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Author Topic: Can something travel faster than the speed of light if travelling in opposite directions?  (Read 10762 times)

Offline thedoc

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Arley Morton asked the Naked Scientists:
   
I know nothing can travel faster than light. But I also know that speed can only be measured relative to something else.

If two rockets flew by each other traveling in opposite directions, both traveling at 51% the speed of light relative to a nearby planet, would not the two objects be traveling faster than the speed of light relative to each other?

Thanks. Love the show,

Arley in New York

What do you think?
« Last Edit: 02/05/2014 10:30:01 by _system »


 

Offline Ethos_

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Relativity is a very difficult phenomenon to explain in simple terms. But to answer the question, one needs to remember that the relative velocities between both rockets are limited by c. Therefore, the answer is NO.
 

Offline Bill S

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The complication here, Arley, is that first you have to specify what the speed is relative to. In this case, if the rockets are flying past the Earth, you would note that neither was travelling faster than light, relative to the Earth.

The next question (the one you are almost certainly asking) is; would either rocket be travelling faster than light, relative to the other? 

The answer is “no” because to calculate the speed of one relative to the other you must use the relativistic velocity addition formula. 

I've no idea how to put an equation into a post (Luddite 1st class), but no doubt someone will.  :)

 

Offline evan_au

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The equation may be found here: http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity

If you plug in the numbers for two spacecraft traveling at 51% of the speed of light (in opposite directions), you get:
Apparent closing velocity=(0.51+0.51)/(1+0.51*0.51) = 1.02/1.2601=80.9% of the speed of light
So the total doesn't exceed the speed of light.

Footnote: The Big Bang theory assumes an extremely short period of "inflation", where points in the universe did suddenly separate at speeds greater than the speed of light. Nobody knows what might have triggered this acceleration. However, it does imply that there are distant points in the universe today that cannot observe each other, because they are separating at faster than the speed of light.
 

Offline JP

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The complication here, Arley, is that first you have to specify what the speed is relative to. In this case, if the rockets are flying past the Earth, you would note that neither was travelling faster than light, relative to the Earth.

However, and key to a lot of confusion about special relativity, is that it predicts that if you measure the velocity of any other object with respect to yourself, it will be moving at less than the speed of light.  However, the distance between the two rockets as observed from the earth is not an object moving with some speed, so that distance can increase at a rate that is faster than the speed of light, even if neither rocket alone is moving at that speed.  Say, for example, rocket 1 moves at 0.75 c and rocket 2 moves at 0.75 c in the opposite direction.  Each one is moving at 75% of the speed of light, but the distance between them increases at a rate equal to 1.5 c.
 

Offline Bill S

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Quote from: JP
Say, for example, rocket 1 moves at 0.75 c and rocket 2 moves at 0.75 c in the opposite direction.  Each one is moving at 75% of the speed of light, but the distance between them increases at a rate equal to 1.5 c.

I didn’t go there because I was still trying to get my head round it.  It links to something in Gott’s “ Time Travel in Einstein’s Universe”; but one step at a time.

Each craft is moving relative to the Earth at 75% c.

An observer on Earth sees the gap widening at 1.5 c.

This does not contravene relativity because neither craft is observed as travelling faster than c.

Neither craft can observe the other craft as travelling faster than c relative to itself.
(That’s ambiguous: craft 1 cannot observe craft 2 as travelling faster than c, relative to craft 1)

Therefore, neither craft can observe the gap as widening faster than c.

Because neither craft can claim to be moving/stationary in an absolute sense; if one could measure the gap as widening faster than c, it would have to concede that this could be due to one or other craft travelling faster tan c, and that that speed was measurable.

Is the reasoning OK so far?

There’s another question to come, but, like I said, one step at a time for us old codgers.
 

Offline David Cooper

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The actual relative speed between the two rockets may or may not be greater than the speed of light depending on which theory you're using to inform your answers. What is beyond dispute though is that if the speed of either rocket is measured from the other rocket they will both calculate that their relative speed to each other is less than the speed of light.
 

Offline Ethos_

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The actual relative speed between the two rockets may or may not be greater than the speed of light depending on which theory you're using to inform your answers. What is beyond dispute though is that if the speed of either rocket is measured from the other rocket they will both calculate that their relative speed to each other is less than the speed of light.
Very good answer David, direct, concise, and less confusing for those unfamiliar with Relativity.
 

Offline Bill S

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Quote from: DC
The actual relative speed between the two rockets may or may not be greater than the speed of light depending on which theory you're using to inform your answers. What is beyond dispute though is that if the speed of either rocket is measured from the other rocket they will both calculate that their relative speed to each other is less than the speed of light.

I agree that the answer is direct and concise, but it leaves me with questions. 

Obviously there are different theories; would you say a bit more about what they are, and what they establish?

Does your quote, above, differ significantly from my statements: “An observer on Earth sees the gap widening at 1.5 c.” and “neither craft can observe the gap as widening faster than c.”?

 

Offline Ethos_

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Does your quote, above, differ significantly from my statements: “An observer on Earth sees the gap widening at 1.5 c.” and “neither craft can observe the gap as widening faster than c.”?
A simple illustration to answer this question involves the experiments being conducted at the LHC. Accelerating protons at near light speed in opposite directions would certainly appear to an observer to be surpassing c relative to one another. However, in their own individual frame of reference, they would not. Speed is a function of distance per time, and for every individual frame of reference, one must remember that time is the variable. Every object in the universe has it's own particular frame of reference which is determined by it's velocity relative to all others. And velocities near light speed slow that frame's passage of time relative to all others.
 

Offline David Cooper

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Obviously there are different theories; would you say a bit more about what they are, and what they establish?

I commented because I was unhappy about some of the absolute answers which had been given on the assumption that Einstein's Relativity is the only game in town. I think Lorentz Ether Theory is still a viable contender, and it does allow objects to travel apart at relative speeds up to twice the speed of light (as well as for the speed of light to be different in different directions, something which cannot be detected because the speed of light can only be measured on a round trip).

Quote
Does your quote, above, differ significantly from my statements: “An observer on Earth sees the gap widening at 1.5 c.” and “neither craft can observe the gap as widening faster than c.”?

No; it ties in with that. The point of conflict between the two sides is where anyone claims that the gap is definitely widening at greater than the speed of light or where they claim that it is not doing so and that you are not allowed to add the speeds together directly without putting them through a formula to adjust them. It is quite acceptable to make such claims, but the people making them should always frame them under a label which makes it clear which theory they are applying rather than making an absolute claim without a label to put it in its proper context. I'm not asking everyone to explain rival theories every time they explain how something works within their favoured one, but they should get into the habit of naming the theory they are applying to guard against putting out what may turn out to be misinformation if their theory is subsequently invalidated.
 

Offline jeffreyH

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Obviously there are different theories; would you say a bit more about what they are, and what they establish?

I commented because I was unhappy about some of the absolute answers which had been given on the assumption that Einstein's Relativity is the only game in town. I think Lorentz Ether Theory is still a viable contender, and it does allow objects to travel apart at relative speeds up to twice the speed of light (as well as for the speed of light to be different in different directions, something which cannot be detected because the speed of light can only be measured on a round trip).

Quote
Does your quote, above, differ significantly from my statements: “An observer on Earth sees the gap widening at 1.5 c.” and “neither craft can observe the gap as widening faster than c.”?

No; it ties in with that. The point of conflict between the two sides is where anyone claims that the gap is definitely widening at greater than the speed of light or where they claim that it is not doing so and that you are not allowed to add the speeds together directly without putting them through a formula to adjust them. It is quite acceptable to make such claims, but the people making them should always frame them under a label which makes it clear which theory they are applying rather than making an absolute claim without a label to put it in its proper context. I'm not asking everyone to explain rival theories every time they explain how something works within their favoured one, but they should get into the habit of naming the theory they are applying to guard against putting out what may turn out to be misinformation if their theory is subsequently invalidated.

Is spacetime curvature a part of LET? I assume it isn't but have not read up on it enough.
 

Offline David Cooper

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Is spacetime curvature a part of LET? I assume it isn't but have not read up on it enough.

There are doubtless many different possible versions of LET, so it could be part of some, but there are simpler mechanisms such as the speed of light being slowed in a gravitational field. The point of curving space in GR is to eliminate gravity as a force, but in LET that isn't an objective.
 

Offline jeffreyH

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From Wikipedia there is one very interesting paragraph.

http://en.wikipedia.org/wiki/Lorentz_ether_theory

"Although the possible connection between electrostatic and intermolecular forces was used by Lorentz as a plausibility argument, the contraction hypothesis was soon considered as purely ad hoc. It is also important that this contraction only affected the space between the electron but not the electrons themselves, therefore the name "intermolecular hypotheses" was sometimes used of this effect. The so-called Length contraction without expansion perpendicularly to the line of motion and by the precise value  (where l0 is the length at rest in the ether) was given by Larmor in 1897 and by Lorentz in 1904. In the same year Lorentz also argued that also electrons themselves are affected by this contraction.[B 4] For further development of this concept, see the section #Lorentz transformation."

The argument that not only the intermolecular distances but matter itself was contracted is very pertinent to investigations of the mechanism of gravitation.
 

Offline jeffreyH

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Looking into LET gave me an idea. I have just formulated an equation describing the spherical distribution of gravitational field strength with increasing distance. This shows that the field is evenly distributed and the wavelength determines the effective gravitation at any point at any distance. I am trying to put it into a simplified form.
 

Offline Bill S

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I mentioned a problem I had with something in Gott’s “ Time Travel in Einstein’s Universe”.  He said:

“If an astronaut’s rocket were to travel by us at faster than the speed of light, a light beam he sent forward could never catch up with the front of his rocket.  The light beam could never catch up because the front of the rocket would be moving faster and have a head start.  Any athlete should know that catching another runner who is running faster and has a head start is impossible.  The astronaut’s observations would be most peculiar: he would take out a flashlight and shine it towards the front of his rocket, but he would never see the beam of light arrive.  That’s not what an observer at rest would see: rather than perceiving he was at rest, this astronaut would know he was moving, and that’s not allowed by the first postulate.” 

Surely, if the astronaut is on the rocket he would be travelling at the same speed as the front of the rocket, which would be stationary in his frame of reference.  At sub-luminal speed he would see the light beam move towards the front at c.  Why would this be different at super-luminal speed?
 

Offline jeffreyH

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I mentioned a problem I had with something in Gott’s “ Time Travel in Einstein’s Universe”.  He said:

“If an astronaut’s rocket were to travel by us at faster than the speed of light, a light beam he sent forward could never catch up with the front of his rocket.  The light beam could never catch up because the front of the rocket would be moving faster and have a head start.  Any athlete should know that catching another runner who is running faster and has a head start is impossible.  The astronaut’s observations would be most peculiar: he would take out a flashlight and shine it towards the front of his rocket, but he would never see the beam of light arrive.  That’s not what an observer at rest would see: rather than perceiving he was at rest, this astronaut would know he was moving, and that’s not allowed by the first postulate.” 

Surely, if the astronaut is on the rocket he would be travelling at the same speed as the front of the rocket, which would be stationary in his frame of reference.  At sub-luminal speed he would see the light beam move towards the front at c.  Why would this be different at super-luminal speed?

The photons that should be moving forwards in the direction of motion of the observer would actually be detected as moving backwards. However the approaching photons opposing the direction of travel would still be detected as moving in the right direction but at super-luminal speeds. Nothing behind the observer would be visible and in front things would be running faster. The photons approaching the observer would possibly then be outside the range of visible light so the observer could be blind to any observations. Depending upon how much faster than light they were traveling the light could be equivalent to x-rays or cosmic rays. It wouldn't be a very healthy situation.
 

Offline Bill S

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Quote from: Jeffrey
The photons that should be moving forwards in the direction of motion of the observer would actually be detected as moving backwards.

Which observer?  Surely the on-board observer would see the photons moving towards the front at c.  You must mean an outside observer, who would see the photons as travelling forward at c, relative to her, but backwards, relative to the craft.  Right?

Quote
However the approaching photons opposing the direction of travel would still be detected as moving in the right direction but at super-luminal speeds.

I’m not sure I understand this.  Are you saying that observers (both on-board and outside) would see photons that were approaching each other as travelling at c, but with the gap between them closing faster than c?


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Nothing behind the observer would be visible and in front things would be running faster.

This must be the on-board observer?  Why would nothing behind him be visible?  He must see light approaching him, from every direction, at c.

Quote
The photons approaching the observer would possibly then be outside the range of visible light so the observer could be blind to any observations. Depending upon how much faster than light they were traveling the light could be equivalent to x-rays or cosmic rays. It wouldn't be a very healthy situation.

Are we looking at red-shift here?  If that were detectable, wouldn’t that tell the on-board observer that he was moving?


 

Offline jeffreyH

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Quote from: Jeffrey
The photons that should be moving forwards in the direction of motion of the observer would actually be detected as moving backwards.

Which observer?  Surely the on-board observer would see the photons moving towards the front at c.  You must mean an outside observer, who would see the photons as travelling forward at c, relative to her, but backwards, relative to the craft.  Right?

Quote
However the approaching photons opposing the direction of travel would still be detected as moving in the right direction but at super-luminal speeds.

I’m not sure I understand this.  Are you saying that observers (both on-board and outside) would see photons that were approaching each other as travelling at c, but with the gap between them closing faster than c?


Quote
Nothing behind the observer would be visible and in front things would be running faster.

This must be the on-board observer?  Why would nothing behind him be visible?  He must see light approaching him, from every direction, at c.

Quote
The photons approaching the observer would possibly then be outside the range of visible light so the observer could be blind to any observations. Depending upon how much faster than light they were traveling the light could be equivalent to x-rays or cosmic rays. It wouldn't be a very healthy situation.

Are we looking at red-shift here?  If that were detectable, wouldn’t that tell the on-board observer that he was moving?

This is related to super-luminal speeds, which are not possible anyway. To all observer's this would be a strange situation.
 

Offline Bill S

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Quote from: jeffreyH
This is related to super-luminal speeds, which are not possible anyway. To all observer's this would be a strange situation.

Am I missing something here, or are you, uncharacteristically, side stepping the questions?
 

Offline jccc

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If the speed of force is c, then the speed limit is c.

A 100 miles per hour train cannot push a man move faster than 100 miles per hour.

The force we use is electromagnetic force, its speed is c. Therefore, we can never travel at light speed.
 

Offline jeffreyH

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Quote from: jeffreyH
This is related to super-luminal speeds, which are not possible anyway. To all observer's this would be a strange situation.

Am I missing something here, or are you, uncharacteristically, side stepping the questions?

Sorry Bill I am not trying to side step anything. I am thinking about a lot of stuff at the moment not only physics. I would simply disregard the post that prompted your questions. It was speculation into areas that I believe would be improbable. If this caused confusion then accept my apologies. I may not be posting here much for a while as I have some full time commitments elsewhere. Keep up the learning you are a good level headed contributor.
 

Offline jccc

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If the speed of force is c, then the speed limit is c.

A 100 miles per hour train cannot push a man move faster than 100 miles per hour.

The force we use is electromagnetic force, its speed is c. Therefore, we can never travel at light speed.

Do I have a point?
 

Offline Bill S

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Quote from: jccc
Do I have a point?

I think you make a number of valid points:

Quote
If the speed of force is c, then the speed limit is c.

Agreed.

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A 100 miles per hour train cannot push a man move faster than 100 miles per hour.

Agreed, but in terms of this discussion, it must be said that two trains approaching each other, both travelling at 100 mph would be travelling at 200 mph, relative to each other. 

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The force we use is electromagnetic force, its speed is c. Therefore, we can never travel at light speed.

Agreed, but this is where the discussion came in.  If two entities (eg photons) are travelling in opposite directions; is there a F of R in which they are observed as approaching each other at 2c?
 

Offline jccc

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Looks like we'll be bounded in our solar system forever.

The only way to travel afar is imagination.

Thank God for it. Dream high.

 

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