Example about bending of trajectory near to Sun

There is the famous observation of bending of light near to Sun.
So the bending of light is predicted both by Newton theory and by GR, but GR gives twice of the angle value and this is correct prediction confirmed by observations.

I would like to discuss the cause for this bending on rather unusual example.

Lets imagine, we have a neutrino on trajectory near to Sun. Neutrino has almost zero invariant mass, but it is not zero, it has very very tiny value.

In first case is the neutrino flying with 99,999999% of speed of light and it has some effective ("relativistic") mass, which is significantly higher than the almost zero invariant mass of neutrino. Prediction based on GR is predicting bending angle similar to bending angle of light and twice the value compared to value predicted by Newton theory.

In second case the neutrino is flying very slow, lets say 10 m/s and what I have found the measured value of bending is the same as calculated by GR or by Newton theory (please correct me, if Im not right).

So it seems to me, that the additional bending of neutrino when comparing GR to Newton theory is caused primarily by relativistic effects, specifically by time dilation which hast the biggest effect by speeds near to speed of light.

 

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My understanding is that all objects follow the geodesic, whether it be a baseball, a neutrino or a photon. The curvature (as seen by a remote viewer) is due to the speed of the object. Since a photon always moves at c it always has the same 'curvature'. Other objects moving at different speeds will give a different curvature. A mountain or a baseball moving at the same speed will show the same curvature. I also believe that is one of the finer points that shows that it is a GR is discussing the bending of spaceTIME not just space.
The curvature or bending that I state is based on what a remote observer would detect.

Good question! We will see if someone who is actually trained in physics can tell me if I am on the right track or if I have completely derailed into a ball of flames.

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Its a pitiable situation that supporters of GR are so ignorant...

First and foremost the geometry of spacetime is independent of observer. Second the curvature of spacetime is determined by the mass/energy of the massive object..

Path followed by a particle naturally depends on the initial velocity of a particle...

 

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But you must notice that relative speed based time dilation is SR stuff, signifying flat spacetime......

In fact you have raised a very valid point....The Newtonian is applicable and termed as approximation of GR....so a comet flying pass sun will have a deflection which is in conformity with Newtonian.......so when and at what point actually this deflection becomes double ? Is it double for light only ? Bringing SR (flat spacetime) will become a matter of convenience?

 

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GR is near certain particularly after confirmation of gravitational waves by aLIGO: You continually denying that just makes you look foolish and without credibility.

But are you not denying curvature??

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All particles and light will tend to follow straight lines unless acted on by a force [Newtonian] or influenced by curved spacetime, [GR]

 

On the straight line motion issue...............
I won't make the common error that the god and his ilk are always making, in asking for proof of the above statement that has been raised often in recent times.....Is there practical every day Earthly evidence of the above, of course is the proper way to go.
Let's look at the following situation.
I'm travelling standing up on a crowded bus and the driver makes a sharp right hand turn......
I immediatley fall to the left, landing in a young blondes lap.
She quickly admonishes me, and asks for an explanation: I say don't blame me, blame the centrifugal force!
Rubbish she exclaims...I'm not one of them dumb blondes....Centrifugal force is a fictitious force and your excuse is just as fictitious!
The fiery blonde continues to demand an answer and claims I'm an old perv. I soon notice a policeman on the corner who has observed the bus turn.
Let's ask him I say!
OK the policeman says, There was no centrifugal force, you are correct. You simply kept travelling in a straight line while the bus, including the blonde kept turning right and she consequently put her lap immediately under your trajectory.

 

Yes. All you need to do is stand in the right place and wait for the bus to turn right. The mistake was doing it to the same blonde every day for five weeks.

 

Today I realized, that in the second example, the real bending would not exactly match the Newtonian bending, because there is also the time dilation caused by gravity of Sun, but generally I would say it would be very similar to Newtonian bending, because the effect of gravitational time dilation is rather small compared to time dilation at near speed of light in first example.

If I had more time, I would actually calculate it all, but I dont have so much time and it would take me much more time like to some people more versed in this type of calculations.

 

I would expect the answers to be very close to each other but not exactly the same. The curvature of spacetime in GR is supposed to just tell someone how much an object is being affected by the force of gravity. The only situation where the results should greatly differ is measuring the curvature of a photon, assuming it has zero mass. In Newtonian physics, it shouldn't have any curvature, because it has no mass. It should be ruffly the same in each theory for everything else, because the only real experimental difference between these two theories is the prediction of the orbit of Mercury, which Newtonian physics didn't get exactly right.

That would be why the prediction made by Einstein, that light should curve in a gravitational field, is so significant.

 

So it can be easily culled from your thoughts, that what path a massed object should follow and what path a packet of energy in presence of massive source ?

I see there is a big problem here, if spacetime has anything to do with reality of space, then curvature should ensure path irrespevtive of initial speed ? Why is that curved path depends on initial speed, ideally curvature should be independent of that.

 

The initial speed should matter, just like different objects should have different orbits from their relative speed. I read the OP's post as meaning that Newtonian and GR gave close to the same predictions at both speeds. That should be true, but they should not give close to the same predictions at 99% the speed of light and 10 m/s.

A photon should follow the geodesic of the curvature of spacetime, since it has no mass. The only gravitational forces that would affect the photon is the curvature of spacetime itself.

I find it hard to explain why the curved path depends on initial speed, but I know that it does for an object with mass.

 

Photons invariant mass (rest mass) is zero (due to standard GR interpretation), but this is only theoretical value which would apply only in case of photon standing still without any additional energy, which is not possible in reality. Real photon is moving at speed of light (which can change depending on whether it is moving in vacuum or not) and has a non zero energy. Higher frequency means higher energy and higher energy means bigger effective mass (relativistic mass) of photon. This a normal mainstream knowledge which is in line with General relativity, this is not something cranky or some alternative view.
Similarily this is applying to neutrino used in the example. Neutrino has very tiny invariant mass (rest mass), but it has significantly bigger effective mass (relativistic mass) when flying with speed of 99,9999% of c.

So your statement that "photon should follow the geodesic of the curvature of spacetime, since it has no mass" is not true, because it has effective mass and Im trying to show in example in OP that the real situation of bending of light is not that simple as described in common popscience descriptions. And additionally the effective mass of photon means that if would also bend due to Newton theory, but it gives only the half or correct value predicted by GR.

 

Sorry to have to say this, but it sure sounds like it. No experiment has been able to measure the mass of a photon. Then this line of reasoning would fall out of experimental verification. It hasn't been measured to have mass at high or low frequencies. Then you are right about one thing, a photon couldn't exist at rest, so I do not feel it is necessary to talk about it's rest mass.

I don't know if you saw my other response to your question in the other forum, but the curvature of spacetime has been proven, in a sense. Since light has no mass, the curvature of light can only be explained by the presence of spacetime curvature. If you believe that a photon has mass, then you wouldn't believe this explanation either. There lies your problem of your understanding of it.

 

What are these "popscience descriptions" that you speak of?

 

But one can speak of the mass equivalent of the photon. And if the photon had a rest mass, this would put limits on electromagnetism that have been tested and that put a very small upper bound on the possible rest mass of the photon.

This is not the case. There could be many reasons why light would curve, some of which are simply derived from (or added to) Newtonian theory and some of which are more fanciful. There is little or no evidence, however, for these explanations.

 

I believe it to be the number one reason why popular science (mainstream science) believes that spacetime curvature actually exist, even though it may not be a good reason to some people.

 

It's not a good reason to scientists who work on gravity. Are you saying that you should continue to promote something that is wrong merely because you believe it to be popular?

 

See the curved path through flat background will be initial speed dependent, there is no ifs and buts here.

But if an object moves through curved spacetime due to presence of a massive source, then the dependence of curvature on the object's speed is bad. It boils down to a fact that GR equation and spacetime curvature is nothing but mathematical explanation of motion of an object under gravity. Like a projectle is a parabolic path and dependent on initial velocity, but that does not mean space there is parabolic...space is not spacetime.

 

I dont know how to write it that you and others get it: Invariant mass (rest mass) of photon IS ZERO. Effective mass (relativistic mass) of photon IS NOT ZERO.

 

There are more reasons why I believe that spacetime exist, but a lot of those reasons deal with my own interpretation of quantum mechanics, which probably wouldn't be appropriate here.

I see how physicist working on Quantum Loop Gravity or with gravitons could have a problem with this, since both theories seem to want to replace spacetime curvature. Then the Higgs Field description of gravity never really seemed to get that much attention out of physicist. Although, I think it should get a lot more attention due to the discovery of the Higgs Boson. It would make me think that they should switch to trying to explain gravity solely in terms of the Higgs Field and how that could give rise to spacetime curvature.