Is it Possible to Travel Faster than the Speed of Light?

[Mentz114]

But now there is where things seem to get a little confusing. The distance of 2 Ls between us got reduced to 0 in only 1.333 secs. That means that he traveled a 2Ls distance toward me in only 1.333 secs. That is 1.5 times the speed of light.

No, your twin only traveled 1Ls, because you meet at the sign. So you calculate that both of you traveled at 0.75c.

How did you double the distance traveled ?

This is how it looks from the sign's frame. This diagram is accurately to scale. You can read off distances and times and work out the time on your clock T² = t² - x² and divide by distance to get 0.96 !

 

[James S Saint]

OK, so what's the big issue? In the ground frame, the ships close at 1.5c. So?

Note that that says nothing about the relative speed of the ships when they are moving. If you wanted that speed, you can calculate it to be 0.96c.

What it says, because there are no "ground observers" (no absolute frame), the OBSERVED speed by the only observers present is 1.5c. Thus in the scenario pointed out, the observers, the travelers, would "see", by their measurements, that one of them traveled at 1.5c.

THAT is relevant.

The theory is that no such observation, measurement, could ever be made. "No observer will measure anything traveling faster than light."

But there is an even greater consequence.

 

[James S Saint]

No,
your twin only traveled 1Ls, because you meet at the sign. So you calculate that both of you traveled at 0.75.

How did you double the distance traveled ?

I am measuring the distance between the two travelers. Later in the thread, I removed the ground from the story all together leaving the only observers seeing only each other and thus measuring only that in 1.333 secs, a distance of 2Ls vanished. Thus they would measure 1.5c

 

[Tomsk]

The INITIAL frame, which is also the FINAL frame. It is in that frame that both measurements, both initial and final time and distance, get measured by both parties.

You have taken a distance measurement and time measurement (2ls and 1.333s) in one frame (the ground frame, which you're now trying to forget) and assuming those distances and times are the same in other frames (the traveler's frame and his brother's). This is not true.

there are no "ground observers" (no absolute frame)

Having no ground observers is completely different to having no absolute frame. The ground is a perfectly valid reference frame, it's not absolute.

 

[espen180]

What it says, because there are no "ground observers" (no absolute frame), the OBSERVED speed by the only observers present is 1.5c. Thus in the scenario pointed out, the observers, the travelers, would "see", by their measurements, that one of them traveled at 1.5c.

Nope. As has been explained, that's not the case.

 

[Doc Al]

What it says, because there are no "ground observers" (no absolute frame), the OBSERVED speed by the only observers present is 1.5c.

Again that's the closing speed only in the ground frame!

Thus in the scenario pointed out, the observers, the travelers, would "see", by their measurements, that one of them traveled at 1.5c.

Nope! If they used measurement made while they were moving, they would measure their relative speed as 0.96c. If they just use the measurements made in the ground frame, their closing speed would be 1.5c. In no frame is anything moving greater than c.

The theory is that no such observation, measurement, could ever be made. "No observer will measure anything traveling faster than light."

Given the statements you've made in this thread, I don't think you're in a position to tell us what relativity says.

But there is an even greater consequence.

Beware: Garbage in = garbage out.

 

[Mentz114]

I am measuring the distance between the two travelers. Later in the thread, I removed the ground from the story all together leaving the only observers seeing only each other and thus measuring only that in 1.333 secs, a distance of 2Ls vanished. Thus they would measure 1.5c

See the diagram I added. I think you are still miscalculating it by mixing frames.

 

[James S Saint]

Again only in the ground frame!

They are BOTH in the ground frame when they take their measurements.

If they used measurement made while they were moving, they would measure their relative speed as 0.96c.

But they didn't

If they just use the measurements made in the ground frame, their closing speed would be 1.5c. In no frame is anything moving greater than c.

Those two statements are contradictory. In the ground frame where they made their measurements, they measured 1.5c (not supposed to be possible). But then you said, "In no frame is anything moving greater than c.".

Make up your mind.

 

[Borg]

Well, this has been fun. I've got to go for now but, I'm definitely going to check back to see if:

A. My question from post 76 ever gets answered.
B. The thread gets locked.
C. James gets banned.
D. B and C.

 

[espen180]

But they didn't

They did. You just can't/won't realize it.

Those two statements are contradictory. In the ground frame where they made their measurements, they measured 1.5c (not supposed to be possible). But then you said, "In no frame is anything moving greater than c.".

Make up your mind.

Closing speed =/= velocity

 

[James S Saint]

See the diagram I added. I think you are still miscalculating it by mixing frames.

I think you missed my last point. There are only two measurements (now). There is a distance of 2Ls between two people. 1.333 secs later, there is no distance between them. To both of those people, the distance between them vanished in only 1.333 secs yet they both know tht light could have only traveled that distance in 2 secs.

From their perspective, one of them traveled at 1.5c.

 

[Doc Al]

They are BOTH in the ground frame when they take their measurements.

OK, then you admit that measurements are being made in the ground frame. Good!

Those two statements are contradictory. In the ground frame where they made their measurements, they measured 1.5c (not supposed to be possible). But then you said, "In no frame is anything moving greater than c.".

Make up your mind.

In the ground frame, the closing speed is 1.5c. That's obviously not the speed of the ships! That was given as 0.75c. Or have you forgotten already?

Please tell us what frame measures the speed of a ship to be 1.5c? Answer: No frame does!

 

[Austin0]

I am measuring the distance between the two travelers. Later in the thread, I removed the ground from the story all together leaving the only observers seeing only each other and thus measuring only that in 1.333 secs, a distance of 2Ls vanished. Thus they would measure 1.5c

If you understand logic then you must understand the limitations of abstractions.
Your assumption of 1.5 c is an abstraction based on a concept of distance /time that has no physical meaning. In any frame. No entity travels from your intial point to the other initial point i.e. 2 ls
It is no different that the faster than c sweep of a laser dot which also has no physical meaning because no single entity actually traverses the distance from the first point to the last.

 

[Bussani]

I'm just wondering if you're trolling everyone at this point. You're saying yourself that all your measurements are made from the ground's frame--that is, when everything is standing still before the experiment. You've been told again and again that from the ground's frame--from those measurements you took--you can conclude that the closing speed was 1.5c. You seem to think that means something, but it doesn't. All you've done is closed your eyes through part of the experiment, looked at the results from the ground's point of view, and come to the incorrect conclusion that one of you moved faster than light. This isn't what relativity talks about at all.

 

[James S Saint]

In the ground frame, the closing speed is 1.5c. That's obviously not the speed of the ships!

Not obvious to whom?? The only observers measure 1.5c.

That was given as 0.75c. Or have you forgotten already?

That was the reality. But from that reality, we get the only observers seeing a 1.5c speed. There is no observer who stands on any ground and watches the event so as to tell the travelers how fast they were going.

Please tell us what frame measures the speed of a ship to be 1.5c? Answer: No frame does!

You JUST said yourself that the 1.5c is measured from the ground frame!? "In the ground frame, the closing speed is 1.5c." == 1.5c as seen by the ONLY observers.

 

[Mentz114]

I think you missed my last point. There are only two measurements (now). There is a distance of 2Ls between two people. 1.333 secs later, there is no distance between them. To both of those people, the distance between them vanished in only 1.333 secs yet they both know tht light could have only traveled that distance in 2 secs.

From their perspective, one of them traveled at 1.5c.

The diagram is never wrong. Here it is from your frame. You calculate your twin's speed to be ~10.1/10.5 = 0.96, which is close enough considering the read-off error.

 

[Borek]

Closing speed is NOT A REAL SPEED OF ANY OBJECT.

 

[Doc Al]

Not obvious to whom?? The only observers measure 1.5c.

No. The ground observers measure the speeds of the ships as 0.75c.

That was the reality. But from that reality, we get the only observers seeing a 1.5c speed. There is no observer who stands on any ground and watches the event so as to tell the travelers how fast they were going.

Huh? You started this thread by saying that the ships both moved at 0.75c with respect to the ground!

You JUST said yourself that the 1.5c is measured from the ground frame!? "In the ground frame, the closing speed is 1.5c." == 1.5c as seen by the ONLY observers.

Yes, it's a closing speed. It is not the speed of the ships with respect to any frame. It just measures how quickly they close the distance according to ground observers.

Nothing is moving at that speed!

 

[James S Saint]

If you understand logic then you must understand the limitations of abstractions.
Your assumption of 1.5 c is an abstraction based on a concept of distance /time that has no physical meaning. In any frame. No entity travels from your intial point to the other initial point i.e. 2 ls
It is no different that the faster than c sweep of a laser dot which also has no physical meaning because no single entity actually traverses the distance from the first point to the last.

The theory concerns the ability to observe anything travleing faster than light. It is irrelevant as to whether anything actually was with respect to some absolute frame, because it is accepted that no absolute frame exists.

The ONLY frames that have any observer are the travelers. But the travelers make no measurement as they travel, they merely measure before and after and conclude a speed of 1.5c. There is no one else there to tell them how it occurred, thus THEY must perceive a 1.5c occurrence.

 

[jcsd]

Not obvious to whom?? The only observers measure 1.5c.


That was the reality. But from that reality, we get the only observers seeing a 1.5c speed. There is no observer who stands on any ground and watches the event so as to tell the travelers how fast they were going.


You JUST said yourself that the 1.5c is measured from the ground frame!? "In the ground frame, the closing speed is 1.5c." == 1.5c as seen by the ONLY observers.

But when you revert to their frames, their relative speeds are less than c. If there was no obserevr on the ground then no-one observes their closing speed to be 1.5 c.

What you're saying would be valid (well not valid, but in some way correct) for Gallilean relativity, but it just doesn't work that way for special relativity.

 

[James S Saint]

Yes, it's a closing speed. It is not the speed of the ships with respect to any frame. It just measures how quickly they close the distance according to ground observers.

How fast a distance closes IS the speed.

 

[Bussani]

the travelers make no measurement as they travel

Which is exactly why you're getting a result according to the ground frame, where the closing distance is allowed to be 1.5c. If you come to the conclusion that someone moved faster than c from that then it's your own fault for using measurements from one frame in a different frame.

 

[Doc Al]

The theory concerns the ability to observe anything travleing faster than light.

Right. And nothing does.

For some reason, you seem desperate to conclude that somehow that proscription has been violated by your ships. Not so.

I can only suspect some hidden 'philosophical' agenda.

 

[jcsd]

How fast a distance closes IS the speed.

Only when one object is stationary, but when you choose a frame when one of the objects is stationary their closing speed is less than c.

 

[Passionflower]

If I understand James S Saint's 'logic' correctly he thinks that if an ultra-relativistic rocket reaches a star system 10 million light years away in one year on the rocket's clock the rocket's speed must have been 10 times the speed of light. If so, he clearly does not properly understand time dilation and length contraction.

 

[Mentz114]

The theory concerns the ability to observe anything travleing faster than light.

If you want to know about traveling faster than light read this, it's accessable and accurate.

"The Rindler Horizon", by Greg Egan.
http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

 

[jcsd]

Thing to note here is that closing speed is invariant in gallielean relativity in inertial frames, but not in special relatvity, that's one of the many differences.

 

[James S Saint]

But when you revert to their frames, their relative speeds are less than c.

Only IF there was someone watching them travel. There wasn't. They have no way to know which of them traveled or how fast except to surmise that one had to be going faster than light to get to the other in 1.333secs.

If there was no obserevr on the ground then no-one observes their closing speed to be 1.5 c.

THEY measured, from the "ground" (initial frame) a distance of 2Ls and a time (0). After the event, THEY measured a distance of 0 and a time of 1.333secs. Thus THEY both measured a distance of 2Ls reduced to 0 in 1.333 secs.

 

[James S Saint]

Only when one object is stationary, but when you choose a frame when one of the objects is stationary their closing speed is less than c.

From the frame of either observer, the distance of 2Ls vanished in 1.333secs = 1.5c

There is no "stationary".

 

[Doc Al]

From the frame of either observer, the distance of 2Ls vanished in 1.333secs = 1.5c

From the ground frame only, the closing speed is 1.5c.

You are switching frames all over the place.

 

[James S Saint]

If I understand James S Saint's 'logic' correctly he thinks that if an ultra-relativistic rocket reaches a star system 10 million light years away in one year on the rocket's clock the rocket's speed must have been 10 times the speed of light. If so, he clearly does not properly understand time dilation and length contraction.

The time dilation involved at merely .75c is minuscule to the 1.5c measurement realized. Neither travelers clock would slow by 25%.

 

[James S Saint]

Thing to note here is that closing speed is invariant in gallielean relativity in inertial frames, but not in special relatvity, that's one of the many differences.

"Closing speed" is the ONLY speed there is unless you accept an absolute frame.

 

[jcsd]

Only IF there was someone watching them travel. There wasn't. They have no way to know which of them traveled or how fast except to surmise that one had to be going faster than light to get to the other in 1.333secs.


THEY measured, from the "ground" (initial frame) a distance of 2Ls and a time (0). After the event, THEY measured a distance of 0 and a time of 1.333secs. Thus THEY both measured a distance of 2Ls reduced to 0 in 1.333 secs.

Stick to measurements tkaen in the same frame. The distance and time measured byu a gorund based observer is not the distance and time measured by our two traveling observers.

Relatvity is specifically constructed so that an object traveling at c travels at c in all inertial frames. One of the side effects of this is that objects traveling at less than c in some inertial frame always appear to be traveling at less than c in all other inertial frames.

 

[Tomsk]

THEY measured, from the "ground" (initial frame) a distance of 2Ls and a time (0). After the event, THEY measured a distance of 0 and a time of 1.333secs. Thus THEY both measured a distance of 2Ls reduced to 0 in 1.333 secs.

They have to BOTH have been stationary in the ground frame in order to make that initial measurement. In order to reach 0 distance in 1.333 seconds, they both have to have traveled towards each other. This means they BOTH ACCELERATED. Acceleration is absolute in special relativity. The only way for them to meet up in 1.333s is to both accelerate- which they can objectively measure.

 

[jcsd]

"Closing speed" is the ONLY speed there is.

No when we talk about speed we usually mean dx/dt in some (let's assume inertial) cooridnate system and that is the speed we're talking about when we say it can't exceed the speed of light. If we use another definition of speed we may find what we have previously said not to be true about that definition which is what you're doing.