Help understanding the Relativity of Simultaneity

[Renato Iraldi]

In the stationary frame the moving clocks run SLOWER. And they don't just seem to do that, they actually do.

The fact that they may not be synchronized doesn't change this. In other words, they run slower in the stationary frame, whether they are synchronized or not.

I think it should be specified what it means that one clock runs slower than another. The Lorentz transformation gives us t' =t*gamma for x =0 Time on the train seems to go faster. And t' = t/ gamma for x'=0. Time on the train runs slower
If you don't understand this you have to study.

I suspect @Renato Iraldi is imagining looking at a stream of clocks moving past his location, ignoring all but the one right in front of him. The slow ticking plus the changing zeroing conspires to make "the clock in front of him" tick fast, if you ignore the fact that it's not one clock.

 

[FactChecker]

The IRF that is assumed to be "stationary" is only observing one moving clock to determine how fast it is running. But in order to do that, it compares that one moving clock to at least two of it's own clocks along the moving clock's path. For any of that to make sense, the two "stationary" clocks should be synchronized. The synchronization is where the "stationary" and "moving" IRFs disagree. They can not agree on what events along the relative path are simultaneous. That is the "relativity of simultaneity". The disagreement allows either IRF to consider itself to be "stationary" and the other to be the "moving" IRF with slow clocks.

 

[FactChecker]

I suspect @Renato Iraldi is imagining looking at a stream of clocks moving past his location, ignoring all but the one right in front of him. The slow ticking plus the changing zeroing conspires to make "the clock in front of him" tick fast, if you ignore the fact that it's not one clock.

In that sense, the observer is not observing the ticking speed of one moving clock. He is observing the synchronization of multiple moving clocks as they pass one "stationary" location. And he would say that those moving clocks are not synchronized correctly.

 

[Ibix]

In that sense, the observer is not observing the ticking speed of one moving clock

Agreed. @Renato Iraldi is correct that the reading on the ever-changing clock in front of him is advancing faster than the one in his rest frame, but is wrong to call this "the time" in any frame, since no clock is measuring it, and no one clock can ever do so.

 

[jbriggs444]

I think it should be specified what it means that one clock runs slower than another. The Lorentz transformation gives us t' =t*gamma for x =0 Time on the train seems to go faster. And t' = t/ gamma for x'=0.

That is not a comparison between two clocks, exactly. Instead, it is a comparison between two coordinate systems -- observing the relationship between the two time coordinates ($t$ and $t'$) while agreeing to hold a particular position coordinate (either $x$ or $x'$) fixed.

Alternately, since the coordinate time delta between two events along a geodesic with constant spatial coordinate is constructed to be identical to the proper time along that trajectory, the coordinate comparison is functionally identical to a comparison between one clock and one coordinate system. Not really a comparison between two clocks.

One cannot compare two relatively moving clocks for rate without invoking a synchronization convention. A choice of coordinate system is one way of adopting a synchronization convention -- two events are synchronous if they share the same time coordinate.

 

[Renato Iraldi]

Agreed. @Renato Iraldi is correct that the reading on the ever-changing clock in front of him is advancing faster than the one in his rest frame, but is wrong to call this "the time" in any frame, since no clock is measuring it, and no one clock can ever do so.

this is why i say "it seem to go faster"

 

[FactChecker]

this is why i say "it seem to go faster"

That is a bad way to state it because you are not looking at how fast one clock is ticking. You are looking at a series of moving clocks that are at different positions of the relatively moving IRF. You do not get to see how fast each is ticking as they go by. For all you know, they might all be stopped and might have been initially set wrong. There is a saying: "Ahead is behind and behind is ahead." That expresses the way that the "synchronized" clocks in the relatively moving IRF are set.
The only way to know how a fast a clock in the relatively moving IRF is ticking, you must follow it as it passes different positions in your "stationary" IRF. That involves a series of clocks in your IRF and only one clock in the "moving" IRF that you are following.