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Wed Jul 24, 2013, 08:32 AM

Question about FTL Travel

Imagine a line (L) with three points (P1,P2,P3):



Earth is represented by P2, P1 and P3 represent crafts moving away from Earth at .75 the speed of light.

To an astronaut on craft P1, is P3 moving faster than light?

What if a third craft traveled at a 45 degree angle to L, stopped, turned around, and viewed P1 and P3?

It seems to me that from the perspective of the third craft, P1 and P3 are increasing the distance between themselves at a speed greater than the speed of light.

Knowing little to nothing about Physics, I don't know why my perspective is inaccurate, but I believe it must be. I'm confident that someone here can straighten me out!



10 replies, 1219 views

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Arrow 10 replies Author Time Post
Reply Question about FTL Travel (Original post)
demwing Jul 2013 OP
Old Codger Jul 2013 #1
Xipe Totec Jul 2013 #2
Old Codger Jul 2013 #5
Xipe Totec Jul 2013 #6
Xipe Totec Jul 2013 #3
pokerfan Jul 2013 #4
jobendorfer Aug 2013 #10
caraher Jul 2013 #7
demwing Jul 2013 #8
caraher Jul 2013 #9

Response to demwing (Original post)

Wed Jul 24, 2013, 08:49 AM

1. Actually

You are correct but the faster than light speed is only relative to those 2 objects, so relative to each other yes but only to each other.

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Response to Old Codger (Reply #1)

Wed Jul 24, 2013, 09:06 AM

2. Not even relative to each other

If two object are moving ftl relative to each other, they could not even see each other because signals from one would never reach the other. They are for all intents and purposes in different universes.

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Response to Xipe Totec (Reply #2)

Wed Jul 24, 2013, 02:15 PM

5. Hmmm

I don't really see anything that has anything to do with whether or not they can see each other or not, if you are traveling at any speed whatsoever and someone else is traveling at any speed whatsoever and you are going in 180 degree opposite directions you are traveling at the combined speeds relative to each other, irrespective of anything else. It has nothing to do with the actual speed of light or being able to see each other in any way....

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Response to Old Codger (Reply #5)

Wed Jul 24, 2013, 04:08 PM

6. That's a non-relativistic argument.

That is postulating an absolute observer; one who is a universal speed arbiter. That is precisely what relativity says does not exist. All speeds are measured relatively, that is, relative to each observer's frame of reference. The faster an object moves relative to me, the larger the mass becomes, the shorter the size becomes, and the slower time passes.

From my frame of reference any object that receded from me faster than the speed of light, if it were possible, would be invisible because no signal from that object would ever reach me, so I could not detect it. Any object approaching me faster than light would arrive before any signal from it arrived.

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Response to demwing (Original post)

Wed Jul 24, 2013, 09:12 AM

3. Here is a relativity calculator that might help

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Response to demwing (Original post)

Wed Jul 24, 2013, 09:17 AM

4. Under special relativity addition (or subtraction) of velocities works differently

Imagine two velocities that you wish to add, u and v. Instead of simply adding the velocities: w = u + v, under SR velocities must be combined using the formula:

w = (u + v) / (1 + uv/c2)

When the velocities are very small with respect to c, then the formula approaches w = u + v. It's weird, but it seems to be the way the universe works. More here: http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

If you really want to bend your brain, check out the train/tunnel "paradox."
http://web.hep.uiuc.edu/home/g-gollin/relativity/p112_relativity_11.html

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Response to pokerfan (Reply #4)

Fri Aug 2, 2013, 12:38 AM

10. a slight amplification, which may or may not help!

If velocities u and v are a small fraction of the speed of light, say 10% or less --
then the term (1 + uv/c^2) approaches the value 1.
That's because in our case u*v is less than 1/100th the speed of light c, and very very much smaller than c^2.
So for very low velocities, the term uv/c^2 is very, very close to zero -- so close we may as well call it zero.

Then w= (u+v)/(1 + uv/c^2) -> (u+v)/(1+0) = u+v

The galilean transformation w = u + v works very well in our everyday world.
The effects of relativity are very, very small at the velocities we usually deal with in our daily lives.
But if you're dealing with particles (or spaceships) moving at big fractions of c, you have to
apply the lorentz transformation because the relativistic effects are significant at those speeds.

The interesting bit is that you can make Newtonian mechanics fall out of relativistic mechanics
by applying the same kinds of approximations that pokerfan showed us.

Anybody working on a Theory of Everything is taking on a huge challenge, because the first
tests of it will be making both relativity and quantum field theory fall out of it, in the limit of
small velocities and small scales, respectively. That's a tall order!

We seem to be less tolerant of provisional theories these days. Bohr published a theory that
worked for one type of atom, hydrogen, and was clearly wrong for every other element.
But it did lead very shortly to quantum mechanics, which was spectacularly more successful.
I'm not sure any theorist would get that kind of slack, these days.

Cheers!

J.


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Response to demwing (Original post)

Tue Jul 30, 2013, 08:18 AM

7. Just to emphasize...

You're not going to get anywhere in understanding this problem until you've studied Einstein's special relativity. Which is where the significance of the speed of light comes from in the first place.

Forget applying your intuition based on everyday life and "common sense." From that perspective, you calculate relative velocities as what's known as Galilean relativity, and in that case yes, they would seem to be moving faster than the speed of light relative to one another. The trouble is, that's not how the world actually works when you reach those speeds.

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Response to caraher (Reply #7)

Tue Jul 30, 2013, 04:43 PM

8. "relative to one another. The trouble is, that's not how the world actually works"

Thanks for the info, but I don't believe I said what you are attempting to contradict. My main question was not regarding the speed of points 1 and 3 "relative to one another," but rather the speed at which the distance between P1 and P3 increases, as viewed from any point on any line that ran perpendicular to L1.

Look back at the line L1. It's a straight line with three points. If P1 moved away from P2 at 95,000 mile per second, and simultaneously, P3 moved away from P2 at 95,000, then after 1 second, P1 and P3 would be 190,000 miles apart. That's 4000 miles further than an object traveling at the speed of light would have traveled in that same 1 second period.

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Response to demwing (Reply #8)

Tue Jul 30, 2013, 06:00 PM

9. Sure, but there's no prohibition in relativity on that

In your reference frame at P2, neither body is moving faster than c. There's nothing in relativity that says the distance between two objects can't increase at a rate faster than the speed of light.

You're right that I was interpreting your claim in a different way - sorry!

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