Can gravitational time dilation explain the photon's deflection near the Sun?

[Ibix]

Newtonian physics emerged long before GR.

I'm not talking about history. A successor theory must always simplify to its predecessor in the appropriate limit. Otherwise it can't explain the things the predecessor theory explains.

The maths of Newton emerges from the time component of GR in the weak field slow speed limit. It's spatial curvature you need to add back in. (Note that there are coordinate-dependent aspects to this statement, but I can't imagine switching to other coordinate systems making life easier in this case).

 

[A.T.]

I don't see how "by accident" comes into it.

Because you are randomly adding up 'effects' which are meant as alternatives to model the same thing. It makes zero sense, but even a broken clock is right twice a day.

 

[jeremyfiennes]

I'm not talking about history.

That a new theory supplants an old one, does not make the old one is invalid over the range it covers.

 

[jeremyfiennes]

Because you are randomly adding up 'effects' ...

If a Newton+time-dilation model gives the correct result, then it is valid, independently of how it was arrived at. And if not, then not. What I'm wanting to know is: does it give the correct result?

 

[Dale]

Ok. But not all models can cover all situations. If a Newton+time-dilation model predicts the correct deflection in this particular case, then it is valid in this particular case. With no claim to any extended validity.

That is not the issue I was raising. It is clear that no model other than a theory of everything will have an unlimited domain of validity. What I was pointing out is that Newtonian gravity plus time dilation may not even be logically self consistent. A model’s self consistency is different from its domain of validity which relates instead to experimental consistency.

 

[Ibix]

That a new theory supplants an old one, does not make the old one is invalid over the range it covers.

I believe that's exactly what I just said. The point you seem to be failing to grasp is that time dilation comes from the $g_{tt}$ element of the metric (expressed in Riemann normal coordinates). Newtonian physics also arises from the approximation that the $g_{tt}$ component of the metric is the only one that is significantly different from flat. So adding time dilation on top of Newtonian physics would be double-dipping the $g_{tt}$ component. If it works (and you'd need to develop some such theory mathematically to show that it did, because it isn't clear what adding time dilation to Newtonian gravity would mean or even, as Dale points out, that there's a self-consistent way to do it) it would most likely be pure luck and not a generalisable theory.

The PPN approximation allows you to add in the effects of the $g_{rr}$ component being different from its flat spacetime value. That gets you the full GR answer in this case.

 

[Vanadium 50]

If a Newton+time-dilation model gives the correct result, then it is valid, independently of how it was arrived at.

That is completely silly. It's vague, but depending on what you meant it's either false or trivial. As pointed out, the fact that a stopped clock is right twice a day does not make it an accurate timepiece.

I'm trying to figure out what your goals are. If it's to convince us relativity is wrong, you're destined to be no more successful here than your other N threads. If it's to learn relativity, you should follow the past advice and work through Taylor and Wheeler.

 

[jeremyfiennes]

Time dilation comes from the gttgttg_{tt} element of the metric ...

Can gravitational time dilation not be derived from a photon's energy loss, and hence frequency reduction, as it rises up from a massive body out into space? And hence the slower running clocks in a gravitational field seen by an observer in outer space?

 

[Nugatory]

Can gravitational time dilation not be derived from a photon's energy loss,

No.

If you substitute "flash of light" for "photon" and "red shift" for "energy loss" (without these substitutions, we're talking total nonsense - photons are not what you seem to think they are) the equivalence principle can be used to develop a convincing heuristic argument for gravitational time dilation. But to actually derive gravitational time dilation, we need to do as ibix says: Solve the EFE for the metric, then write the metric components in the coordinate system of interest to us. In the particular case of the Schwarzschild solution written in Schwarzschild coordinates, the $g_{tt}$ term then describes gravitational time dilation.

 

[jeremyfiennes]

No. If you substitute "flash of light" for "photon" and "red shift" for "energy loss" ...

Ok. Seen from outer space, frequencies in a gravitational field are red-shifted. Atomic clocks depend on caesium frequencies. And so run slower in a gravitational field. Time dilation.

 

[Ibix]

Can gravitational time dilation not be derived from a photon's energy loss, and hence frequency reduction, as it rises up from a massive body out into space? And hence the slower running clocks in a gravitational field seen by an observer in outer space?

As Nugatory says, you can make a compelling argument along those lines. But that only reinforces what I was saying. Time dilation isn't something you can add-on to Newtonian gravity - it's part of the same thing.

V50 has a point. I can only keep repeating myself. You can either accept my word or learn enough maths to understand it yourself.

 

[PeterDonis]

Since both the Newtonian and the GR models predict the Earth's orbit

The PPN model is not the Newtonian model. Nor is it a Newtonian model plus time dilation. PPN stands for "parameterized post-Newtonian", and is a framework for describing any theory of gravity that includes corrections to the Newtonian model that take a certain form (basically a power series expansion in the weak field parameter).

I 100% agree with this.

I don't. The "no single model has a monopoly" part is ok, but the rest is not. The Newtonian model does not predict the Earth's orbit; we have accurate enough measurements now to have measured Earth's perihelion shift, which is not predicted by the Newtonian model.

The perihelion shift does appear in the PPN model for Earth's orbit, but as above, that is not the Newtonian model, nor is it the Newtonian model plus time dilation.

 

[Dale]

I don't. The "no single model has a monopoly" part is ok, but the rest is not. The Newtonian model does not predict the Earth's orbit; we have accurate enough measurements now to have measured Earth's perihelion shift, which is not predicted by the Newtonian model.

Excellent point! It is accurate enough for the Earth orbit to launch rockets etc., but we have more precise measurements. I had forgotten.

 

[Herman Trivilino]

If a Newton+time-dilation model predicts the correct deflection in this particular case, then it is valid in this particular case. With no claim to any extended validity.

That's an insufficient criterion for a model to be a part of any theory, in my opinion. It seems to me that if it were sufficient then "double-the-Newtonian-value" would be a model.

You are correct in that all models have limits of validity. This means there's a competition, theories with more restricted limits of validity lose.

 

[A.T.]

If a Newton+time-dilation model gives the correct result,

It wouldn't give the correct result, because it would double the local light bending. The correct result is that the local bending corresponds to Newtonian 1g acceleration (see Equivalence Principle), and the doubling happens only as a global effect if the light traverses vast distances of curved space around the big mass.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

The thread has run its course and will remain closed. A number of posts have also been deleted.