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## When accelerating at high %c, can apparent velocites exceed c?

Hi, jartsa,

Thanks for helping out. I very much appreciate it.
 Quote by jartsa Let's consider a spaceship with constant proper acceleration. Accelerometers and clocks don't care anything about "motion" caused by Lorentz contraction.
Makes sense.
 Same is true for a device that measures relativistic Doppler shift.
By "relativistic," you mean that as my Target "accelerates" toward me, length compression compresses waves emitted or reflected by the Target toward me, which would raise their frequency except they are exactly compensated for by time dilation? Thus I see no Doppler changes from Lorentz effects? Is that correct?
 Also an observer that was left standing on the launch pad does not observe Lorentz contraction. These three things have the same opinion about the velocity of the spacesip.
The three things being 1) the onboard accelerometer and clock, 2) onboard Doppler toward the target, and 3) an Observer that is not on the Rocket -- but could be on the Target?
 (if we ask the guy standing on the launch pad: "what velocity does a person on the spaceship obtain, using his clock", he will answer: "on the spaceship the motion of the clock hand slowed down, while on the launch pad the motion of the hand of the velocity meter measuring the speed of the spaceship slowed down, so the velocity obtained using the onboard clock happens to be the real velocity, the same velocity that I am observing")
I think I get that, and it's something I hadn't thought of, but I think it might be a red herring here. I fear it's my inexperience in asking these kinds of questions that's causing the problem.

For now I want to eliminate the Observer on Earth and deal only with Observers on the Rocket and Target.

Initially, Rocket has a fixed relative velocity toward Target. This has occurred long enough that Target, observing Rocket, sees the same velocity. The situation is symmetric as each observer sees the same thing -- the other moving directly toward them at the same rate. There are no other objects (Earth, background stars, etc).

I believe both objects can be said to share the same inertial frame. They will also see the same Doppler. Their accelerometers read zero. Their clocks remain synchonized as far as each's ability to read the other's. Distance and velocity measurements to the other using parallax, subtended angle, or visual magnitude are identical. In other words, I'm trying to zero out as many things as possible, including eliminating all other objects besides Rocket, Target, and their measuring apparatuses (apparati? ;-) ).

Rocket accelerates.

This "breaks" the inertial frame into two(?). Rocket sees instantaneous changes in accelerometer, Doppler, and distance measurements. Target will see these later.

There are a lot of relativistic effects -- distance compression, angular compression, time dilation, optical abberation et al -- and many of these effects cancel out with respect to Rocket at constant velocity or constant acceleration, and some do not.

So here's my question: How does Rocket know that what it observes using whatever measuring devices it has at it disposal, that any differences in what it measures which are at odds with Newtonian predictions, are due to relativistic effects, and are NOT due to coincidental motion changes initiated by Target?

[EDIT 2012-12-08 2036 I'm not trying to discredit Relativity, but find where it is (and isn't) symmetric between Rocket and Target.]

Thanks!
Chris

 Quote by BitWiz Hi, jartsa, By "relativistic," you mean that as my Target "accelerates" toward me, length compression compresses waves emitted or reflected by the Target toward me, which would raise their frequency except they are exactly compensated for by time dilation? Thus I see no Doppler changes from Lorentz effects? Is that correct?

Let me calculate "the relativistic Doppler shift" at speed 0.87 c, that might clarify some things.

A one light second long beam of light is absorbed into an object at rest. That takes one second. Now the object is accelerated to 0.87 c, now the same process takes 0.53 seconds (beam shrinks at pace 1.87 c, so the time for beam to disappear is 1/1.87 seconds)

Observer attached to the object says the absorbtion takes 0.27 seconds, because his clock runs at half speed.

So the frequency of the light is multiplied by 1/0.27 = 3.7
That is the relativistic Doppler shift.

The length of the light beam according to an observer sitting on the object is 0.27 light seconds. Is the beam Lorentz contracted or not, I don't know.

 The three things being 1) the onboard accelerometer and clock, 2) onboard Doppler toward the target, and 3) an Observer that is not on the Rocket -- but could be on the Target?
Yes.

 For now I want to eliminate the Observer on Earth and deal only with Observers on the Rocket and Target. Initially, Rocket has a fixed relative velocity toward Target. This has occurred long enough that Target, observing Rocket, sees the same velocity. The situation is symmetric as each observer sees the same thing -- the other moving directly toward them at the same rate. There are no other objects (Earth, background stars, etc). I believe both objects can be said to share the same inertial frame. They will also see the same Doppler. Their accelerometers read zero. Their clocks remain synchonized as far as each's ability to read the other's. Distance and velocity measurements to the other using parallax, subtended angle, or visual magnitude are identical. In other words, I'm trying to zero out as many things as possible, including eliminating all other objects besides Rocket, Target, and their measuring apparatuses (apparati? ;-) ). Rocket accelerates. This "breaks" the inertial frame into two(?). Rocket sees instantaneous changes in accelerometer, Doppler, and distance measurements. Target will see these later. There are a lot of relativistic effects -- distance compression, angular compression, time dilation, optical abberation et al -- and many of these effects cancel out with respect to Rocket at constant velocity or constant acceleration, and some do not. So here's my question: How does Rocket know that what it observes using whatever measuring devices it has at it disposal, that any differences in what it measures which are at odds with Newtonian predictions, are due to relativistic effects, and are NOT due to coincidental motion changes initiated by Target?

If the person on the rocket pays attention to the accelerometer, then he knows if the change of relative velocity between the rocket and the target was caused by the acceleration of the rocket or the acceleration of the target.

If he does not pay attention, then he does not know.

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 Quote by jartsa Let me calculate "the relativistic Doppler shift" at speed 0.87 c, that might clarify some things. A one light second long beam of light is absorbed into an object at rest. That takes one second. Now the object is accelerated to 0.87 c, now the same process takes 0.53 seconds (beam shrinks at pace 1.87 c, so the time for beam to disappear is 1/1.87 seconds) Observer attached to the object says the absorbtion takes 0.27 seconds, because his clock runs at half speed. So the frequency of the light is multiplied by 1/0.27 = 3.7 That is the relativistic Doppler shift. length of the light beam according to an observer sitting on the object is 0.27 light seconds. Is the beam Lorentz contracted or not, I don't know.
Thanks for this, jartsa. I've copied it to my working notes.
 If the person on the rocket pays attention to the accelerometer, then he knows if the change of relative velocity between the rocket and the target was caused by the acceleration of the rocket or the acceleration of the target. If he does not pay attention, then he does not know.
I'm still not asking this right. Are there any circumstances where a single observer accelerating toward an object, and who has access to competent measuring instruments, cannot tell by how much (if any) that object is (constant) accelerating toward the observer? In other words, can relativistic effects obscure observer's measurements or make them ambiguous regarding the true state of the object's acceleration?

Again, I'm trying to simplify by stating that only observer, his instruments, and object exist in gravity-free spacetime. There are no background stars and no other observers. The history of object and observer prior to the measurements is arbitrary. Whether or not the object subtends a measurable angle is also arbitrary. Please simplify this further if there's a way.

The reason I'm asking is that there are effects that can cause false readings, but which can be corrected for by other measurements. For instance, speed can cause a star that is perpendicular to my heading to appear in front of me, but its Doppler will give me its true angular position.

But in this situation, I do not have background stars and the object is directly in front of me. If the object does not subtend a measureable angle, that probably eliminates the Terrell and headlight effects, but that might presume I know the object's true shape and brightness. I seem to be left with length compression, but I'm not sure.

What is the minimum I need to know, either instantly or over time, to determine the object's true distance and acceleration while I am accelerating toward it?

Chris

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 Quote by BitWiz But in this situation, I do not have background stars and the object is directly in front of me. If the object does not subtend a measureable angle, that probably eliminates the Terrell and headlight effects, but that might presume I know the object's true shape and brightness. I seem to be left with length compression, but I'm not sure. What is the minimum I need to know, either instantly or over time, to determine the object's true distance and acceleration while I am accelerating toward it? Thanks again for your time! Chris
Directly in front will eliminate Terrell rotation, but not headlight effect.

True distance needs clarification - there really is no such thing. You have to say what you want: for example the distance that would be computed for a momentarily comoving inertial frame. Especially for an accelerated observer, there is not any particular strong reason to choose this definition, and some reasons not to. However, assuming this is what you want, and given your constraint the the object subtends no measurable angle and you don't know about its size or intrinsic brightness, you would need to be either bouncing signals off of it or have two detectors separated enough to detect parallax - you need some source of raw distance information.

So let's say you have two separated detectors attached to your rocket that can measure parallax to any needed precision. To get relative speed, the easiest raw information would be Doppler, assuming you know some natural frequency emitted by the source. If you don't, in principle, you could measure rate of change in parallax measurement. From either of these (parallax + Doppler; parallax over time), plus your own accelerometer measurements, you could, in principle, compute the distance and speed as they would be represented in a momentarily comoving inertial frame.

 Quote by BitWiz I'm still not asking this right. Are there any circumstances where a single observer accelerating toward an object, and who has access to competent measuring instruments, cannot tell by how much (if any) that object is (constant) accelerating toward the observer?
No, I guess. It's difficult to give any reasons.

Is the following correct, experts?

An observer that accelerates towards a galaxy sees a contracting galaxy, because different parts of the galaxy are at at different altitudes in the "pseudo gravityfield", that is caused by the acceleration.

The gravitational time dilation of the "pseudo gravityfield" causes different parts of the galaxy to move at different speeds, this is the reason for the contracting.

The observer sees the contraction happening, when light emitted by the contracting galaxy reaches him.

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Hi, PAllen. Thanks for the reply. Sorry to be tardy -- work took me away.
 Quote by PAllen Directly in front will eliminate Terrell rotation, but not headlight effect. True distance needs clarification - there really is no such thing. You have to say what you want: for example the distance that would be computed for a momentarily comoving inertial frame. Especially for an accelerated observer, there is not any particular strong reason to choose this definition, and some reasons not to. However, assuming this is what you want, and given your constraint the the object subtends no measurable angle and you don't know about its size or intrinsic brightness, you would need to be either bouncing signals off of it or have two detectors separated enough to detect parallax - you need some source of raw distance information. So let's say you have two separated detectors attached to your rocket that can measure parallax to any needed precision. To get relative speed, the easiest raw information would be Doppler, assuming you know some natural frequency emitted by the source. If you don't, in principle, you could measure rate of change in parallax measurement. From either of these (parallax + Doppler; parallax over time), plus your own accelerometer measurements, you could, in principle, compute the distance and speed as they would be represented in a momentarily comoving inertial frame.
Just to make sure I understand: There are two components that affect perceived/measured distance to the object. 1) is relative velocity (Vr) which can be measured by Doppler; 2) is (presumed) changes in Lorentz length compression (Vx) which cannot be measured by Doppler. Do I have that correct?

Further, parallax will see the total (Vt) of both elements such that Vx = Vt - Vr?

So my question involves Vx or presumed Lorentz which 1) I'm asking if this is a sum of changes in my own Lorentz (I'm accelerating) and by potential acceleration of the object toward me at a time in the past equivalent to our light-distance (local frame?), and if so 2) how I would sort out the values of those two components of Vx.

In other words, can the Object's acceleration toward me mimic some or all of my acceleration toward it such that I can't rely on my measurement or extrapolation of the object's distance?

Chris

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 Quote by jartsa No, I guess. It's difficult to give any reasons. Is the following correct, experts? An observer that accelerates towards a galaxy sees a contracting galaxy, because different parts of the galaxy are at at different altitudes in the "pseudo gravityfield", that is caused by the acceleration. The gravitational time dilation of the "pseudo gravityfield" causes different parts of the galaxy to move at different speeds, this is the reason for the contracting. The observer sees the contraction happening, when light emitted by the contracting galaxy reaches him.
Hi, jartsa, thanks for replying. I've had a work problem that's kept me from replying back sooner.

I think the Observer would see the galaxy contract right away as he "catches up" to light emitted more recently.

Anyway, I'm trying to take Tarrell and distortion out of the problem becase they would rely on a known configuration of the object. Similarly, headlight effects presume knowledge of absolute brightness, and with either small objects, large distances, and fast speeds -- all of which I believe are equivalent according to this kind of measurement -- fall apart as you approach the resolution of the apparatus until finally there is no effect at all. So if we can make this a point-like object, it takes some noise out of the problem.

I'm looking for a kind of "universal truth" here concerning relativity distance that is free of contrivance, and though I think I (now) understand it when velocities are fixed btween two objects, my understanding seems to fall apart during accelerations, primarily because I don't see a way of separating my own measured acceleration from the acceleration I observe from the other obejct versus length compression. I seem to have three unknowns and only two equivalences to work them out. If that is indeed he case, then there's a symmetry here that would be important to me.

Chris

 Quote by BitWiz I think the Observer would see the galaxy contract right away as he "catches up" to light emitted more recently.
I disagree, because I remember that I have taken a walk, looking at the stars, and I did not see any weird things happening, although I was bouncing (accelerating) slightly while walking.

What happens when acelerating towards a distant star is the following: A charge that is vibrating on the star starts to vibrate at ridiculous frequency, and light starts to move at equally ridiculous speed near the star.

We can conclude that the wavelength of the light that is produced by the aforementioned vibrating charge is "normal". The only "abnormal" thing about the light is the speed, which becomes "normal" when the acceleration stops.

So my conclusion is: No immediate weird visual effects, and no weird visual effects after a delay, when walking and looking at the stars.

EDIT: Let's consider what happens when the acceleration does not stop:

The light slows down when moving down in the "pseudo gravity field", this causes a shortening of the wavelength, analoguously to what happens when light enters a piece of glass. This is the blueshif effect.

And I guess this is the Lorentz contraction effect too.