Alpha Centauri to Earth: Apparent Speed > c?

[clamtrox]

Suppose I'm at my spacecraft orbiting Alpha Centauri. Then I speed up to v/c = 0.999 towards Earth. In my new coordinate system the distance between A.C. and Earth is shrunk by the usual Lorentz transformation formula, and the time it takes (in my coordinate system) to travel is this new distance (4ly/22 or whatever) divided by 0.999c.

However, my mate observing at Earth sees my spacecraft just sit there for a while until one day it apparently accelerates to 22c. My mate measures the time the spacecraft apparently takes to travel from A.C. to Earth, and gets the same answer as I do (4ly/(22*0.999c)). Am I correct?

 

[Nabeshin]

Where did the 22 come from?

 

[clamtrox]

$\gamma = \frac{1}{\sqrt{1-(v/c)^2}} \simeq 22$

In the second case, you have the rocket traveling in the Earth reference frame for ~4 years until the photons from the boost reach Earth, at which time the rocket starts moving towards Earth according to my mate. In this frame, the rocket takes only a little more than 4 years to reach Earth, so according to him, the rocket must have moved at a speed of
$v = \frac{\Delta x}{\Delta t}.$
Now that I think of it, I guess the apparent speed ought to be more like 22^2 c.

 

[Fredrik]

However, my mate observing at Earth sees my spacecraft just sit there for a while until one day it apparently accelerates to 22c.

Not really. You have already said that the speed in this frame is 0.999c:

Suppose I'm at my spacecraft orbiting Alpha Centauri. Then I speed up to v/c = 0.999 towards Earth.

Make up your mind.

 

[clamtrox]

Not really. You have already said that the speed in this frame is 0.999c:

Hence the word "apparently". So, let's elaborate: suppose that the spacecraft is big enough that you can measure the distance to it by trigonometry (you also know the size). Now, the observer here at Earth sees the ship start to move from it's location at Alpha Centauri. A few months later, the ship arrives here. It has apparently moved faster than the speed of light (suppose our observer knows nothing about relativity, or assumes that the speed of light is infinite).

Then, suppose the spaceship has a gigantic clock on it. The observer from Earth would see the clock running faster when the spaceship approaches Earth due to the same apparent effect.

I'm not trying to overthrow physics here, I'm just trying to explain why the effect that the clock is running faster isn't weird at all.

 

[ZikZak]

No. In the frame of the Earth, the speed is 0.9999c and the trip takes 4 years.

 

[clamtrox]

No. In the frame of the Earth, the speed is 0.9999c and the trip takes 4 years.

This is obviously true, and not what I asked. I asked what it looked like from Earth, and the time difference you observe between leaving Alpha Centauri and arriving at Earth in the Earth coordinates is not 4 years.

 

[Doc Al]

This is obviously true, and not what I asked. I asked what it looked like from Earth, and the time difference you observe between leaving Alpha Centauri and arriving at Earth in the Earth coordinates is not 4 years.

What ZikZak described is what you observe from Earth. Something traveling at almost the speed of light and taking four years to traverse the distance.

What you are trying to describe is how a spacecraft traveling at great speed with respect to the Earth could travel great distances as measured from earth in much less time as measured in the spacecraft . True enough. And if you mixed frames and divided the distance in the Earth frame by the time in the spacecraft frame you'd get a quantity that could well be greater than c. (But it's not really the speed of anything.)

 

[DrGreg]

clamtrox is talking about what the person on Earth sees with their eyes, not what they calculate in their coordinates. The time that elapses on Earth between the observer seeing the image of the spaceship departing and the ship's arrival will much shorter than 4 years.

This is related to the transit time as measured by the ship by the Doppler factor

$$\sqrt{\frac{1+v/c}{1-v/c}}$$​

which differs from the time dilation factor

$$\frac{1}{\sqrt{1-v^2/c^2}}$$​

The point is that if you measure the Doppler factor by observation, then calculate the time it took for the light to reach you and make allowance for that, the final answer you get is the time dilation factor.

 

[clamtrox]

Jeez, thanks for setting me straight. I can be pretty stubborn when I get a stupid idea. :-) I just found it weird that the situation would be so unsymmetric between the two reference frames.

 

[Doc Al]

clamtrox is talking about what the person on Earth sees with their eyes, not what they calculate in their coordinates. The time that elapses on Earth between the observer seeing the image of the spaceship departing and the ship's arrival will much shorter than 4 years.

Indeed. If that's what clamtrox meant by "apparent speed" then that will be about 1000c, not just 22c.

 

[Phrak]

More, the apparent speed of light, under this definition of 'apparent speed', would be infinite.

 

[GoodPR]

What you are trying to describe is how a spacecraft traveling at great speed with respect to the Earth could travel great distances as measured from earth in much less time as measured in the spacecraft . True enough. And if you mixed frames and divided the distance in the Earth frame by the time in the spacecraft frame you'd get a quantity that could well be greater than c. (But it's not really the speed of anything.)

Thats what I don't get, you say it's not the speed of anything yet, clearly if you wanted to measure how long it would take a traveller to get somewhere far at a certain speed in his time, that's how you would do it. It would provide an incredible speed, it may not be able to be compared to other speeds, but it is still his speed realistically. He could even tell the aliens how long it took to get there, proving he traveled faster than light.
Yes we know that it was distance that shrank instead of him moving faster than light, but that's just semantics.

You could have faster than light one way communication using light also. Imagine a traveller going to that alpha centurai as mentioned before. Let's say it takes him 4 years of his time to get there. If Earth started sending communications from the point when he left, when he arrived there he would be receiving communications from Earth that are current, to him.

 

[Doc Al]

Thats what I don't get, you say it's not the speed of anything yet, clearly if you wanted to measure how long it would take a traveller to get somewhere far at a certain speed in his time, that's how you would do it.

OK.

It would provide an incredible speed, it may not be able to be compared to other speeds, but it is still his speed realistically. He could even tell the aliens how long it took to get there, proving he traveled faster than light.
Yes we know that it was distance that shrank instead of him moving faster than light, but that's just semantics.

It's not "just semantics". The speed of something with respect to a frame is well-defined. Using that standard definition, there's nothing moving faster than light in this scenario.

You could have faster than light one way communication using light also. Imagine a traveller going to that alpha centurai as mentioned before. Let's say it takes him 4 years of his time to get there. If Earth started sending communications from the point when he left, when he arrived there he would be receiving communications from Earth that are current, to him.

How is this an example of faster than light communication?

 

[GoodPR]

semantics: "The meaning or the interpretation of a word, sentence, or other language form: We're basically agreed; let's not quibble over semantics."

There for when the rocketeer gets to the aliens he could say he traveled faster than light to make it there in 4 years. The difference between what he means and what you mean by faster than light, is semantics.

 

[Doc Al]

There for when the rocketeer gets to the aliens he could say he traveled faster than light to make it there in 4 years.

And that will puzzle them a bit and prompt them to ask the rocketeer to explain why he thinks he must "travel faster than light" to make it there in 4 years.

The difference between what he means and what you mean by faster than light, is semantics.

If you want to talk and be understood, especially when discussing relativity, you'd better not misuse terms that already have established meanings.

If you really think it's "just semantics" then you should have no problem using the standard terminology. Right?

 

[russ_watters]

I need to tell my bank "its just semantics" when I add a couple of zeroes to my paycheck!

 

[GoodPR]

It's sad that you both feel the need to discredit such a true statement. If I want to calculate rocket trajectories, I need to know relativity. If I want to tell my buddy bob the alien how fast I got there I just tell him it took me four years to get there, if bob felt like it he could say okay that's a thousand light years away so you must have went like 300 times the speed of light, If bob was a rocket scientist then he can go figure out my relative speed if he wants.
Like, seriously guys, your all so negative even to each other. You spend the bulk of all your time here criticizing each other, like children.

I made a statement it's semantics, and there's three or four posts of your opinions against that, what a useless thing to argue against. You guys are all so brilliant you should spend more of your time working together, helping each other on projects, what a powerful network this could be for those of you intellectually gifted. You guys could truly create some incredible experiment ideas, then approach billionaires who might want to do them, then you would be controlling your own scientific study fitting what you want to do instead of your boss deciding.
GO TEAM SCIENCE

 

[matheinste]

Hello all.

Some open questions. How do we measure our velocity with respect to another object.

If the questioner used this method to measure his defined speed for the proposed scenario should he have also used the same method for measuring his speed traveled for the journey.

By using the method he used to get the measurements he uses to calculate the speed during the journey, would he perhaps have had a defined speed for the scenario of greater than c.

Is it not the case that in this scenario the two methods used are not the same for both speeds.

Matheinste.

 

[ZikZak]

Like, seriously guys, your all so negative even to each other. You spend the bulk of all your time here criticizing each other, like children.

Critique IS science. Correction and skepticism ARE science.

I made a statement it's semantics, and there's three or four posts of your opinions against that, what a useless thing to argue against. You guys are all so brilliant you should spend more of your time working together...

What do you think criticism IS, other than "working together?" When someone makes a claim, everyone else reviews and critiques it, in light of known empirical data, to ensure that the claim and the data are consistent with each other. That is what science is. If you don't like it, perhaps you shouldn't be a scientist then. Perhaps you would make a good philosopher.