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mfb

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The theorem is exact, you just have to keep its requirements in mind. Triangles in the real world are just approximations to perfect [strike]rectangular[/strike] right triangles, but that is not part of the theorem. Real triangles are not three ideal lines connected at three ideal points anyway.

In special relativity, space is flat. The theorem can be applied by every observer, if the (idealized) triangle has a right angle for this observer (that is frame-dependent).

In special relativity, space is flat. The theorem can be applied by every observer, if the (idealized) triangle has a right angle for this observer (that is frame-dependent).

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-In special relativity, space is flat. The theorem can be applied by every observer, if the (idealized) triangle has a right angle for this observer (that is frame-dependent).

In General relativity space time is curved. I'm confused. Surely the flat space of SR must also be an ideal.

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mfb

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Sure, special relativity is general relativity without gravity. You asked about Lorentz transformations, they are mainly a tool of special relativity.In General relativity space time is curved. I'm confused. Surely the flat space of SR must also be an ideal.

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SteamKing

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I'm still working on what a 'rectangular triangle' is.

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Nugatory

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It's the other way around - Pythagoras's theorem is exact and real triangles drawn on real surfaces in the real world are approximations of that ideal.Since there is no such thing as a perfectly flat surface, Pythagoras's Theorem results can only be seen as an approximation.

This will be true of just about any application of mathematics to engineering and experimental science.

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It's the other way around - Pythagoras's theorem is exact and real triangles drawn on real surfaces in the real world are approximations of that ideal.

This will be true of just about any application of mathematics to engineering and experimental science.

Pythagoras's Theorum is exact and therefore can only give an approximate

result to a real situation in an imperfect world. I think we're saying the same thing. I'm confused again.

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mfb

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I'm still working on my second language.I'm still working on what a 'rectangular triangle' is.

There is no "therefore". Nothing can give exact results in the real world, as there are no exact values or measurements.Dappy said:Pythagoras's Theorum is exact and therefore can only give an approximate

result to a real situation in an imperfect world.

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Would you please stop saying Theorum? It's really distracting. Why not say theorem?

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Would you please stop saying Theorum? It's really distracting. Why not say theorem?

My apologies, theorem.

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WannabeNewton

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Would you please stop saying Theorum? It's really distracting. Why not say theorem?

What's distracting are your irrelevant and pointless comments.

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What's distracting are your irrelevant and pointless comments.

I didn't make any comments. I asked Dappy for a favor and he was happy to oblige. Thank you Dappy. Now who is making pointless comments.

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Thankyou

We, I assume, accept that Pythagoras's theorem is an ideal. Is that ideal realized in the real world when calculating Lorentz transformations for time, length and relativistic mass?

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Provided gravitational effects are not significant, then yes.

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mfb

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If you take gravitational effects into account, no experiment has ever found a deviation from Lorentz transformations. And there are experiments testing that with a precision of better than one part in a billion.Can we trust Lorentz transformations as being accurate?

German.Pardon me for asking, but what is your first language?

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If you take gravitational effects into account, no experiment has ever found a deviation from Lorentz transformations. And there are experiments testing that with a precision of better than one part in a billion.

That's almost good enough for me. Can you imagine how flat a surface would have to be for Pythagoras's theorem to be accurate to better than one part in a billion. The mirror in the Hubble telescope comes to mind. I wonder how accurate it is in that context.

I don't know how to double quote, but German, I would never of guest. I'm dyslexic and slip up a lot more than that.

Reagards Dappy.

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mfb

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Flatter than one part in a billion? :DCan you imagine how flat a surface would have to be for Pythagoras's theorem to be accurate to better than one part in a billion.

To have length deviations of one part in a billion on a perfect sphere with the size of earth, the triangle needs an area of ~0.05 km^2.

1 part in a billion is just a random number, the quality of the tests depends on the tested quantity. The stability of the speed of light in different directions can be tested way better (wikipedia gives 1 part in 10

The next generation of ring lasers is expected to measure the rotation of earth more precise than satellites and telescopes. That's a 1 part in 1 billion measurement for an already tiny effect.

More: Modern searches for Lorentz violation

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Chestermiller

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Flatter than one part in a billion? :D

That isn't quite what I said, but it made me laugh and when I realized what I actually said, it was equally ridiculous.

Now that you've pointed that out, I have to say "right angled triangle". ;-)

Thankyou mfb for the link. I found it most informative and need to give it more attention, to allow it all to soak in.

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Over large spans of space-time in a region of large mass-induced curvature, it is not possible to define a set of coordinates that accurately describes distances using the Minkowski metric.

So can I assume that Lorentz violation may exist there, but only because of our inability to define a set of coordinates?

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mfb

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