- #1

- 125

- 1

## Main Question or Discussion Point

Introduction

I've been reading and thinking about special relativity recently and when I started to delve into relativity of simultaneity. I’ve seemed to of missed how relativity of simultaneity is compatible special relativity. I found it very difficult to describe this problem and it comes across rather pretentious, but if any of you can sift though it and work out what is missing from the rationale, it would be really helpful.

PART 1: The Clocks Paradox

A newly built, 1 light second long space colony begins it's journey to a distant planet, with an initial acceleration from what it considers stationary to 0.5C. As this acceleration was conducted and no problems have occurred during thrust, the captain decides that there will be a second period of acceleration, to reduce the duration of the voyage. The captain chooses to reach a velocity of 0.8C relative to the crafts pre take-off velocity or 0.5C relative to current velocity.

Before initial take off, clock at the front of the vessel was made to run 0.5 seconds behind the one at the back of the vessel so that post acceleration the clocks would be synchronised based on relativity of simultaneity calculations (XV/C^2). This process is to repeated again so that the clocks will be synchronised when the second stage of acceleration is complete. Before the captain makes the call to change the clocks, he makes an unusual announcement.

“After some thought, I’ve concluded based on the fact that we set the back clock 0.5 seconds ahead of the front clock, before the first stage of acceleration and that they are now synchronised after accelerating to 0.5C, relative of initial velocity, that our velocity is in absolute terms 0.5C or 0C. Yes, you heard correct! I've concluded that our absolute velocity is either 0.5C or 0C!”

An uproar breaks out on the bridge.

PART 2: The Captains Rationale

Before making the decision to change the clocks times, the captain had considered the fact that the two stage acceleration, accelerating to 0.5C relative to initial velocity and then another 0.5C relative the the current velocity was the same as a one stage acceleration to 0.8C relative to initial velocity.

The Captain considers if he knew that there was a good chance that the craft would be able to accelerate for a second time, he would of set the trailing clock 0.8 seconds ahead of the leading clock (based on the formula XV/C^2, which determines how ahead the leading clock, of a pair of synchronised clocks in a rest frame) so once both phases of acceleration were complete the clocks would be synchronised and he wouldn't have to adjust the clocks twice.

Considering that simultaneous events in the initial frame at each end of the space colony appear on-board to be out by 0.5 seconds, as light from the leading event reaches the centre of the craft 0.5 seconds before light from the trailing event reaches the centre. If these events were the reaching of midnight on a clock at each end. Light would be emitted by both of them simultaneously according to the the initial velocity frame with the same result of 0.5 seconds ahead for the leading. If the clocks are changed so that before take off the lead is 0.8 seconds behind, when at a velocity of 0.5C relative to initial velocity, midnight occurs according to the trailing 0.3 seconds before the leading. Based on this rationale the prescribed adjustment should be to have the leading 0.3 seconds behind the trailing so they are synchronised upon the second stage of acceleration.

Special relativity holds that any inertial frame of reference can be considered stationary. A second set of rationale, where you consider the vessel currently is at rest yields a prescribed adjustment of 0.5 seconds to the trailing clock; identical to the prescribed adjustment before the initial stage of acceleration. What is evident is that prescription will vary depending as to what reference frame is considered to be at rest and that only one of these prescription can be correct, giving substantial insight into an absolute velocity.

As the prescription for the first clock adjustment was correct, there is only two possible initial velocities. that being 0C or -0.5C as the adjustments prescribed by these initial velocities are the same as the required adjustment. Which evidently means that the current velocity of the colony is either 0.5C or 0C in absolute terms.

PART 3: Determining An Absolute Velocity

Although I am at rather odds to describe this well. The absolute velocity of an inertial reference frame, in a particular axis can be seemingly obtained, by accelerating an object twice, from relative rest with a trailing clock, a leading clock and some on-board object measurements of the time each clock displays.

This is achieved by considering V within the formula, (leading clock time – trailing clock time) = (XV)/C^2 is equivalent to S - V with V equal to the absolute velocity of the observer frame and S being equal to the absolute velocity of the object. Their for S – V = ((delta T)C^2)/X

S - V is also equal to U(1 – ((SV)/C^2)), which is obtained by rearranging the velocity subtraction formula U = (S – V)/(1 – ((SV)/C^2)). Their for ((delta T)C^2)/X = U(1 – ((SV)/C^2))

V cannot be solved from the above formula and there exists the requisite of two accelerations to effectively calculate V. The measurements required are:

(delta T) after the first phase of acceleration = Ta

(delta T) after the second phase of acceleration = Tb

The relative velocity between the observation frame and the object after the first phase of acceleration = Ua

The relative velocity between the observation frame and the object after the second phase of acceleration = Ub

these variables are then imputed into this formula:

V = ((C^2)/(Tb – Ta))((Ta/Ua) – (Tb/Ub))

Which seemingly gives you the absolute velocity of the observer (got a bit of a headache so I hope derived it properly) .

Thank you for reading. Hopefully you understood. I can elaborate upon request.

I've been reading and thinking about special relativity recently and when I started to delve into relativity of simultaneity. I’ve seemed to of missed how relativity of simultaneity is compatible special relativity. I found it very difficult to describe this problem and it comes across rather pretentious, but if any of you can sift though it and work out what is missing from the rationale, it would be really helpful.

PART 1: The Clocks Paradox

A newly built, 1 light second long space colony begins it's journey to a distant planet, with an initial acceleration from what it considers stationary to 0.5C. As this acceleration was conducted and no problems have occurred during thrust, the captain decides that there will be a second period of acceleration, to reduce the duration of the voyage. The captain chooses to reach a velocity of 0.8C relative to the crafts pre take-off velocity or 0.5C relative to current velocity.

Before initial take off, clock at the front of the vessel was made to run 0.5 seconds behind the one at the back of the vessel so that post acceleration the clocks would be synchronised based on relativity of simultaneity calculations (XV/C^2). This process is to repeated again so that the clocks will be synchronised when the second stage of acceleration is complete. Before the captain makes the call to change the clocks, he makes an unusual announcement.

“After some thought, I’ve concluded based on the fact that we set the back clock 0.5 seconds ahead of the front clock, before the first stage of acceleration and that they are now synchronised after accelerating to 0.5C, relative of initial velocity, that our velocity is in absolute terms 0.5C or 0C. Yes, you heard correct! I've concluded that our absolute velocity is either 0.5C or 0C!”

An uproar breaks out on the bridge.

PART 2: The Captains Rationale

Before making the decision to change the clocks times, the captain had considered the fact that the two stage acceleration, accelerating to 0.5C relative to initial velocity and then another 0.5C relative the the current velocity was the same as a one stage acceleration to 0.8C relative to initial velocity.

The Captain considers if he knew that there was a good chance that the craft would be able to accelerate for a second time, he would of set the trailing clock 0.8 seconds ahead of the leading clock (based on the formula XV/C^2, which determines how ahead the leading clock, of a pair of synchronised clocks in a rest frame) so once both phases of acceleration were complete the clocks would be synchronised and he wouldn't have to adjust the clocks twice.

Considering that simultaneous events in the initial frame at each end of the space colony appear on-board to be out by 0.5 seconds, as light from the leading event reaches the centre of the craft 0.5 seconds before light from the trailing event reaches the centre. If these events were the reaching of midnight on a clock at each end. Light would be emitted by both of them simultaneously according to the the initial velocity frame with the same result of 0.5 seconds ahead for the leading. If the clocks are changed so that before take off the lead is 0.8 seconds behind, when at a velocity of 0.5C relative to initial velocity, midnight occurs according to the trailing 0.3 seconds before the leading. Based on this rationale the prescribed adjustment should be to have the leading 0.3 seconds behind the trailing so they are synchronised upon the second stage of acceleration.

Special relativity holds that any inertial frame of reference can be considered stationary. A second set of rationale, where you consider the vessel currently is at rest yields a prescribed adjustment of 0.5 seconds to the trailing clock; identical to the prescribed adjustment before the initial stage of acceleration. What is evident is that prescription will vary depending as to what reference frame is considered to be at rest and that only one of these prescription can be correct, giving substantial insight into an absolute velocity.

As the prescription for the first clock adjustment was correct, there is only two possible initial velocities. that being 0C or -0.5C as the adjustments prescribed by these initial velocities are the same as the required adjustment. Which evidently means that the current velocity of the colony is either 0.5C or 0C in absolute terms.

PART 3: Determining An Absolute Velocity

Although I am at rather odds to describe this well. The absolute velocity of an inertial reference frame, in a particular axis can be seemingly obtained, by accelerating an object twice, from relative rest with a trailing clock, a leading clock and some on-board object measurements of the time each clock displays.

This is achieved by considering V within the formula, (leading clock time – trailing clock time) = (XV)/C^2 is equivalent to S - V with V equal to the absolute velocity of the observer frame and S being equal to the absolute velocity of the object. Their for S – V = ((delta T)C^2)/X

S - V is also equal to U(1 – ((SV)/C^2)), which is obtained by rearranging the velocity subtraction formula U = (S – V)/(1 – ((SV)/C^2)). Their for ((delta T)C^2)/X = U(1 – ((SV)/C^2))

V cannot be solved from the above formula and there exists the requisite of two accelerations to effectively calculate V. The measurements required are:

(delta T) after the first phase of acceleration = Ta

(delta T) after the second phase of acceleration = Tb

The relative velocity between the observation frame and the object after the first phase of acceleration = Ua

The relative velocity between the observation frame and the object after the second phase of acceleration = Ub

these variables are then imputed into this formula:

V = ((C^2)/(Tb – Ta))((Ta/Ua) – (Tb/Ub))

Which seemingly gives you the absolute velocity of the observer (got a bit of a headache so I hope derived it properly) .

Thank you for reading. Hopefully you understood. I can elaborate upon request.