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- Thread starter Delta2
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https://en.m.wikipedia.org/wiki/Four-vector

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I knew about this but this is not quite what I was thinking.. For example we put the energy together with the momentum as a 4-vector for reasons that suit our computations and equations to be expressed in a compact and elegant form. I mean i just view Energy as just the

https://en.m.wikipedia.org/wiki/Four-vector

I expected the time component to be defined in some sort of very special way...

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I don’t see the difference with this and what you said previouslyI mean i just view Energy as just the4th componentof the energy-momentum 4-vector.

The time component is just the one with the opposite sign in the signature.I expected the time component to be defined in some sort of very special way...

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You can't transform 3-momentum between frames. To put it crudely, the "energy" in one frame is made up of some of the energy and some of the momentum, as measured in another frame. That's pretty deep.I knew about this but this is not quite what I was thinking.. For example we put the energy together with the momentum as a 4-vector for reasons that suit our computations and equations to be expressed in a compact and elegant form. I mean i just view Energy as just the4th componentof the energy-momentum 4-vector.OR is there some deep conceptual reasonthat you called the energy thetime componentof the energy momentum vector?

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Huh? Excuse me I don't understand. I guessThe time component is just the one with the opposite sign in the signature.

Ok fine, that's an interesting property, the ability to transform 4-momentum between different frames. I was expecting that you would tell me that conservation of the 3-momentum relates to the translational spatial symmetry, while conservation of energy relates to time symmetry, that's another deep reason I can think of.You can't transform 3-momentum between frames. To put it crudely, the "energy" in one frame is made up of some of the energy and some of the momentum, as measured in another frame. That's pretty deep.

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Yes, that is true too.I was expecting that you would tell me that conservation of the 3-momentum relates to the translational spatial symmetry, while conservation of energy relates to time symmetry, that's another deep reason I can think of

Sorry, I mistakenly assumed since you knew about four-vectors you also knew about signatures. I am not sure now what you know and what you don’t, so please forgive me if I under or over explain.Huh? Excuse me I don't understand. I guessdeepspecial humour hehe?

In relativity everything stems from the metric. In an inertial frame (and in units where c=1) the metric can be written ##ds^2=-dt^2+dx^2+dy^2+dz^2##. As you can see, there are three terms with a + sign and one term with a - sign, so this metric has a (-+++) signature. The only thing that distinguishes time from space is that there is only one time component and the signature is opposite.

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