- #1

Stephanus

- 1,316

- 104

I'd like to know how we measure speed, distance clock in space?

##v = 0.6c \gamma = 1.25##

Supposed the distance between A and B is 900 ls.

And supposed A and B keeps exchanging signal for 6 seconds interval.

Because the distance between A and B is 900 ls, there are 150 signals from A to B in that 900 ls space and 150 signals from B, too.

Clocks are synchronized and they start sending signals. Now at T900, then the first signal from A reaches B (and the first B signal reaches A) Now, A moves toward B...

When A reaches B, (I don't include the calculations here, I think this is very simple for the good mentors and advisors) B clock will shows 900 + 1500 = 2500 seconds and B clock shows 900 + 1200 = 2100 seconds.

A will receive (900/6 + 1500/6) 400 signals.

How does A reconcile with this?

*"I'm receiving 400 signals for 1200 seconds, so 3 seconds for each signal. The frequency for I receive signal is twice what I should have, so I'm picking the signal and move at 1c, because I receive the signal at half what I should receive.*

WAIT. This is not the case, I study SR, I know Lorentz contraction, so I have to calculate it again.

The distance of signal is NOT 6s . It's length contracted according to Lorentz Factor."

WAIT. This is not the case, I study SR, I know Lorentz contraction, so I have to calculate it again.

The distance of signal is NOT 6s . It's length contracted according to Lorentz Factor."

Remember A doesn't know the speed yet. So this is what A should have calculated.

The signal moves at c, A moves at V, the distance is contracted.

##V = \frac{F^2-1}{F^2+1}## F is the frequency of receiving signal.

##V = \frac{2^2-1}{2^2+1} = 0.6##

I comes up with ##V = \frac{F^2-1}{F^2+1}## through a long way equations, so I don't include them.

So basically, A can determine its speed through something like Doppler effect. Is this true?

How can A determine distance? A will see the B clock is 900 sec late, so B is 900ls away. But clock can be deceiving right? What if B moves backward and forward and B light cone reaches A showing 900 ls late?

Second problem.

Consider this:

Three observer A, B1 and B2:

Distances:

A -> B1: 100 lys

B1 -> B2: 3 lys

Clocks are synchronized

B1 and B2 would move together toward A.

So here is the situation.

A stays

B1 and B2 move together toward A at say... 0.6c

100 years later A will see that B1 is moving toward A at 0.6c, distance is contracted. B1 would be at 80ly away. But A still see B2 at 103 lys away. Is this true? This statement seems contradicted length contraction. I'm not against the SR theory, much less disputing it, understanding it is very difficult.

_______________________________________________________________________________

So what I ask here is this:

With all the observers receive are signals from the other observers, all they see are lights/signals coming from the other observers...

1. How can we measure speed? Through Doppler effect?

2. How can we measure distance? Through clock? But clock can be deceiving right? Altough

*"nature can be fooled"*(Richard Feynman)

3. How can we measure other time (dilation)? Through speed (Dopper) and therefore using Lorentz formula?

4. In problem 2. Concerning A, B1 and B2. How can we reconcile this? Drawing space time diagram would be cheating right. Because we 'already know' the problem.