# Can any object approach another at greater than light speed?

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Can any object approach another at greater than light speed?

For instance the two protons racing towards each other in the Large Hadron ColIider. is the gap between them closing faster than c?

Alan

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In Special Relativity nothing that has rest-mass can travel faster than speed of light.

(and particles with rest-mass equal zero travel at speed of light)

You should use Special Relativity velocity addition formula:

Edited by Sensei
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It is my understanding that from your perspective they are approaching each other at faster than c. Since noTHING is moving faster than c, no laws have been been violated.

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Can any object approach another at greater than light speed?

For instance the two protons racing towards each other in the Large Hadron ColIider. is the gap between them closing faster than c?

Alan

The speed of something is how far it traveled in a certain amount of time, not how fast a gap closes I think.

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In the frame of the LHC, the closing speed between the protons is greater than c, however, in frame of either of the protons, you have to use the addition of velocities formula as mentioned by Sensei and it will not be greater than c. (neither proton will measure the other as approaching faster than c.)

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It is my understanding that from your perspective they are approaching each other at faster than c. Since noTHING is moving faster than c, no laws have been been violated.

I know this is thought true by many physicists but it seems to defy the fundamental law of nature namely c.

Is the closing gap really nothing?

It is really a mathematical construct that has nothing to do with the real world where c is always c

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In a sense you can have separation and approaching speeds greater than the speed of light. However, this is not the relative velocity of any of the two bodies as measured by any inertial observer.

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I know this is thought true by many physicists but it seems to defy the fundamental law of nature namely c.

The fundamental principle you are referring to is the fact the laws of physics are the same in all inertial frames; the invariance of c is a consequence of this.

This principle is not violated in your example, since no matter which rest frame you choose, no relative velocity will exceed the speed of light.

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I know this is thought true by many physicists but it seems to defy the fundamental law of nature namely c.

Is the closing gap really nothing?

It is really a mathematical construct that has nothing to do with the real world where c is always c

In the frame of either proton, the other is not approaching faster than c. So yes, closing speed of two objects that are both moving in the frame where the measurement is being taken can be greater than c (but no greater than 2c) as long as there is no frame in which anything is traveling faster than c within that frame.

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In the frame of the LHC, the closing speed between the protons is greater than c, however, in frame of either of the protons, you have to use the addition of velocities formula as mentioned by Sensei and it will not be greater than c. (neither proton will measure the other as approaching faster than c.)

Could I put it another way, if it were possible for an observer to position himself in the gap, from his perspective would the combined speed of the objects close to c close the gap at excess of c+?

In the frame of either proton, the other is not approaching faster than c. So yes, closing speed of two objects that are both moving in the frame where the measurement is being taken can be greater than c (but no greater than 2c) as long as there is no frame in which anything is traveling faster than c within that frame.

Thank you!

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In the frame of either proton, the other is not approaching faster than c. So yes, closing speed of two objects that are both moving in the frame where the measurement is being taken can be greater than c (but no greater than 2c)

Strictly, less than 2c.

(I have seen too many hardware and software bugs caused by using less/greater instead of less/greater-or-equal. Or vice-versa.)

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Strictly, less than 2c.

(I have seen too many hardware and software bugs caused by using less/greater instead of less/greater-or-equal. Or vice-versa.)

Yes, you are correct, and I should have caught that myself for similar reasons.
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Could I put it another way, if it were possible for an observer to position himself in the gap, from his perspective would the combined speed of the objects close to c close the gap at excess of c+?

Thank you!

The observer could measure the distance between the objects shrinking at >c. Note, however, that the rate of distance shrinkage isn't actually the velocity of anything. It's not even a velocity, though it does have the units of velocity. The objects themselves would measure each other to be moving at <c.

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The observer could measure the distance between the objects shrinking at >c. Note, however, that the rate of distance shrinkage isn't actually the velocity of anything. It's not even a velocity, though it does have the units of velocity. The objects themselves would measure each other to be moving at <c.

Thus in the real world the shrinking gap between the protons is a mathematical equation or construct.

What if, hypothetically we used mountains, instead of protons, then the observer could see one mountain approaching him at say 90% c and the other mountain also at 90% c The two mountains if they had the means to see each other, would still observe the other approaching at less than c (speed of light)

At this much larger scale a person could put himself between/middle of the two approaching mountains, at 90%c From his perceptive would the gap in which he has put himself shrink at greater than the speed of light or 180% c?

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At this much larger scale a person could put himself between/middle of the two approaching mountains, at 90%c From his perceptive would the gap in which he has put himself shrink at greater than the speed of light or 180% c?

Yes. (Although they wouldn't have much time to think about it!)

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Yes. (Although they wouldn't have much time to think about it!)

Yet paradoxically if he stood in the exact middle or path of the two approaching at mountains 90% light speed they would "crash" into him at a less than combined speed of light say 98% c?

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Yet paradoxically if he stood in the exact middle or path of the two approaching at mountains 90% light speed they would "crash" into him at a less than combined speed of light say 98% c?

No, that's a formula that applies in a different frame.

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No, that's a formula that applies in a different frame.

Then what happens to the person in the middle does the poor guy get hit with the force of two mountains crashing into him at 180% c?

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Then what happens to the person in the middle does the poor guy get hit with the force of two mountains crashing into him at 180% c?

Yes.

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Yes.

Although you have more than 32,000 posts in this forum I do not believe you? However, I will research it futher.

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Then what happens to the person in the middle does the poor guy get hit with the force of two mountains crashing into him at 180% c?

Yes.

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Although you have more than 32,000 posts in this forum I do not believe you? However, I will research it futher.

What if you had 4 mountains each with half the mass, or 20 mountains, each with 1/10 of the mass, moving slower such that the momentum is the same?

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What if you had 4 mountains each with half the mass, or 20 mountains, each with 1/10 of the mass, moving slower such that the momentum is the same?

Yes but we are talking near c light speed, which according to that dear old fella Albert Einstein, as far as I know, can never be succeeded from any vantage Point?

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Yes but we are talking near c light speed, which according to that dear old fella Albert Einstein, as far as I know, can never be succeeded from any vantage Point?

And what object is exceeding c, from the target's frame?

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Yes but we are talking near c light speed, which according to that dear old fella Albert Einstein, as far as I know, can never be succeeded from any vantage Point?

'Closing speed' is not the velocity of any single object in the scenario, therefore nothing is violated, but is actually an artifact* of combining the measurements of two objects.

* Artifact - something observed in a scientific investigation or experiment that is not naturally present but occurs as a result of the preparative or investigative procedure.

Edited by StringJunky

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