requires 2940 trillion MegaJoules! Which is what stops you from reaching c (imagine what the numbers would be if you add a few more 9's)

Thats relativity for ya!

 

**edit**

Oooh more online calculators!

At 0.99c, your 1ton mass has a relativistic mass of 7.08tons.

At 0.999c ... 22.3tons

At 0.9999c ... 70.7tons

At 0.99999c ... 220.6tons

http://www.ultimate-theory.com/en/2012/12/26/special-relativity-mass-calculator

This mass increase (which is a real, measurable increase in mass, although it is different to "real" or "rest" mass) only partially explains the huge energies associated with high relativistic travel, there are also weirder effects caused by time dilation and length contraction.

Edited February 23, 2017 by p1t1o

[Gaarst]

52 minutes ago, p1t1o said:

[big quote snipped]

You know, you don't need online calculators. Special relativity is nice enough to simply scale every dilated or contracted parameter by the Lorentz factor, dividing or multiplying is just a matter of if you want a smaller or bigger number.

 

Also, please don't use relativistic mass people, it confuses everyone and is not necessary for calculations, just add a γ in your formula and don't touch intrinsic parameters of particles.

Edited February 23, 2017 by Gaarst

[p1t1o]

10 minutes ago, Gaarst said:

You know, you don't need online calculators. Special relativity is nice enough to simply scale every dilated or contracted parameter by the Lorentz factor, dividing or multiplying is just a matter of if you want a bigger or smaller number.

 

Also, please don't use relativistic mass people, it confuses everyone and is not necessary for calculations, just add a γ in your formula and don't touch intrinsic parameters of particles.

lol I know I know, I just got carried away with calculators!

Relativistic mass is not used often, but it does quite graphically illustrate that something weird is going on.

[Piscator]

Maybe the original poster can elaborate on what exactly he meant, but as far as I understand the question, relativity doesn't even come into it. At least not in the parts that are concerned with the apparent age of the planet when the hypothetical traveler arrives. (And it seems pretty obvious that the parts concerned with the voyage itself use earth time and not ship time.)

[HebaruSan]

6 minutes ago, Piscator said:

Maybe the original poster can elaborate on what exactly he meant, but as far as I understand the question, relativity doesn't even come into it.

It sort of does, here:

13 hours ago, DrowElfMorwen said:

"This particular system is 40 light years away, meaning even if we could travel at light speed it would take 40 years to reach it. However, realize that as you began your journey and say, for example, you can see it from Earth or your space ship telescope--you're looking at a planet 40 years in the past. As you travel toward the planet and periodically look at it again, do you know how how much time would have passed on that planet, say, ten years into your journey?

At light speed, it wouldn't "take 40 years to reach it," and there is no "ten years into your journey," for the reasons discussed above. There are false assumptions built into the question, so answering it as asked doesn't make sense.

[DrowElfMorwen]

I should clarify some of the questions in this thought experiment, though I do think my questions were answered (so far). 

I will set up this little thought experiment like this;

Scientist A hops on his ship and looks at the planet, knowing he is seeing it 40 years younger than it actually is at that moment (from hid Earth time reference frame). He takes off toward the planet traveling at 0.999% the speed of light. How long does it take him and how does he see the planet changing along the way?

From answers so far, the travel and changes are pretty much instantaneous, and the planet will suddenly be 40 years older when he arrives BUT will have gone through 80 yrs worth of physical changes from his initial viewpoint back on Earth. 

Scientist B, on Earth, watches Scientist A leave. For the purposes of this thought experiment let's say he spends the next 40 years observing his colleague and can see him with some magnificent telescope. I suspect he will not see his friend arrive for 80 years, as he would observe his friend's journey slowing to account for time "looking into the past" and the light of his friend's journey would take longer to "report back" his position relative to Earth and the new planet. Would you guys agree? 

[p1t1o]

20 minutes ago, Piscator said:

Maybe the original poster can elaborate on what exactly he meant, but as far as I understand the question, relativity doesn't even come into it. At least not in the parts that are concerned with the apparent age of the planet when the hypothetical traveler arrives. (And it seems pretty obvious that the parts concerned with the voyage itself use earth time and not ship time.)

I think the answer was reached pretty quickly. After that we, or I anyway, just started thinking about all the other interesting stuff that goes with it.

[Piscator]

Well, that's kind of my point. As ten years ship time wouldn't make much sense, it seems rather obvious that ten years earth time or in other words a quarter of the journey was meant. And for the question how much apparent time on the target world would have passed at this point, it doesn't really matter, whether you're still moving at near lightspeed or made your observation from a standstill.

I agree, that the question is not all that complicated, but at the time of my first post noone seemed to have given an explicit answer to it anyway.

[Green Baron]

Well, the original question was "if we could travel at the speed of light".

I understand it like this: as the traveler approaches c space contracts ever more and time passes ever faster, relative to an outside observer. At c (or better at the speed limit, which is strongly assumed to be c but might be just a little bit above) space is infinitely contracted and time infinitely compressed. Imagine, no space, no entropy, no time.

Edit: "10 years into the journey" indeed does not make sense since the journey at the speed of light does not take time. On the other hand, for an outside observer, it takes infinite time.

This is for a fictitious traveler at exactly the speed limit and does not contradict the calculations for a journey with a speed just below c.

Hope that was not totally wrong ...

Edited February 23, 2017 by Green Baron