Can light speed be exceeded?

[GoodPR]

If two planets were traveling at .99c away from a planet in the center. What would be the speed difference between them?

If you were on one of those traveling planets and launched a rocket in the direction you were already travelling, you could get it to go .99c away from you. If you related that rocket to the planet in the middle it's now traveling at 1.98c correct?

You may say that's not possible, but If you didnt compare yourself to the planet in the middle, you wouldn't even know how fast your travelling. Similarly how do we know which direction and how fast Earth is actually moving? We could send a rocket .99c relative to us in any direction we want, that could be traveling faster than light relative to another celestial body.

Its true that you cannot travel past the speed of light, because light always travels light speed away from you, but it seems can you travel faster than light, relative to another stationary body.

 

[stovepipe]

If two planets were traveling at .99c away from a planet in the center. What would be the speed difference between them?

If you were on the planet in the middle, the distance between them would appear to grow faster than c. If you were on either of the other planets the distance would appear to grow at less than c.

 

[stovepipe]

If you were on one of those traveling planets and launched a rocket in the direction you were already travelling, you could get it to go .99c away from you. If you related that rocket to the planet in the middle it's now traveling at 1.98c correct?

No, it's still traveling at less than c. To the observer on the planet that launched the rocket, the distance between the rocket and the middle planet would appear to be growing faster than c.

You have to use the velocity addition formula to calculate the speed of the rocket with respect to the middle planet. It will always come up less than c.

Distances are allowed to grow faster than c because they do not have mass. Rockets and planets have mass, so they cannot travel faster than c.

 

[stovepipe]

If you want more information, read this http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html

 

[GoodPR]

This is because of the difference in the passage of time when stationary vs. traveling at near light speed correct?
Distance itself is also either compressed or expanded as well as time, when looking at the planet from either in front or behind it?
Because mass increases with speed, if something with mass x traveled at me at .99c its mass would increase, and the distance it occupies is smaller.
Could it travel with high enough velocity that to me it appears to be a black hole because of its incredible mass and shrunk distance?

 

[Phrak]

If two planets were traveling at .99c away from a planet in the center. What would be the speed difference between them?

The difference (actually the addition) of velocites as measured by the planet in the middle is what addition has always been.

If you were on one of those traveling planets and launched a rocket in the direction you were already travelling, you could get it to go .99c away from you. If you related that rocket to the planet in the middle it's now traveling at 1.98c correct?

This is where addition of velocites will fail you. Velocities do not combine in special relativity by the addition of vector components in this scenario. Maybe someone can supply an equation for the combination of velocities.

 

[GoodPR]

Yes phrac stovepipe explained that to me, thank you. Got an idea for my question in my last post?

 

[GoodPR]

I wanted to say two things I picked up on in that link you sent me stove pipe.
That one, relativity and Einstein did not directly say that FTL is not possible only that it would require infinite energy to do so.
Also, that velocity can only be measured in reference to something else.
So let's say I'm the only thing in the universe, I could accelerate at 1g constantly, why would my mass increase as I approached light if for all I know I could be standing still?

So, then if I were in a black hole, with nothing to compare my speed to, I could accelerate indefinitely without adding mass. Which is why I asked the question, if something were traveling at you nearly light speed, is it possible that it could appear as a black hole.

 

[russ_watters]

That one, relativity and Einstein did not directly say that FTL is not possible only that it would require infinite energy to do so.

Which means the same thing...

Also, that velocity can only be measured in reference to something else. So let's say I'm the only thing in the universe, I could accelerate at 1g constantly, why would my mass increase as I approached light if for all I know I could be standing still?

According to you, your mass never increases. Relativity effects are something that exists between two reference frames - like velocity.

So, then if I were in a black hole, with nothing to compare my speed to, I could accelerate indefinitely without adding mass. Which is why I asked the question, if something were traveling at you nearly light speed, is it possible that it could appear as a black hole.

I still don't know what a black hole has to do with anything, but yes, you can accelerate forever at 1g if you could find a a power source to do it. But that doesn't mean you'll ever get to C.

[edited to fix quotes]

 

[GoodPR]

Sorry, that didn't entirely answer my question, could I accelerate so that I had so much mass I would be perceived as a black hole from whatever I'm traveling towards.

 

[Nabeshin]

Maybe someone can supply an equation for the combination of velocities.

In one dimension,
Frame S' moving with velocity v with respect to frame S,
Object moving with velocity u' with respect to frame S', u with respect to S:
$$u=\frac{u'+v}{1+\frac{v u'}{c^2}}$$

$$u'=\frac{u-v}{1-\frac{v u}{c^2}}$$

 

[eekf]

Light speed is the speed of light in a vacuum. The way theat Einstein originally (1905) came to the conclusion that light speed can not be exceeded basically boils down to providing energy using light to an object and then trying to accelerate it to faster than light. This can not be done. If the object is going faster than light, the light you use to supply the energy with can not catch the object.

You have to understand that once emitted, the light is not connected to the emitter or the receiver. It travels at its own speed, independent of any observer, only link to the medium it is in. You can compare this with sound traveling through water. Once you emit the sound, it travels at a fixed speed independent of the boat you are on.

Therefore, even if you are traveling at -0.99c (with regards to Earth) and sending a radio message to your friend traveling at 0.99c in the other direction, your message will be traveling at c in the medium (vacuum) and will eventually reach your friend.

For a comparison, if you were traveling at 300 m/s through the atmosphere and your friend passes you at -300 m/s, if you shout a message, it will still be heard by your friend, as the sound travels at 330 m/s irrespective of your velocity.

If you and your friend were blind (and could not detect any electromagnetic waves), you would have to measure time somehow. You can decide to measure time through a "click" every second. If you are brilliant, you can derive a set of equations where the speed of sound is constant irrespective of the observer (which it is). However, you need a way to synchronise your clocks. A clever way to do this would be to transmit a click to an object which is stationary with respect to you, get the reflection of the click and divide the time by 2 to get the distance to the reflecting object. Now that you know the distance, you can synchronise your clocks. You would not be able to synchronise your clocks if you were moving faster than sound though, as your reflected click would not be able to get back to you or reach the object, depending on whether or not the reflecting object is in front or behind you.

This will lead you to a Lorentz transformation with s (the speed of sound) as your maximum speed. This is not a physical limitation though. All it would mean is that if somebody was to shoot you, you would probably feel the shot before you hear it. In your reference frame, the bullet would hit you before the shot went off.

Whether these ramblings point you to if it is possible to move faster than light, only you can tell. I do know that if there was something moving faster than light, we can not detect it (our eyes being sensitive to light). We would also have trouble with causality. We would therefore struggle to find cause and effect.

 

[A.T.]

You have to understand that once emitted, the light is not connected to the emitter or the receiver. It travels at its own speed, independent of any observer, only link to the medium it is in.

Light doesn't need a medium.

You can compare this with sound traveling through water. Once you emit the sound, it travels at a fixed speed independent of the boat you are on.

No, the speed you measure for the sound in your frame depends on how fast you move relative to the water (the medium). This is very different from light, where every inertial observer measures the same speed of any light ray in vacuum.

 

[eekf]

Quite the contrary.

If I have two boats moving in the same direction at a fixed distance from each other and define c as the speed of sound in the water, I can use the Lorentz transform exactly, provided I define my clocks and synchronisation according to c. Just remember you have to also measure distance using the sound (actually you set your clocks according to sound and then measure distance according to your clocks on the two boats).

Einstein used this method in 1905 (only using light instead of sound). The consequence of the transform is that you do not need to have a velocity relative to an absolute medium. You just need relative velocities between two boats.

 

[eekf]

Light doesn't need a medium.

No, the speed you measure for the sound in your frame depends on how fast you move relative to the water (the medium). This is very different from light, where every inertial observer measures the same speed of any light ray in vacuum.

If the vacuum is not a medium, you are right.

Actually I meant the speed is not linked to the speed of the boat when you emitted the sound or the speed at which you are receiving it.

In order to measure the one-way speed of sound/light, you need to have synchronised clocks. Einstein's method for sychronising the clocks was to have light travel in both directions (reflected) to measure distance between two "stationary" objects and divide it by. You then use the "constancy" of the speed of light to determine the distance. This you can then use to synchronise the clocks, allowing you to measure lengths.

If I follow exactly the same procedure with sound, I can use exactly the same transformations.

 

[vin300]

You used a complete analogy of light as sound and that is a disaster.The speed of sound is constant,true.
But you cannot use the lorentz trnsform with the speed of sound instead of c because that simply gives a completely different interpretation of theLT so all the concepts in relativity change altogether.
You can definitely travel faster than sound but not if used this way, so it is plainly false
To measure velocities with sound you can only use the doppler effect but the frequency becomes ultrasonic at comparatively very less velocities.
Sound does not bend as light to make up transformations.It follows the same path in every frame

 

[eekf]

You used a complete analogy of light as sound and that is a disaster.The speed of sound is constant,true.
But you cannot use the lorentz trnsform with the speed of sound instead of c because that simply gives a completely different interpretation of theLT so all the concepts in relativity change altogether.
You can definitely travel faster than sound but not if used this way, so it is plainly false
To measure velocities with sound you can only use the doppler effect but the frequency becomes ultrasonic at comparatively very less velocities.
Sound does not bend as light to make up transformations

Please do not blame me for interpretations people make.

I am only making observations with respect to the LT and the way Einstein set up the original derivations in his paper. I also show you new ways (actually not that new) to use the same mathematics.

I believe that is actually progress. May I just note that there was a time when people believed it impossible to move faster than sound (and for that matter that the Earth was flat).

Many people believe you can not move faster than light (most of them because of the Lorentz transformation and Einstein's derivation. I personally have no opinion on this matter. I believe it is impossible to tell. I am merely suggesting that you do not have to limit yourself because of the Lorentz transformation. Maybe somebody finds a way...

If a scientist tells you something is possible, he is probably right. If he tells you something is impossible, he is probably wrong...

 

[vengy]

Can light speed be exceeded? Tug-Of-War

I've often wondered that too. The speed of light in a vacuum is 299 792 458 m/s.

Recently I was thinking of this example:

In a game of tug-of-war, suppose the rope is 299 792 458 m in length and
the players pulled on it. Would both teams have to wait at least 1 second
before the affect of a tug reached the opposite end? Or would the tug effect
be propagated instantaneously thereby violating the speed of light? ;)

Just curious!

Thanks.

 

[Dmitry67]

Yes, of course they will have to wait.
And the pull or push impulses propagate with the speed of sound (usually few km/s), so in your example the game would be quite boring.

 

[vin300]

And the pull or push impulses propagate with the speed of sound (usually few km/s), so in your example the game would be quite boring.

First, he was talking of the speed of light and second, the speed of the impulse has nothing to do with either light or sound speed, this was discussed in an earlier thread
The tug affect woud be propogated instantaneously if none of the masses on the tug reaches close to light speeds(the masses on the tug increase with speed and such speeds also require more force than the trditional calculations) but this does not violate nothing because no mass trvels faster than c

 

[Dmitry67]

no impulse can travel faster then c because it carries INFORMATION (even if parts of the rope move slower then c). So if you were right ('woud be propogated instantaneously ') then you would be able to use a rope to send info using Morse code instantaneouly :)

 

[DrGreg]

Dmitry67 is right. "Causal effects" can never travel faster than light. Event A cannot influence event B if you would have to travel faster than light to travel from A to B. If it were possible to do that, the maths proves that it would also be possible to send influence backwards in time.

And, yes, the speed at which pressure or tension travels through a solid, liquid or gas is the speed of sound. Sound is a pressure wave.

 

[vengy]

I'm assuming the rope is "ideal" and not subject to tension/pressure/friction, and the game is being played in a vacuum. ;)

 

[Dmitry67]

In special relativity (contrary to the classical mechanics) no ideal, absolutely rigid objects (including ropes) exist.
So SR does not allow your 'ideal' rope to exist.

 

[A.T.]

Many people believe you can not move faster than light (most of them because of the Lorentz transformation and Einstein's derivation. I personally have no opinion on this matter. I believe it is impossible to tell.

Yeah: Some people say Elvis is dead, some say he's still alive. But I'm a skeptic and don't believe neither the first not the later.

- A sound-signal propagates at different speeds in different directions if the medium is moving in the reference frame.

- A light-signal propagates at the same speed in all directions in every inertial reference frame.

Sound are light are not the same.

 

[Phrak]

Light doesn't need a medium.

No, the speed you measure for the sound in your frame depends on how fast you move relative to the water (the medium). This is very different from light, where every inertial observer measures the same speed of any light ray in vacuum.

It's certainly not a classical medium that can have two natural velocities: a zero velocity in which the medium is at rest, and the velocity at which waves propagate. Spacetime seems to have only one natural velocity.

 

[stovepipe]

Spacetime seems to have only one natural velocity.

Would it be wrong to assert, that the speed of light is the rate at which change in space-time occurs?

 

[Phrak]

I'm already pushing the boundries of this folder toward the philosophical. Afterall, what in the world does 'natural' velocity mean, anyway?

But what would you mean by change--that is, change with respect to what?

 

[Wangf]

Space itself can expand faster than light speed. This is exactly what is happening to those galaxies running away from us faster than light.
it does not violate anything in relativity.

 

[Phrak]

Space itself can expand faster than light speed. This is exactly what is happening to those galaxies running away from us faster than light.
it does not violate anything in relativity.

Could you supply a list of effects that are faster than c?

 

[GoodPR]

As for you guys arguing about sound, I don't know about in a mathmatical way, but in a thought experiment way sound is identical to light.
As someone moving very quickly towards you emits a sound, the sound waves compress giving a higher pitched sound with more energy, and opposite when they move away from you.
Light does the same, the wavelength compresses and it gives you more energy,
And in both cases sound or light shone at you from perpendicular to the object is unchanged.


my question remains however,
Can you travel with enough velocity towards Earth, that from Earths perspective, you would appear as a black hole, (because of your incredible mass).

 

[GoodPR]

Also, in closer relation to the title of the thread,
If I am accelerating at a rate that feels like 1 g constantly it would provide me with a constant acceleration regardless of how fast I am going,

It is known that the faster you travel the more mass you accumulate, however we know that the rocket itself will never feel itself to have more mass, because it is always in a rest frame.
Therefor, traveling closer and closer to the speed of light, will not require more rocketfuel to maintain the 1g acceleration, from the perspective of the rocket itself. It is only the time that rocketfuel burns for, that changes relative to the rocket and Earth. From the rockets perspective it burns 1 kg of fuel persecond.
From Earth perspective it burns 1kg of fuel per .1 second, or whatever.

Therefor, if accelerating at 1g took 2 years to reach light speed relativity excluded, if we gave the rocket 3 years of fuel, the rocket would feel as though it is traveling faster than light compared to Earth, even though from the rockets perspective light is still traveling light speed away from the rocket, and from the Earths perspective we have not attained light speed.

And the method which allows all of this to be true at the same time without violating relativity, is that the relative mass would play an increasing role in balancing the passage of time, so that all parties can experience the same things, without any laws being violated.

In the case where the rocket thinks its going faster than light based on its acceleration over time, from Earths prospective the rocket would appear to be a black hole moving towards earth, at less than light speed. From the rockets perspective, Earth would appear to be a black hole moving towards him at less than light speed.
Due to the warping of space time of the black holes nothing is violated.

 

[russ_watters]

If a rocket had an inertial navigation system that was programmed to calculate velocity via v=a*t, then yes, it could calculate a velocity faster than C. But so what? That just means it was programmed wrong.

 

[GoodPR]

Not entirely true.
Rest mass does not change in any frame regardless of your velocity, and time always ticks by at 1 second per second.
So for the sake of the rocket, that would be an accurate measurement of its true velocity.

It is only when you want to compare your velocity with something else that you need to account for relativity.(which obviously for the case of a rocket is always true)
Since we know that the rocket's rest mass never changed, it is time that is different between the rocket and the observer. The rocket perceives itself buring 1 kg of fuel per second. However on Earth it seems to burn 1kg per 0.1 seconds, or whatever.

Since Light speed is a constant regardless of your velocity or gravity, I believe you could relate your speed directly to that, when you reach the speed of light based on your simple formula, I believe any photon you are emitting directly in front of you would either double in Energy or become two photons as observed by the stationary object your traveling towards.
Keep in mind that despite the simple calculation showing your going faster than light, I'm not claiming light doesn't move light speed away from you in all directions.

 

[russ_watters]

Not entirely true.
Rest mass does not change in any frame regardless of your velocity, and time always ticks by at 1 second per second.
So for the sake of the rocket, that would be an accurate measurement of its true velocity.

No, it wouldn't - otherwise, you could plug that number into appropriate equations and get nonsensical responses. Velocity is something you measure between two objects.

What you would be measuring is rapidity: http://en.wikipedia.org/wiki/Rapidity