Speed of light

Spaceboy · Post by **Spaceboy** » Tue Sep 29, 2009 8:00 pm

Since the speed of light is always the speed of light, what happens when you have two spaceships traveling side by side, both going 2mph under the speed of light, then spaceship B accelerates to only 1mph below the speed of light?

Even though spaceship B only accelerated 1mph, does it appear to have accelerated to half the speed of light from the perspective of Spaceship A?

I always hear that it would take an infinite amount of energy to reach the speed of light but never fully believe it, though if the above thought is true then I think I figured it out...

It takes an infinite amount of acceleration to reach the speed of light even when you're almost there; as shown by the spaceship example, spaceship B has to accelerate to half the speed of light from spaceship A's perspective just to actually go 1mph faster. therefore acceleration is actually asymptotic with a constant force causing the acceleration.

ccb056 · Post by **ccb056** » Tue Sep 29, 2009 8:06 pm

F=MA

Your mass gets larger the faster you go.

Stroodles · Post by **Stroodles** » Tue Sep 29, 2009 8:08 pm

Brain...hurts....light is fast?

fliptw · Post by **fliptw** » Tue Sep 29, 2009 8:13 pm

it would appear to spaceship a that spaceship b has accelerated 1 mph faster.

Spaceboy · Post by **Spaceboy** » Tue Sep 29, 2009 8:16 pm

fliptw wrote:it would appear to spaceship a that spaceship b has accelerated 1 mph faster.

That can't be though... It would only appear that way from an outside observer.

If you're going 2mph under the speed of light yet from your perspective light is still going the speed of light, that means time has slowed enough for you so that 2mph appears to be as fast as the speed of light.
That would mean 1mph is half the speed of light, from your perspective.

ccb056 wrote:F=MA

Your mass gets larger the faster you go.

That confuses me a little, because wouldn't the mass and energy of your fuel increase aswell? Making no difference?
I haven't really thought of that at all yet though, so I'm not sure what I'm talking about with the F=ma so much..

fliptw · Post by **fliptw** » Tue Sep 29, 2009 8:27 pm

umm... no.

The thing about relativity is that its relative.

both ships start in the same relative time frame, an increase of 1 mph isn't a significant increase in speed, so the observed affect is of the same degree.

from spaceship a POV, B would've gotten a bit shorter, the clocks on that ship would have gotten faster, and its moving a bit faster.

the stranded space-hitchhiker would see both as a blur.

Spaceboy · Post by **Spaceboy** » Tue Sep 29, 2009 8:45 pm

If you're saying it would only increase 1mph from the pov of spaceship A, spaceship B would appear to have gotten longer with slower clocks as much as anything that just accelerated 1mph would, which would be practically nothing.

This point I might have posted on the board earlier, but I can't find it so I'll restate it...

Imagine the speed of light was 100mph. Now imagine you are going 99mph...

Even though you are going 99mph, the speed of light still appears to be going 100mph.

This is because your time has slowed down, so it appears everything around you has sped up.

Since everything around you has sped up, the 1mph difference between you and the speed of light appears to be 100mph... it appears that things around you have speed up to 100x faster.

I'm saying here, that, imagining the speed of light is still 100mph, spaceship A is going 98 mph, and spaceship B is going 99 mph.

in this case, the speed of light is only going 2mph faster than spaceship A, but from spaceship A's POV, it appears to be going 100mph. This is because time has slowed down enough for spaceship A for 2mph to seem like 100mph, so by a factor of 50x.
Since spaceship B is going 99mph, 1mph faster than spaceship A, 1mph from spaceship A's pov is still affected by the factor of 50x... so spaceship B appears to be going 50mph to spaceship A if the speed of light appears to be going 100mph.

fliptw · Post by **fliptw** » Tue Sep 29, 2009 8:48 pm

So, zeno's paradox.

You hypothesis is that if x is faster than y, then x must appear to be traveling at the speed of light to y.

Spaceboy · Post by **Spaceboy** » Tue Sep 29, 2009 9:15 pm

More like... the difference between the speed of light and an obj A divided by the speed of light = the percentage of time obj A is experiencing relative to a stationary object.

You could also flip it around saying the speed of light divided by the difference in the speed of light and obj A = the amount of times the universe has sped up from the POV of obj A

Edit: Just read zeno's paradox on wiki, it starts assuming you can move any distance at all, which already contradicts the point it's trying to prove. I don't know what that proves in itself, though...

fliptw · Post by **fliptw** » Tue Sep 29, 2009 9:28 pm

I think you are over thinking it.

remember the principle of relativity: regardless of frame of reference, the laws of physics don't change.

so, what you ask either therefore must happen for any speed, or it can't happen at all.

which leads back to the hypothesis in my previous post.

Spaceboy · Post by **Spaceboy** » Tue Sep 29, 2009 9:39 pm

Well, that's what I'm saying. It does happen for any speed ...

I haven't taken physics, I'm mostly just thinking about this stuff but I just talked to someone who's gotten a physics degree,

I was saying the equation was (x-c)\\c

when the equation is (gamma) = 1\\(Square root(1 - (v^2\\c^2))

v = the difference in velocity between two objects, and if gamma is 2, that means a clock would go .5 seconds on one object in comparison to the stationary object.

so something going 20,000mph would have a gamma of 1\\.99999999996 (A tiny amount greater than 1)

something going half the speed of light would have a gamma of 1.154700538

So, a spaceship clock would go .87 seconds on one object compared to a stationary object.

You can't use this equation directly on the spaceship example though because apparently it takes a few transformations and alot of math...

Spaceship b probably isnt going half the speed of light from spaceship A's perspective, but it's also not going 1mph faster.

fliptw · Post by **fliptw** » Tue Sep 29, 2009 9:56 pm

... which means its testable at any speed.

Spaceboy · Post by **Spaceboy** » Tue Sep 29, 2009 10:06 pm

Yes, which means it applies to any speed.

fliptw · Post by **fliptw** » Tue Sep 29, 2009 10:56 pm

http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox

the v in lorentz equation is the relative velocity between observer and observed.

which would be 1 for your example.

Stroodles · Post by **Stroodles** » Wed Sep 30, 2009 5:28 am

Ha! Now it starts to make a bit of sense.

Foil · Post by **Foil** » Wed Sep 30, 2009 9:22 am

fliptw is right.

The thing about relativity is that it's consistent in every frame of reference:

A's frame of reference:
A isn't moving
B is moving away at 1mph
=> looks like 1mph difference.

B's frame of reference:
A is moving away at 1mph
B isn't moving
=> looks like 1mph difference.

Observer's (our) frame of reference:
A is moving at C - 2mph
B is moving at C - 1mph
=> looks like 1mph difference.

Spaceboy, the asymptotic behavior you're talking about is in energy/mass, not perceived relative motion.

fliptw, feel free to correct me. It's been 10 years since my undergrad Physics courses.

Spaceboy · Post by **Spaceboy** » Wed Sep 30, 2009 12:59 pm

If it was 1mph from reference point A and B, AND 1mph from reference point C, the speed of light would not always appear to be traveling the speed of light.

If what you're saying is true, it seems assuming A is going c - 2, and B is going c - 1 From Reference point C
that if B was only going 1mph more from reference point A, that would mean the speed of light is only going 2mph from reference point A.

That was proven to be impossible, I thought.

Foil · Post by **Foil** » Wed Sep 30, 2009 1:20 pm

...Ah, I think I see what you're saying now.

Let me see if I can summarize what you're saying:

From C's reference frame:
A is travelling at (speed of light - 1mph)
B is travelling at (speed of light - 2mph)
Thus the speed of light in C's reference frame is (A's speed + 1mph).

In B's reference frame:
A is travelling at 1mph

Since the speed of light is constant in every frame of reference, isn't that a contradiction because it would imply the speed of light is (A's speed + 1mph) = 2mph?

Is that correct?

If so, it's just a matter of misunderstanding about what \"speed of light constant in every reference frame\" really means.

Spaceboy · Post by **Spaceboy** » Wed Sep 30, 2009 5:06 pm

From C's reference frame:
A is travelling at (speed of light - 1mph)
B is travelling at (speed of light - 2mph)
Thus the speed of light in C's reference frame is (A's speed + 1mph).

In B's reference frame:
A is travelling at 1mph

Since the speed of light is constant in every frame of reference, isn't that a contradiction because it would imply the speed of light is (A's speed + 1mph) = 2mph?

Yes, so I'm asking how fast would A seem to be going from B's perspective Given the information from our perspective at C.

fliptw · Post by **fliptw** » Wed Sep 30, 2009 5:48 pm

an stationary observer outside of the two ships would witness both as a blur, and notice a more marked time dilation for spaceship b.

He would not have any information on what spaceship A is seeing at that moment.

Spaceboy · Post by **Spaceboy** » Wed Sep 30, 2009 8:50 pm

That's kindof beside the point.

Imagine they're at a great distance with a really big light source. You could see them then.

fliptw · Post by **fliptw** » Wed Sep 30, 2009 8:53 pm

regardless, the outside observer would have no information about what spaceship A sees - wrong frame of reference.

It all being relative and such.

Foil · Post by **Foil** » Wed Sep 30, 2009 11:46 pm

Exactly. Spaceboy, information (e.g. relative speeds) don't transfer from one reference frame to another. In other words, you can't use information in C's reference frame to make any conclusions about A's frame or B's frame.

Spaceboy · Post by **Spaceboy** » Thu Oct 01, 2009 1:38 am

I don't believe it's impossible to calculate or measure...relativity isn't random.
B does see A doing something, but what?

fliptw · Post by **fliptw** » Thu Oct 01, 2009 2:06 am

Spaceboy wrote:I don't believe it's impossible to calculate or measure...relativity isn't random.
B does see A doing something, but what?

I thought we where talking about what C sees? We've discussed A and B already.

woodchip · Post by **woodchip** » Thu Oct 01, 2009 7:51 am

ccb056 wrote:F=MA

Your mass gets larger the faster you go.

Perhaps a bit off course but what happens to a objects mass as it travels through a medium where the speed of light is reduced?

"Light, which normally travels the 240,000 miles from the Moon to Earth in less than two seconds, has been slowed to the speed of a minivan in rush-hour traffic -- 38 miles an hour. "

http://www.news.harvard.edu/gazette/199 ... light.html

Would travel through such a medium mean time would stop when you hit 38 mph?

Would 38 MPH be the fastest you could travel thru the medium or could faster speeds be attained?

Foil · Post by **Foil** » Thu Oct 01, 2009 8:12 am

Spaceboy wrote:I don't believe it's impossible to calculate or measure...relativity isn't random.
B does see A doing something, but what?

I should clarify. No, it's not random; but a perceived velocity in one frame of reference is not the same in another.

Foil · Post by **Foil** » Thu Oct 01, 2009 11:13 am

woodchip wrote:...what happens to a objects mass as it travels through a medium where the speed of light is reduced?

Ah, there's a difference. The relativistic 'speed limit' (speed of light in a vacuum) isn't changed.

What's causing the light to "slow down" to 38mph in that Bose-Einstein condensate is the photons colliding with the matter.

An admittedly-goofy analogy would be sending Usain Bolt through a crazy obstacle course. He's still just as fast, but it takes him longer to get from A to B.

Spaceboy · Post by **Spaceboy** » Thu Oct 01, 2009 11:14 am

Well, that's what I'm saying, how A and B appear to eachother appear different than what C can see.

Bah I have trouble wording stuff like this.

but, given what C can see, what are A and B experiencing?

so we're shifting to the A and B reference from the C reference.
With that I'm asking, we have the C reference of viewing A = c - 1 and B = c - 2

so, we shift to the B reference, does A look like c\\2 instead of the A = c - 1 info that reference point C can see?

fliptw · Post by **fliptw** » Thu Oct 01, 2009 12:40 pm

Isaac · Post by **Isaac** » Thu Oct 01, 2009 12:56 pm

I'm blown by the fact gravity can't travel faster than the speed of light. For a long time I imagined we would have gravity based communications someday. But then I heard that not even gravity waves travel faster than the speed of light. Major bummer.

Foil · Post by **Foil** » Thu Oct 01, 2009 1:06 pm

Isaac wrote:I heard that not even gravity waves travel faster than the speed of light.

Yep. It really makes sense, though:

Gravity can be seen as the curvature of spacetime around a mass...

... and the speed of light is the maximum speed that spacetime can be deformed.

Duper · Post by **Duper** » Thu Oct 01, 2009 1:17 pm

Isaac wrote:I'm blown by the fact gravity can't travel faster than the speed of light. For a long time I imagined we would have gravity based communications someday. But then I heard that not even gravity waves travel faster than the speed of light. Major bummer.

This is why Star Trek uses tacion and neutrino emitters for their communication. They are faster than light particles. (in theory of course)

On the other hand, gravity lenses are pretty cool.

Alter-Fox · Post by **Alter-Fox** » Thu Oct 01, 2009 9:17 pm

fliptw wrote:so, what you ask either therefore must happen for any speed, or it can't happen at all.

It would happen for any speed.

If a car was going 60 mph, then in order for the driver of the car to observe this effect on another car that car would have to be moving at 60 mph less than half the speed of light. Because of relative velocities, the driver of the first car would see the other car moving at half the speed of light. (This is Grade 11 physics).
If you're driving on the highway at 60 mph, and another driver passes you doing 70 mph in the same direction you're moving, from you perspective it looks like he's passing you at 10 mph because he's going 10 mph faster than you. If he passes you at 70 mph in the opposite direction (coming towards you) he'll look like he's doing 130 mph.

I read something (I think it was in "The Search for Time") that said that an observer will always observe light as moving at the speed of light, regardless of how fast the observer is moving. (i.e. relative velocity doesn't apply to the speed of light.) That's the central idea that would make this effect possible.

What I mean is, to make Spaceboy's idea work, the spaceships would have to be moving in opposite directions, either towards or away from each other. If they were moving in the same direction, then spaceship A would only see spaceship B going 1 mph faster. If they were moving in opposite directions, (i.e. spaceship B was moving towards spaceship A), then the pilot in spaceship A would see spaceship B moving at half the speed of light relative to his position, which he percieves as stationary (the spaceship is moving, the pilot is just sitting in his chair.)

snoopy · Post by **snoopy** » Fri Oct 02, 2009 11:11 am

I think some of these answers are partially wrong.

The main problem is that it's all about frames of reference. I did lots of frames of reference stuff in dynamics in school, got an A in the class, and still don't intuitively get it all... so I'd say that at the end of the day it's hard to get it all straight, even when you're not dealing with near-C speeds. (The hard part of Dynamics was mostly about accelerations, which make speeds look easy.)

So, here are our 3 reference planes: Spaceship A, Spaceship B, and Spacerock.

Now, we have to assume that something is fixed, and then say what the other two objects are doing, relative to that object.

For simplicity's sake, we'll assume a one-dimensional world, and that -is to the left and + is to the right.

So, first, let's assume that spaceship A is fixed.
Spaceship B is moving -1 MPH away from SS-A
Spacerock is moving -(C-1) MPH away from SS-A

Let this be our definition of the problem.

Now, lets say, no wait, we want SS-B to be the fixed frame. Then:

SS-A is moving +1 MPH away from SS-B (Exactly 1 MPH, as defined in the previous scenario)

SR is moving ~-(C-2) away from SS-B (It would always be approximate, because you always have relativistic effects, but this close to C you'd be able to measure the relativistic effects.)

Note that it's in the range of C-2.... The relative motion between SR and SS-B is still very close to C

Finally, lets say now we want SR to be our fixed frame. Then:

SS-A is moving +(C-1) away from SR... by definition
SS-B is moving ~+(C-2) away from SR... again approximate.

That's talking about strictly fixed speeds. Now, if you want to get into accelerations, then you can start talking about Mass & Energy changing as you approach C. For now, I'm ignoring how the things got to their speeds, I'm just saying that's how it is.

Here's the trick about relativity (and speeds/accelerations in general) that trips everyone up: Nothing is \"still\" and nothing is just \"moving\" without a frame of reference. All defined speeds/accelerations always have to be relative to something else. Consider the fact that while you're sitting there in your chair you're not moving, and moving at very nearly the speed of light (and everything in between) all at the same time... depending on your frame of reference.

snoopy · Post by **snoopy** » Fri Oct 02, 2009 11:22 am

I'll tell you what I don't get about relativity: time dilation.

Assume this scenerio:

I jump in a space ship, leave earth, haul off to the nearest star and back. During most of the trip, I'm traveling at very nearly C for most of the time, and (I think) at that speed time is slowed for me.

From my perspective, though, I'm just sitting there, and earth goes shooting off away from me at almost C, and then back. So, from my perspective, time should have slowed for earth for the whole trip.

If you say that acceleration is the time dilator, then we (me and earth) had equal and opposite accelerations, depending on frame of reference.

The only difference between me and people on earth during the trip is who is under what gravity effects.

So, when I get back, what will my age be relative to my (imaginary) twin who sayed on earth, and why?

Alter-Fox · Post by **Alter-Fox** » Fri Oct 02, 2009 11:51 am

I think time dilation is what makes your perception of the speed of light constant no matter how fast you're moving. So the amount of time dilation for any velocity has to keep the speed of light at 3.00ee8 m/s (three times ten to the eight meters per second) relative to your velocity.

Gravity exists everywhere in space (gravitational fields from any body never actually reach zero). Pluto is pulling you towards it right now, but the pull is so weak at this distance that it has no real consequences.

snoopy · Post by **snoopy** » Fri Oct 02, 2009 1:25 pm

Right... I mean what degree of gravity effects from the most pertinent bodies.

My point is that velocity and acceleration are both relative... thus two bodies that are separated and then returned would expect equal and opposite aging effects if you tried to base your calculations on velocity and/or acceleration, so if there are differing aging effects, it can't be caused by the acceleration or velocity factors... I think it has to do with gravitational effects- meaning that gravity affects the way we age. Either that, or both bodies would age equally and it'd all come out in the wash.

Foil · Post by **Foil** » Fri Oct 02, 2009 1:57 pm

You're talking about the \"twin paradox\", Snoopy.

At first it seems strange, because it seems like the relativistic effects would be symmetric (each twin sees the other accelerate away and then back), right? In fact, it's really not symmetric, as explained here, because only the twin who 'turns around' is undergoing acceleration, or changing reference frames.

Your reference to gravity is also somewhat correct; the difference can be seen as gravitational time dilation.

Spaceboy · Post by **Spaceboy** » Fri Oct 02, 2009 5:46 pm

snoopy wrote: So, first, let's assume that spaceship A is fixed.
Spaceship B is moving -1 MPH away from SS-A
Spacerock is moving -(C-1) MPH away from SS-A

SS-A is moving +1 MPH away from SS-B (Exactly 1 MPH, as defined in the previous scenario)

SR is moving ~-(C-2) away from SS-B (It would always be approximate, because you always have relativistic effects, but this close to C you'd be able to measure the relativistic effects.

Finally, lets say now we want SR to be our fixed frame. Then:

SS-A is moving +(C-1) away from SR... by definition
SS-B is moving ~+(C-2) away from SR... again approximate.

This is one thing I don't get though.

Bolded points here are essential to understanding what I'm trying to say-

Assume there are 3 spaceships on a line, all traveling to the left.
c--A--B-----------------E
E is Earth.
A is a spaceship.
B is a spaceship.
c is light.
People on Earth see B traveling c-2.
People on Earth see A traveling c-1.
People on Earth see themselves as stationary.
People on Earth, A, and B view c as c.

Assume Earth's position.
People on Earth view c as c.

Assume A's position.
People on A view c as c.

Aassume B's position.
People on B view c as c.

Now, remember how Earth views A and B and c.

People who say

Since people on Earth see A = c-1 and B = c-2
People on B see A as c-1 and people on A see B as c-2

seem to be forgetting about relativity.

Here is my main point:
People in spaceship B are looking forward to spaceship A.
Remember that c is going c.
If people on Spaceship B only saw A as going 1mph faster than themselves, since A is c-1 and is going 1mph faster, that would mean the speed of light would only be 2mph from B's perspective

That is definitely not correct.

because of relativity, I propose that when people on Earth see A traveling C-1, and B traveling C-2,

When you go to the eyes of someone in Spaceship B
A is traveling much much faster than 1mph. If A was traveling 1mph from B's perspective, c would only be 2mph.

That 1mph difference from Earth's perspective is something totally different from B and A's perspective. It has to be, otherwise the speed of light is not always the speed of light from each reference point.

So, what I'm asking is if B saw itself as stationary, what speed would A appear to be going? It can't be 1mph, otherwise the speed of light is only 2mph.
I was thinking along the lines of half the speed of light

This is because:
From Earth's perspective, B only has 2mph to go to reach the speed of light. A is already halfway there as it only has 1mph to go instead of 2mph.
If B is stationary, the speed of light still appears to be the speed of light. If A is already halfway there, A is going half the speed of light.

I'm sure it's somewhere along those lines, but the answer would only be half the speed of light assuming relativity is linear, which I'm sure it is not.

Speed of light

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