Understanding Time Dilation: How Passing Photons Affect Time Measurement

[Dale]

There is no "good math" or "bad math". Mathematics serves. You can use it to create your own reality.

You really cannot use math to create your own reality. No amount of mathematical wrangling will change the outcome of an experiment. We use the math of relativity because it correctly predicts the outcome of such a wide variety of experiments:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

To the best of our knowledge there is no other math that correctly predicts the outcomes of all of these experiments. I.e. no other math describes reality.

this gets a bit complicated to explain if ...

Yes, sometimes reality is a bit complicated to explain.

 

[Frabjous]

We correct GPS for relativity. If relativity was wrong, we would be making the wrong corrections.
Here’s an excerpt of relativistic effects for GPS https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gps.html

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.

 

[Nugatory]

OK, I say it differently. My source sends out a pulse of light and T seconds later a second pulse of light.

Saying it that way is much clearer. Now we have four events:
A) first flash is emitted at the source.
B) first flash is received by you.
C) second flash is emitted at the source.
D) second flash is received by you.

The time between A and C can be directly measured by a clock at the emitter.
The time between B and D can be directly measured by your wristwatch.
These are proper times: invariant, the same for all observers, the same no matter which frame we’re using when we analyze the problem (these are different ways of saying the same thing).
These two times will be equal only if the you and the emitter are at rest relative to one another, meaning that no matter which inertial frame we choose they are both moving in the same direction at the same speed (which may be zero, in which we would say that they are both at rest in that frame.

The time between A and B and the time between C and D cannot be measured. Instead it is something we calculate by making an assumption about what your wristwatch reads at the same time that event A or C happens, and then subtracting that from the time on your wristwatch when flashes are received. “At the same time” means different things in different frames so we’ll be making different assumptions when we use different frames; the result of this calculation will depend on our choice of frame and doesn’t tell us much of anything about anything.

The light pulses are on their way to me with speed c (km/s). The distance in space between the two light pulses is T x c km. I observe the light pulses and measure a time of T seconds between the two light pulses. Agree?

This will be true only if we choose to analyze the problem using one particular frame, the one in which you and the source are both at rest, and then choose to use that frame’s natural definition of “at the same time”.

 

[Nugatory]

For over a hundred years. It is a choice to accept reality that way.

Experiments and observations tell us what reality is so we don’t have a choice to accept it one way or another, we have to accept it the way it is. The choice we do have is to use math that accurately describes reality, or to use math that does not accurately describe reality. This does not seem to be a particularly difficult or controversial choice….

 

[PeterDonis]

It is a choice to accept reality that way.

No, it's not, because reality tells us which way it is through experiments. Experiments have told us to very high accuracy that relativity is correct and Newtonian physics is not.

 

[PeterDonis]

For whom that is no problem, I wish good luck in his wonderful relativistic world.

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