Why do we always need to define simultaneity in relativity. The

[arydberg]

Why do we always need to define simultaneity in relativity. The moving train with a light signal at the mid point reaches the engine and caboose at the same time and gives us a way to define simultaneity. But what is it's purpose.

if G = gamma = 1/ ( [ 1-V*V/C*C ] ) ^1/2

And from the Lorenz equation T' = ( T + [V/C*C] *X ) *G

It appears that T' The time seen when a fixed observer is looking at a moving train is a function of X. As the caboose passes the observer the engine (with a bigger X) is older than the caboose.


What is the purpose of simultaneity?

 

[WannabeNewton]

Simultaneity is a necessary component of constructing coordinate systems for observers and hence for writing down an explicit form of the Lorentz transformations. Just like coordinate systems, there is nothing fundamental about simultaneity as far as SR is concerned.

 

[Chestermiller]

I think what you are saying is "With the Lorentz Transformation, I can analyze pretty much any problem I run into in special relativity, so what do I need concepts like simultaneity, length contraction, time dilation, etc." Well, yes, at the mathematical level, you can analyze problems and get the right answer, but that doesn't help with understanding what is happening mechanistically. If someone analyzes a problem and I ask him to explain his results mechanistically, and he tells me "that's what the equations say," I conclude that he is not able to explain it mechanistically, and he goes down in my opinion. Concepts like simultaneity, length contraction, time dilation, etc. help you get used to the counterintuitive realities of relativity at the gut level, and then provides a basis for explaining your results mechanistically.

 

[arydberg]

I think what you are saying is "With the Lorentz Transformation, I can analyze pretty much any problem I run into in special relativity, so what do I need concepts like simultaneity, length contraction, time dilation, etc." Well, yes, at the mathematical level, you can analyze problems and get the right answer, but that doesn't help with understanding what is happening mechanistically. If someone analyzes a problem and I ask him to explain his results mechanistically, and he tells me "that's what the equations say," I conclude that he is not able to explain it mechanistically, and he goes down in my opinion. Concepts like simultaneity, length contraction, time dilation, etc. help you get used to the counterintuitive realities of relativity at the gut level, and then provides a basis for explaining your results mechanistically.

What i am trying to does understand what is happening. The interesting thing is that the equation X' = G* ( X + VT) is very obvious ( other than the G) . Yet the twin equation T' = G* ( T + VX/C*C) is not at all obvious. It says if i look at a distant star i see it being very old because of it's distance from me.

 

[dauto]

What i am trying to does understand what is happening. The interesting thing is that the equation X' = G* ( X + VT) is very obvious ( other than the G) . Yet the twin equation T' = G* ( T + VX/C*C) is not at all obvious. It says if i look at a distant star i see it being very old because of it's distance from me.

It might also be very young if V has the opposite sign. And that's the point. Simultaneity is a relative concept. Whether that is obvious or not is completely irrelevant.

 

[Chestermiller]

What i am trying to does understand what is happening. The interesting thing is that the equation X' = G* ( X + VT) is very obvious ( other than the G) . Yet the twin equation T' = G* ( T + VX/C*C) is not at all obvious. It says if i look at a distant star i see it being very old because of it's distance from me.

Excellent. The second equation you wrote has no counterpart in pre-relativity physics. It is saying that, if there were a person at rest at location X in your frame of reference and he were looking at a person near him in the other frame of reference, he would be seeing a person who is much older than the people you are looking who are near you, even though all the people in the other frame of reference were born at exactly the same time according to the synchronized clocks in their frame of reference.

 

[bahamagreen]

As the caboose passes the observer the engine (with a bigger X) is older than the caboose.

What am I missing here?
The light from the engine seen by the observer will have been in transit longer than the light from the caboose, so while that image itself from the engine is older than that from the caboose, the engine represented in the image is of a younger engine, an engine younger than the caboose represented in its image. You might infer that the engine is older than represented in its observed image, but I'm not seeing how you say that the engine is older than the caboose.

Likewise; with these... are you using some word or concept in a way I don't understand? In both these cases, what would be seen is the image of a younger star or person. That they are older than their image seen, that is a calculation or inference, not what is seen, no?

arydberg - "...if i look at a distant star i see it being very old because of it's distance from me."

Chestermiller - "...he would be seeing a person who is much older than the people you are looking who are near you..."