Can Two Spaceships Perceive Faster-Than-Light Speeds Relative to Each Other?

[fubarite]

erm... just things that i wonder...

ok, I'm basically just a normal average guy and I don't take physics or such but there are things I ponder. My knowledge of the theory of relativity etc is all fairly basic so I can't really back up anything I have just by what I guess is common sense and logic but a lot of the time that's fairly useless.

anyway...

following my understanding of physics we can't travel faster than the speed of light, we can go from A to B faster but actual speed we can't do. However the faster we travel the more time slows down, I'm not sure if it's exponential or linear like half the speed of light is time halved or something...

but we could achieve let's say three-quarters the speed of light. We can't do this now but I'm not sure if you could use an antimatter explosion or something to generate that sort of speed. But my point as it isn't at the speed of light and so you don't have to be weightless it is theoretically possible.

I also believe Time Travel is impossible, not to say slowing down time and then waiting (let's say traveling at the speed of light for 20 years let's you go 20 years into the future) but I don't think it's possible to go back in time unless you count going into some alternate universe that's 10 years in the past or whatever. We "know" that the speed at which light travels allows you to see into the past, an object that's 50 light years away is 50 years in the past when we eventually see it.

Following this logic, if we were say 65 light years away from the Earth NOW and looked back, we'd see 65 years into the past, correct? so if we then went back to Earth and the 65 light years took us 55 light years (if faster then speed of light was possible, again not A to B wormholes but actual speed) then you'd be 10 years into the past.. I think. So in this sense if you could travel faster than the speed of light you would be able to go back in time.

and so to get to my point...

If you were theoretically able to get two spaceships to fly exactly parallel to each other at three-quarters the speed of light each as they passed each other would they in fact be perceiving faster then light relative to each other and so would they be looking into the past? your thoughts if my mumblings made any sense...

p.s. this is my first use of this forum, i have no idea if this is in the right area or if forum even does this sort of thing... I suppose this is quite a philosophical physics question but theoretical physics has always greatly interested me... just not the maths you need to back ideas up...

 

[diazona]

Following this logic, if we were say 65 light years away from the Earth NOW and looked back, we'd see 65 years into the past, correct? so if we then went back to Earth and the 65 light years took us 55 light years (if faster then speed of light was possible, again not A to B wormholes but actual speed) then you'd be 10 years into the past.. I think. So in this sense if you could travel faster than the speed of light you would be able to go back in time.

Actually you're on to something there. According to relativity, if you could travel faster than light, it would be possible to go back in time. But in order to do so, you have to travel around in a loop and return to your starting point. The situation with returning to Earth from 65 light-years away doesn't work quite the way you described, because as you traveled back to Earth, you'd be passing 65 years' worth of light, so by the time you got back to Earth, you would have "caught up" to the Earth's time. Or rather, you would have, if weird relativistic effects didn't get in the way.

If you were theoretically able to get two spaceships to fly exactly parallel to each other at three-quarters the speed of light each as they passed each other would they in fact be perceiving faster then light relative to each other and so would they be looking into the past?

They would actually be perceiving each other traveling at 96% of the speed of light, not faster than light. Yes, I know that probably doesn't make sense, you're used to thinking that 3/4 + 3/4 is greater than 1. But it's more complicated than that. This is one of those weird relativistic effects I mentioned: when two objects are traveling in opposite directions and they pass each other, the relative velocity between them is not just the speed of one plus the speed of the other. There's a formula for adding them that happens to always produce a result less than the speed of light.

 

[slider142]

but we could achieve let's say three-quarters the speed of light. We can't do this now but I'm not sure if you could use an antimatter explosion or something to generate that sort of speed.

While we don't do this with spacecraft , we routinely accelerate protons to 0.999999991 times the speed of light in the Large Hadron Collider.

 

[cjameshuff]

While we don't do this with spacecraft , we routinely accelerate protons to 0.999999991 times the speed of light in the Large Hadron Collider.

We will do so, that is. The LHC is currently only being operated at 3.5 TeV/proton, but will be operated at 7 TeV/proton, where they will have the velocity relative to the accelerator that you quote.

And we will then slam them head on into each other, adding a few nines to their velocity relative to each other, but still only taking it closer to c.

 

[fubarite]

Actually you're on to something there. According to relativity, if you could travel faster than light, it would be possible to go back in time. But in order to do so, you have to travel around in a loop and return to your starting point. The situation with returning to Earth from 65 light-years away doesn't work quite the way you described, because as you traveled back to Earth, you'd be passing 65 years' worth of light, so by the time you got back to Earth, you would have "caught up" to the Earth's time. Or rather, you would have, if weird relativistic effects didn't get in the way.

my point was if you traveled to Earth in 55 years and you were originally 65 light years away would it allow you to be 10 years in the past? I'd say no.. but not sure.

They would actually be perceiving each other traveling at 96% of the speed of light, not faster than light. Yes, I know that probably doesn't make sense, you're used to thinking that 3/4 + 3/4 is greater than 1. But it's more complicated than that. This is one of those weird relativistic effects I mentioned: when two objects are traveling in opposite directions and they pass each other, the relative velocity between them is not just the speed of one plus the speed of the other. There's a formula for adding them that happens to always produce a result less than the speed of light.

I did suspect that a linear perspective was probably a bit simple. This does help a lot.

thank you for the input. I may have some more questions later on but I'm trying to think how to put pen to paper as it were.

 

[diazona]

my point was if you traveled to Earth in 55 years and you were originally 65 light years away would it allow you to be 10 years in the past? I'd say no.. but not sure.

To be honest, that question isn't stated quite precisely enough to answer. How do you define "being in the past"?

One consequence of working with relativity is that, if you're doing it properly, it forces you to be very specific about the questions you ask and not try to compare things that can't really be compared. For example, because time and space can "rotate" into one another in relativity, you actually can't meaningfully compare times at different locations in space - for example, it's not meaningful to compare the time at which you started traveling from 65 ly away to the time at which you arrived on Earth to decide which one is earlier. That's why you have to travel in a loop to make a time machine: in order to be really sure that you did go back in time, you have to come back to your starting position so that you can directly compare the time at which you arrived to the time at which you left.

(Not to mention the fact that relativity prohibits anything which normally travels slower than light from ever traveling faster than light, and vice-versa.)

 

[Rasalhague]

I like Kev's "log of superluminal radio conversation" here in post #3 of this thread:

https://www.physicsforums.com/showthread.php?t=269480

There's a diagram of it in #10, but you need to read up a bit on the basics of special relativity to properly appreciate the logic. Roger Penrose describes a similar example in The Emperor's New Mind (Vintage 1990), pp. 273-276, "Relativistic Causality and Determinism". If it was possible to send a signal faster than this special speed c, the speed of light in a vacuum, there'd presumably be nothing to stop you making such a causal loop.

 

[JDługosz]

However the faster we travel the more time slows down, I'm not sure if it's exponential or linear like half the speed of light is time halved or something...

You might want to see my page http://www.dlugosz.com/nb/physics/denyreality-2.html" where I illustrate it and give a calculator to show length and time effects at whatever speed.

If you were theoretically able to get two spaceships to fly exactly parallel to each other at three-quarters the speed of light each as they passed each other would they in fact be perceiving faster then light relative to each other and so would they be looking into the past? your thoughts if my mumblings made any sense...

You mean in opposite directions? Use the http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_case:_parallel_velocities". I believe that's the same as adding ¾c and ¾c, which comes to [STRIKE]1.25/2.5 = ½c[/STRIKE] 1.5/1.5625 = 0.96c.

You need to understand that c is not a speed limit like on a highway, where you are simply not allowed to go faster. The whole concept of adding velocities is not linear. It just seems to be so at low speeds. When you add two velocities (e.g. throw something forward when moving on a fast rocket, or even hit the boosters again to add to your own speed!) you always get an answer less than c. That's why it is a limit.

 

[diazona]

adding ¾c and ¾c, which comes to 1.25/2.5 = ½c

um... no it doesn't (¾ + ¾)/(1 + ¾*¾) = 0.96

 

[Raza]

um... no it doesn't (¾ + ¾)/(1 + ¾*¾) = 0.96

Where did you get this formula?

I thought that 3/4 + 3/4 = 6/4 = 3/2 = 1.5

But obviously, you did something differently because it's speed of light we are dealing with.

 

[diazona]

Where did you get this formula?

For one thing, from the Wikipedia page that you linked to...

I thought that 3/4 + 3/4 = 6/4 = 3/2 = 1.5

Yes it does...

When you said "adding ¾c and ¾c," I assumed you meant with the relativistic velocity addition formula. If you do it with just plain addition, then sure you get 1.5c, but that's not physical.

 

[JDługosz]

um... no it doesn't (¾ + ¾)/(1 + ¾*¾) = 0.96

Sorry! That's what I get for doing it in my head when I'm supposed to be taking a break from working hard at the keyboard.

 

[JDługosz]

Where did you get this formula?

I thought that 3/4 + 3/4 = 6/4 = 3/2 = 1.5

But obviously, you did something differently because it's speed of light we are dealing with.

Read http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_case:_parallel_velocities" from the message, and the other pages mentioned.

As I said, "The whole concept of adding velocities is not linear. It just seems to be so at low speeds. When you add two velocities (e.g. throw something forward when moving on a fast rocket, or even hit the boosters again to add to your own speed!) you always get an answer less than c."

Meaning, that's the way "it is". The rule you are used to is an approximation that works for low speeds. 30 miles per hour + 30 mph is not actually 60 mph, but is 59.999999999999879927065927987391995163215629525558 mph. Try measuring the difference of one thousandth part of a trillion! If you had two cars, one traveling at 60mph and the other traveling at (that), it would be fifteen thousand years before it made a difference of one inch. So, you never notice. The simpler formula is perfectly fine for most purposes.