SR: Questions on Time Synchronization & Relativity

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In summary, according to special relativity, two stationary cars next to each other should have synchronized clocks. If one car starts moving at 0.5c, both cars will observe each other's clocks to be running slower than their own. This is calculated using the Lorentz factor, which can also be measured through the Doppler shift. The transfer time of light also affects this measurement, and can be observed when one of the cars turns around. The velocity at which the cars are moving away from each other can also be calculated and has physical significance.
  • #1
goodabouthood
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Two cars are stationary and next to each other and not moving relative to each other.

According to SR their clocks should be synchronized. Am I correct in saying that?

Also by saying this am I correct in saying that they agree on the time of events?

Now what would happen if one car starts going at .5c? What is his time now? Why exactly does it mean for his clocks to slow down?
 
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  • #2
goodabouthood said:
Two cars are stationary and next to each other and not moving relative to each other.

According to SR their clocks should be synchronized. Am I correct in saying that?

Good so far.

(**Technically you would have to synchronize the clocks in the first place, but this is implied.)

goodabouthood said:
Also by saying this am I correct in saying that they agree on the time of events?

Yes, this is correct.

goodabouthood said:
Now what would happen if one car starts going at .5c? What is his time now? Why exactly does it mean for his clocks to slow down?

If the cars are moving apart at 0.5c, then both cars will observe each others' clocks running more slowly than their own. This means that, for every tick of one cars clock, the other car's clock would appear to take 1.1547 times to tick once. (At 0.5c, γ=1.15470).
 
  • #3
^how did you know at .5c y=1.15470? Did you manually put the numbers in and figure it out, or is there something you referenced that maybe you could link?
 
  • #4
JT73 said:
^how did you know at .5c y=1.15470? Did you manually put the numbers in and figure it out, or is there something you referenced that maybe you could link?

I did [itex]1/ \sqrt{1-0.5^2}=1/ \sqrt{0.75}[/itex] on my calculator, though I did just find this: http://www.wolframalpha.com/entities/calculators/lorentz_factor_formula/fl/z1/6z/ [Broken].
 
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  • #5
elfmotat said:
Good so far.
If the cars are moving apart at 0.5c, then both cars will observe each others' clocks running more slowly than their own. This means that, for every tick of one cars clock, the other car's clock would appear to take 1.1547 times to tick once. (At 0.5c, γ=1.15470).
First we have to be clear about what we mean by observe.

When two cars move away from each other with a velocity of 0.5c they actually measure each others clocks to go at about 58% of their own clock.

They can make a calculation taking into account the transfer time of light and only then will they infer the other clock goes at 87% of their own clock. But that calculation has no direct physical significance.

But what is measured is not the Lorentz factor instead the Doppler factor is measured.
 
  • #6
Passionflower said:
First we have to be clear about what we mean by observe.

When two cars move away from each other with a velocity of 0.5c they actually measure each others clocks to go at about 58% of their own clock.

They can make a calculation taking into account the transfer time of light and only then will they infer the other clock goes at 87% of their own clock. But that calculation has no direct physical significance.

But what is measured is not the Lorentz factor instead the Doppler factor is measured.
Your post leads to more questions:

Is there any physical significance, direct or indirect, to the measurement that each car makes of the rate of the other one's clock?

What calculation are you talking about that takes into account the transfer time of light?

How does each car know what that transfer time of light is? Is this another calculation, observation or measurement?

Is there any direct or indirect physical significance to that transfer time of the light?

Can each car observe, measure or calculate the velocity at which they move away from each other? If so, how?

Is there any direct or indirect physical significance to the observation, measurement or calculation of that velocity?
 
  • #7
ghwellsjr said:
Is there any physical significance, direct or indirect, to the measurement that each car makes of the rate of the other one's clock?
Most definitely, any signal or form of radiation is adjusted by the same factor as the clock. So for instance if each car shines a light with a certain frequency this frequency will be measured at about 58% of the original frequency.

We calculate:
[tex]\Large {\frac {\sqrt {1-{v}^{2}}}{1+v}}[/tex]
ghwellsjr said:
What calculation are you talking about that takes into account the transfer time of light?
When two objects are retreating or approaching each other the total time for a light signal to reach the other object changes with time, this has a resp. red and blueshift effect. If we disable this part we have a remainder of the total Doppler shift which can be expressed by the Lorentz factor.

ghwellsjr said:
How does each car know what that transfer time of light is? Is this another calculation, observation or measurement?
Let me turn it around, they can measure the Doppler shift, the transfer time of light cannot be directly observed and, as a consequence, the Lorentz factor cannot be directly measured either.

However there is one interesting exception, and that is when the two cars move laterally, in this case the Doppler factor is equal to the Lorentz factor.

ghwellsjr said:
Is there any direct or indirect physical significance to that transfer time of the light?
Yes there is, and this is very important in case of differential aging when for instance one of the cars turns around. The 'at home' car will count a fewer number of waves.

ghwellsjr said:
Can each car observe, measure or calculate the velocity at which they move away from each other? If so, how?
They can if both cars emit for instance some reference frequency. Based on the actual measurement of the frequency (and for simplicity I assume longitudinal motion only) and expressing that as a factor they could calculate it as such:
[tex]\Large v = -{\frac {-1+{{\it ratio}}^{2}}{1+{{\it ratio}}^{2}}}[/tex]
ghwellsjr said:
Is there any direct or indirect physical significance to the observation, measurement or calculation of that velocity?
Yes there is, the fact that two objects are in relative motion is obviously of physical significance. For instance at one point things may bump into each other.
 

1. What is time synchronization?

Time synchronization is the process of coordinating the time between different clocks or timekeeping devices. This ensures that all clocks are displaying the same time and allows for accurate time measurement and coordination.

2. How is time synchronization achieved?

Time synchronization can be achieved through various methods such as using a reference clock, network time protocols, or by adjusting clocks manually. The most accurate method is using a reference clock, which relies on highly precise atomic clocks.

3. Why is time synchronization important?

Time synchronization is important for many scientific and technological applications that require precise timing, such as GPS navigation, financial transactions, and communication systems. It also plays a crucial role in experiments and studies involving time-dependent processes.

4. How does relativity affect time synchronization?

According to Einstein's theory of relativity, time is not absolute but is relative to the observer's frame of reference. This means that time can appear to pass differently for different observers, depending on their relative speeds and positions. Therefore, time synchronization must take into account the effects of relativity to ensure accurate measurements.

5. Can time synchronization be 100% accurate?

No, time synchronization can never be 100% accurate due to various factors such as the limitations of technology, the effects of relativity, and the uncertainty principle in quantum mechanics. However, with advanced methods and technologies, it is possible to achieve a high level of accuracy in time synchronization.

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