Questions concerning the geometry of spacetime

In summary, the rectangle shown in the spacetime diagram has a "spacetime area" that is different from an ordinary area. It is a result of using Minkowskian geometry, which considers both timelike and spacelike dimensions. The "area" is invariant under Lorentz transformations and has different properties compared to an ordinary rectangle in Euclidean space.
  • #106
student34 said:
They both have mass.
Ok.

student34 said:
That is their intrinsic relationship
This doesn't seem like a very useful use of language. You could just as well say that you and I have an "intrinsic relationship" because we both have mass. What does that tell us? Nothing of any use. Certainly there is no "intrinsic relationship" of this kind in any actual physics. Knowing that the proton and electron both have mass doesn't tell you anything else about them or about their relationships.

student34 said:
they both have that as an intrinsic property.
Actually, they don't. The mass of the proton comes from the masses of its quarks plus the energy contained in the strong interaction field that binds the quarks together.

The mass of quarks and electrons comes from their interaction with the Higgs field as a result of electroweak symmetry breaking; in the very early universe, before electroweak symmetry breaking happened, quarks and electrons were massless.

None of this changes what I said above.
 
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  • #107
PeterDonis said:
What are you talking about here? There is no "grandfather paradox" in GR. All solutions in GR are self-consistent.

I think you have read way too much pop science and not enough actual science.
Apparently GR allows time travel. Michio Kaku talks about the grandfather paradox in this video . Start watching at 1:30.
 
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  • #108
student34 said:
Apparently GR allows time travel.
GR has solutions with closed timelike curves, yes. Most physicists consider those solutions to be physically unreasonable. However, even these solutions are mathematically self-consistent and no grandfather paradoxes are possible.

student34 said:
Michio Kaku talks about the grandfather paradox in this video
This video is most certainly not a valid reference for PF discussion. Kaku is giving his personal opinions, not stating what GR says. He might well be giving the impression that he is stating what GR says, but that just underscores why videos like this are not valid references. Kaku and others (Brian Greene is another frequent offender) will say things in these videos that they know they could never get away with in an actual peer-reviewed paper, because the people who would review his work in a peer-reviewed paper know what the actual physics, like GR, says, and will call him on it if he misstates or misrepresents things.
 
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  • #109
PeterDonis said:
Actually, they don't. The mass of the proton comes from the masses of its quarks plus the energy contained in the strong interaction field that binds the quarks together.

The mass of quarks and electrons comes from their interaction with the Higgs field as a result of electroweak symmetry breaking; in the very early universe, before electroweak symmetry breaking happened, quarks and electrons were massless.

None of this changes what I said above.
Interesting, I did not know that.
 
  • #110
PeterDonis said:
There aren't any. Timelike intervals and spacelike intervals are fundamentally different. No matter how many times you try to ask about this in different words, the answer is not going to change. Why is this such a problem?
Ok, then that is where it stands.
 
  • #111
PeterDonis said:
GR has solutions with closed timelike curves, yes. Most physicists consider those solutions to be physically unreasonable. However, even these solutions are mathematically self-consistent and no grandfather paradoxes are possible.This video is most certainly not a valid reference for PF discussion. Kaku is giving his personal opinions, not stating what GR says. He might well be giving the impression that he is stating what GR says, but that just underscores why videos like this are not valid references. Kaku and others (Brian Greene is another frequent offender) will say things in these videos that they know they could never get away with in an actual peer-reviewed paper, because the people who would review his work in a peer-reviewed paper know what the actual physics, like GR, says, and will call him on it if he misstates or misrepresents things.
Ok, fair enough
 
  • #112
PeterDonis said:
Timelike intervals and spacelike intervals are fundamentally different.
basically, for two timelike separated events there is in principle a massive object that can move from the first event to the last. For two spacelike separated events, instead, a such body there is not.

So the measurement of a spacelike path requires in principle an extended body between the two spacelike separated events.
 

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