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

[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.

 

[James S Saint]

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

You are switching frames all over the place.

I am not switching frames AT ALL. THERE IS NO OTHER FRAME involved. What other frame are you thinking of??

 

[jcsd]

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

There is no "stationary".

There is stationary when you're talking in the context of a single frame.

 

[Doc Al]

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

The 'time dilation' factor at 0.75c is about 1.5 (not minuscule), but it has nothing to do with the 1.5c closing speed. At .96c, the relative speed of the moving ships, the time dilation factor is even greater: about 3.6.

 

[Austin0]

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.

If the only measurements they make are before and after then the only measurements they actually have are there own times for their own travel from beginning to end. They have no observations of any kind regarding the other system while in motion. Therefore they can only derive their own velocity of .75c from actual observation.
You do understand that the observations from ground observers, if any , of 1.5 c closing speed has no physical meaning I hope?

 

[Doc Al]

I am not switching frames AT ALL. THERE IS NO OTHER FRAME involved. What other frame are you thinking of??

You seem to want to state that the speed of one ship in the moving frame of the other is somehow 1.5c. Not so.

If you stay in the ground frame, then there's no problem. The ships move at 0.75c and they close at 1.5c. Done!

 

[James S Saint]

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.

You seemed to have missed a point somewhere. The only measurements made are in the "initial/ground" frame.

The measurement is made of 2Ls at t(0), travel is made. When they meet, they stop and look at their clocks. Both clocks read that they traveled for 1.333secs.

All measurements are from the initial frame.

 

[Mentz114]

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

Wrong. Look at the diagram. The time elapsed on the worldline clock is simple to calculate.

 

[jcsd]

I am not switching frames AT ALL. THERE IS NO OTHER FRAME involved. What other frame are you thinking of??

There are 3 frames involved here, the ground frame and the frame of each observer. Don't let the symmetry of the situation fool you these are 3 very distinct frames.

 

[James S Saint]

You seem to want to state that the speed of one ship in the moving frame of the other is somehow 1.5c. Not so.

If you stay in the ground frame, then there's no problem. The ships move at 0.75c and they close at 1.5c. Done!

There is no measuring going on as they move. They take ALL measurements together at the beginning and end while they were not moving with respect to each other. Thus there is no frame changing involved in any measuring. But from the PERSPECTIVE of each, the other seems to have come to them at 1.5c.

 

[jcsd]

You seemed to have missed a point somewhere. The only measurements made are in the "initial/ground" frame.

The measurement is made of 2Ls at t(0), travel is made. When they meet, they stop and look at their clocks. Both clocks read that they traveled for 1.333secs.

All measurements are from the initial frame.

Okay, but in the ground frame, neither of the travellers is traveling at greater than c. We started by specifying that each was traveling at 0.75 C in opposite directions in that frame.

We cannot apply measurements made in one frame to another, so in order to work out what was going on in the other frames we'd either need to take new measurements in those frames or alternatively use the Lorentz transformation to convert our previous measurements into the other frames. And lo and behold when we do this we find that neither traveller obserevrs the other traveling at greater than c.