Stupid Question

  • Thread starter Dave9600
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  • #26
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But a straight path implies direction towards something. What is the photon travelling towards? Or, what is causing photons to move in a straight path?
Saying that a photon travels on a geodesic means a geodesic of spacetime. Spacetime is four dimensional without any particular prefered 3D+T slicing, so you cannot simply translate this geodesic to particular spatial directions.

In 3D space, e.g. how an observer sees the world around him, the path light does not always appear to be a straight line. This is for instance the case when a light path comes near an object of mass. Gravity influences how we observe those paths. Similarly we can observer that a radar signal takes longer when the path between two objects is influenced by gravity. In extreme cases we never even get the return signal from the radar signal we sent.
 
  • #27
Fredrik
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what is causing photons to move in a straight path?
"Conservation of momentum" isn't a bad answer, but I prefer to think of it simply as one of the postulates of the theory. We assume that null geodesics can be used to represent the world lines of massless particles, and only experiments can tell us if the theory (which includes that assumption) agrees with reality.

If we take this to be a postulate, we can derive conservation of momentum. But we can probably drop this postulate and instead postulate something else that implies conservation of momentum, and then use that to derive that the world line of an object with constant momentum is a geodesic.

I'm not saying that DaleSpam's answer is wrong. It isn't. My point is just that something needs to be postulated, and we might as well take this to be the postulate.
 
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  • #28
JesseM
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We assume that timelike geodesics can be used to represent the world lines of massless particles
Minor quibble: timelike geodesics represent the worldlines of massive particles, while lightlike geodesics represent the worldlines of photons and other massless particles. And I don't think this is actually a postulate of the theory, but is rather derived from the Einstein field equations.
 
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  • #29
Fredrik
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Minor quibble: timelike geodesics represent the worldlines of massive particles, while lightlike geodesics represent the worldlines of photons.
Oops. :redface: Thanks for catching it so fast that I could edit it.

And I don't think this is actually a postulate of the theory, but is rather derived from the Einstein field equations.
Hm, I have to think about this, but right now I have to get some sleep. So for now I'll just say that even though Einstein's equation completely defines the mathematical model of spacetime that we use in GR, it doesn't completely define GR as a theory of physics. We also have to postulate what things in the model correspond to things in the real world. For example, we have to postulate that a clock measures the proper time (defined as the familiar integral) along the curve that represents its motion. The idea that the motion of a particle is described by a geodesic must also be postulated.

Of course we're already postulating something like this when we say that the stress-energy tensor represents matter. I believe that a full specification of what the stress-energy tensor represents must include the postulate I'm talking about, but I really have to get some sleep now, so I can't really think about all the details now.
 

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