Conceptual basis for a non-relative rest frame

[Austin0]

This concept would be dependant on having the technology to actually travel at velocities which we can now, only impart to particles Ie: .99c
The plan would be to have 3 ships somewhere in space with negligable gravitational effect.
2 of the ships set out in opposite directions along an arbitrary vector. When they have achieved maximum possible velocity they transmit an agreed frequency back to the base ship. This ship checks they relative doppler shift of the 2 signals and adjusts its velocity along the same vector to reach a point where the shift in both signals is equal.
Would we not be able to say that along that vector the ship was at rest in an absolute sense? Not relative to the velocity of any object in the cosmos but in relation to the only absolute , the speed of light. By repeating this procedure in 2 more orthogonal vectors we could achieve a state of rest relative to all directions.
I realize there is a degree of indefiniteness in the assumption that both ships would achieve the same velocity as well as the problem of determining exactly how close to c they arrive at , but the first question could be addressed by having the ships switch places for a second , error-correcting run along each vector.
As for the problem of determining the actual final velocity , that in a way, may not be that critical. Whatever it might be, it can in a sense be considered absolute. Not that any numeral value could be assigned but because it would be independant of any relative referent
and would be dependant only on its inherent conditions ; inertial mass, energy, propulsion system etc. and their relation to the physics of space itself. On this basis there would seem to be some justification for assuming the final attainable velocity in any direction would be equal to that attainable in any other direction in an absolute sense.
This just occurred to me so I thought I would toss it out there and see what ensues.

 

[HallsofIvy]

This concept would be dependant on having the technology to actually travel at velocities which we can now, only impart to particles Ie: .99c
The plan would be to have 3 ships somewhere in space with negligable gravitational effect.
2 of the ships set out in opposite directions along an arbitrary vector. When they have achieved maximum possible velocity they transmit an agreed frequency back to the base ship. This ship checks they relative doppler shift of the 2 signals and adjusts its velocity along the same vector to reach a point where the shift in both signals is equal.
Would we not be able to say that along that vector the ship was at rest in an absolute sense? Not relative to the velocity of any object in the cosmos but in relation to the only absolute , the speed of light.

I have no idea what you mean by "relative to the speed of light". The speed of light relative to any object is c.

By repeating this procedure in 2 more orthogonal vectors we could achieve a state of rest relative to all directions.
I realize there is a degree of indefiniteness in the assumption that both ships would achieve the same velocity as well as the problem of determining exactly how close to c they arrive at , but the first question could be addressed by having the ships switch places for a second , error-correcting run along each vector.
As for the problem of determining the actual final velocity , that in a way, may not be that critical. Whatever it might be, it can in a sense be considered absolute. Not that any numeral value could be assigned but because it would be independant of any relative referent
and would be dependant only on its inherent conditions ; inertial mass, energy, propulsion system etc. and their relation to the physics of space itself. On this basis there would seem to be some justification for assuming the final attainable velocity in any direction would be equal to that attainable in any other direction in an absolute sense.
This just occurred to me so I thought I would toss it out there and see what ensues.

 

[matheinste]

Hello Austin0

There is no way of determining whether or not the ships were both comoving before they separated.

Matheinste.

 

[Fredrik]

2 of the ships set out in opposite directions along an arbitrary vector. When they have achieved maximum possible velocity they transmit an agreed frequency back to the base ship. This ship checks they relative doppler shift of the 2 signals and adjusts its velocity along the same vector to reach a point where the shift in both signals is equal.
Would we not be able to say that along that vector the ship was at rest in an absolute sense? Not relative to the velocity of any object in the cosmos but in relation to the only absolute , the speed of light.

There are several problems with this argument. They won't ever reach a maximum velocity because there's no such thing as a maximum velocity. c is the least upper bound on the set of possible speeds, but c isn't in that set. And even if there was a maximum velocity, the rockets would have other velocities in other frames.

 

[Dale]

I realize there is a degree of indefiniteness in the assumption that both ships would achieve the same velocity as

That is exactly the problem. If the ships are labeled S1, S2, and S3, and if S2 measures a Doppler factor of 13.1 from both S1 and S3 then that could be explained by S2 being at rest, S1 moving at -.99c, and S2 moving at .99c. However, it could just as well be explained by S1 being at rest, S2 moving at .99c, and S3 moving at .99995c. In fact, there are an infinite number of combinations of velocities that would all satisfy the same Doppler shift scenario.

 

[Saw]

there are an infinite number of combinations of velocities that would all satisfy the same Doppler shift scenario.

Incidentally: When you say an "infinite number of velocities", I understand you mean "velocities" with regard to a hypothetical frame in absolute rest, i.e., a medium for light propagation, if it existed. However, am I right if I assume that if two observers measure the Doppler shift with regard to each other (by sending light signals and observing the frequency shift when they return), they will perceive the same Doppler shift and hence they will calculate that they have, relative to each other, the same relative velocity?

 

[HallsofIvy]

I don't know what you mean by this. There is NO "frame in absolute rest", not even hypothetically. There is no "medium for light propogation" because if there were, objects moving relative to it would see different speeds of light and that doesn't happen. If A measures the speed of B relative to himself and B mearsures the speed of A relative to himself, they will always[/] find the same relative speed (and opposite relataive velocities, of course).

 

[Dale]

am I right if I assume that if two observers measure the Doppler shift with regard to each other (by sending light signals and observing the frequency shift when they return), they will perceive the same Doppler shift and hence they will calculate that they have, relative to each other, the same relative velocity?

Yes.

Incidentally: When you say an "infinite number of velocities", I understand you mean "velocities" with regard to a hypothetical frame in absolute rest, i.e., a medium for light propagation, if it existed.

I wouldn't say it that way; I would interpret it as an infinite number of reference frames in which you can describe the same experiment (one reference frame for each velocity). However, when I wrote the above I was actually just referring to the math. If you use the general Doppler shift formula (last equation)

$$\frac{\nu _a}{\nu _e}=\frac{ 1-\cos \left(\theta _v\right)\frac{ \|v\|}{c}}{1-\cos \left(\theta _u\right)\frac{ \|u\|}{c}} \sqrt{\frac{1-\frac{u^2}{c^2}}{1-\frac{v^2}{c^2}}}$$

and if the Doppler shift and the geometry are known then we are left with u and v as unknowns. So it is one equation in two unknowns, which has an infinite number of solutions.

 

[Austin0]

That is exactly the problem. If the ships are labeled S1, S2, and S3, and if S2 measures a Doppler factor of 13.1 from both S1 and S3 then that could be explained by S2 being at rest, S1 moving at -.99c, and S2 moving at .99c. However, it could just as well be explained by S1 being at rest, S2 moving at .99c, and S3 moving at .99995c. In fact, there are an infinite number of combinations of velocities that would all satisfy the same Doppler shift scenario.

If we assume S1 at rest S2 the mid point ship at .99c and S3 moving in the opposite direction at .99995c then the relative velocities between S1 and S2 =.99c would not be equal to the relative velocities between S2 and S3 =.00995c and therefore we would not expect to see an equal shift in a known signal from the point of view of S2 regarding the comparison of the two signals from S1 and S3

Obviously the shift between any two systems is going to be reciprocal , but in this situation
the point is to compare two other systems and establish the equality of the midpoint velocity relative to both systems that are moving in opposite directions from it.

 

[Austin0]

I have no idea what you mean by "relative to the speed of light". The speed of light relative to any object is c.

The measured speed of light from any inertial frame is always c.
We can and do measure a different speed of light relative to objects outide our frame.

When I said relative to the speed of light I was referring to the speed of light as an ultimate limit of possible velocity. When we accelerate an electron to .99c we can say that this is an actual velocity in that no amount of energy can achieve a significantly higher velocity even though we suppose that a small observer on the electron would still measure the passing photons at c.

So maybe I would have been better to say that, from the base ship at midpoint , when the other two ships were perceived to reach a velocity of near c relative to that frame they would also have reached maximum possible velocity in that direction even if they would still clock light at c.

 

[Dale]

If we assume S1 at rest S2 the mid point ship at .99c and S3 moving in the opposite direction at .99995c then the relative velocities between S1 and S2 =.99c would not be equal to the relative velocities between S2 and S3 =.00995c and therefore we would not expect to see an equal shift in a known signal from the point of view of S2 regarding the comparison of the two signals from S1 and S3

The bold part is wrong. The relative velocity between S2 and S3 is .99c and we would expect to see an equal shift. You need to use the relativistic velocity addition formula. Alternatively you can just use the relativistic Doppler formula I posted above, which has the relativistic velocity addition formula built into it.

I recommend working a few problems until you get the hang of relativistic velocity addition and relativistic Doppler.

 

[Austin0]

The bold part is wrong. The relative velocity between S2 and S3 is .99c and we would expect to see an equal shift. You need to use the http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel2.html#c2". Alternatively you can just use the relativistic Doppler formula I posted above, which has the relativistic velocity addition formula built into it.

I recommend working a few problems until you get the hang of relativistic velocity addition and relativistic Doppler.

Thanks Dale I see the problem now Back to the books