- #1

Stephanus

- 1,316

- 104

Dear PF Forum,

After so many questions about Twins Paradox and Universe Frame of Reference, I'd like to know about Lorentz and Doppler. First.

Here V is ##\sqrt{0.75}## ≈ 86.60%. If we put V in Lorentz Transformation formula as speed, we'll have Gamma = 2.

Okay here's the question.

Two probes A and B.

Clocks are synchorized.

Distance is 100 Ly.

Each year they're sending digital signal, containing their respective time.

A will send A0, A1, A2, A3 for each respective year.

B also send B0, B1, B2,... each year.

Signal from B is always late for 100 years

So each year A will receive:

When B clock (and A clock) shows 100 year, B ignites its rocket RIGHT AFTER B sents B100. Catapulted at 86% c then the rocket stops, leaving B moves steadily at 86% c to the 'west', heading toward A

B will reach A at 115.4701 years.

Because ##\gamma = 2##, then B will reach A according to B clock for 57.7350 years.

When B arrive, A clock will read 115.4701

How will B

From where B stays and A1 there's 1 ly

B travels at V

V

V

##t = \frac{1}{1+V_b}/\gamma##

t = 0.27

How will A receive signal from B?

B is still sending signal.

Signal B101 is not sent 100 lys from A because B is moving.

Signal B101 is sent at V

Signal B101

B01 will be picked by A after 102 years, not 101 years, because 1 year for B is 2 years for A

So B101 will be received by A when T

The difference with A scenario is that the instance B ignites its rocket, the time interval for signal receiving is 0.27. Whlie A has to wait for 200 years to have 0.27 interval.

Is this true?

After so many questions about Twins Paradox and Universe Frame of Reference, I'd like to know about Lorentz and Doppler. First.

Here V is ##\sqrt{0.75}## ≈ 86.60%. If we put V in Lorentz Transformation formula as speed, we'll have Gamma = 2.

Okay here's the question.

Two probes A and B.

Clocks are synchorized.

Distance is 100 Ly.

Each year they're sending digital signal, containing their respective time.

A will send A0, A1, A2, A3 for each respective year.

B also send B0, B1, B2,... each year.

Signal from B is always late for 100 years

So each year A will receive:

Code:

```
Signal A Time Interval
B0 100.00
B1 101.00 1.00 year
B2 102.00 1.00 year
..
..
B98 198.00
B99 199.00 1.00 year
B100 200.00 1.00 year
```

**Is this true?**When B clock (and A clock) shows 100 year, B ignites its rocket RIGHT AFTER B sents B100. Catapulted at 86% c then the rocket stops, leaving B moves steadily at 86% c to the 'west', heading toward A

B will reach A at 115.4701 years.

Because ##\gamma = 2##, then B will reach A according to B clock for 57.7350 years.

When B arrive, A clock will read 115.4701

**Is this true?**How will B

**PICK UP**signal from A?From where B stays and A1 there's 1 ly

B travels at V

_{b}V

_{b}.t + ct = 1 ly, if V_{b}is relative to c, then c = 1V

_{b}.t + t = 1##t = \frac{1}{1+V_b}/\gamma##

t = 0.27

**Is this true?**
Code:

```
Signal B Time Interval
A0 100.00
A1 100.27 0.27
A2 100.54 0.27
..
..
A212 156.81 0.27
A213 157.07 0.27
A214 157.34 0.27
A215 157.61 0.27 B meets A
```

How will A receive signal from B?

B is still sending signal.

Signal B101 is not sent 100 lys from A because B is moving.

Signal B101 is sent at V

_{b}.t distanceSignal B101

*should be*sent at (100-0.86) ly from A. Because ##\gamma = 2##, so B101 is sent at 98.27 ly from A.**Is this true?**B01 will be picked by A after 102 years, not 101 years, because 1 year for B is 2 years for A

So B101 will be received by A when T

_{a}is 102 + 98.27 = 200.27.**Is this true?**
Code:

```
Signal A Time Interval
B0 100.00 when A received B0, A still doesn't know that B has
already traveled.
B1 101.00 1.00 year A still doesn't know that B has moved
B2 102.00 1.00
..
..
B98 198.00
B99 199.00 1.00 Still doesn't know
B100 200.00 1.00 Stil doesn't know
B101 200.27 0.27 Suddenly A begins receiving signals at 0.27
years interval
B102 200.54 0.27 Is this true?
B103 200.80 0.27
..
..
B155 214.74 0.27
B156 215.01 0.27
B157 215.27 0.27 B meets A
```

**Is the table above is true?**The difference with A scenario is that the instance B ignites its rocket, the time interval for signal receiving is 0.27. Whlie A has to wait for 200 years to have 0.27 interval.

Is this true?

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