Neutrinos faster than the speed of light?

I see now that username may be confusing a hypothetical barrier with a real one.

A very interesting phenomenon is the sonic boom, which is the simultaneous arrival of many sound waves "from different times" at once. At least that would be the optical analogue.

Yeah I liked the remarks you found. It reminds us that they knew they were in deep-yogurt by jumping the gun with the press release.

That's a mathematical result which can have interesting physical interpretations. It requires us to speculate about the meaning of, say negative area, here considering the more tangible idea of an imaginary length (only because the square of mass is not as easy to conceptualize).

The other thing to do is to allow t to be negative, which is to say that time is reversing, which is the other thing that makes tachyons out of reach, and it really busts the idea that a positive delay could be observed in a FTL measurement.

 

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Photons are never at rest. They only move at v=c.

 

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So even light has its limitations then. Agree or disagree?

 

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Not sure what you mean. All of the spectra (above and below visible light) are conveyed by photons, and all of these propagate at c. That's not exactly a limit, it's better expressed as constant. The limit applies to any acceleration that approaches c (from the left in the plot I posted). There's a wall there.

 

When light hits a black hole scientist say it is something not even light can escape. What is meant by light not being able to escape something? It means that light doesn’t have a steady state of velocity so not even light can be considered a constant.

 

The reverse is true. Only c remains constant, while space and time undergo severe distortions from the observer's vantage point. At the event horizon these distortions become critical, such that there is too much space and not enough time for the light to reach the plane the observer is on.

 

That's only true in special relativity where the frame of reference is inertial. Einstein demonstrated that wasn't the case in 1907 when he stated th equivalence principle. Later on he derived the expression for the speed of light in general relativity in terms of the speed of light in an inertial frame of referemce thus showing that the speed of light varies in gravitational fields/non-inertial frames of reference. See - http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

 

As light approaches a blackhole it slows down as reckoned by far away observers aka Scwarzschild observers, i.e. observers external to the event horizon. According to such observers the light never reaches the event horizon.

 

Pete,

I sure admire the tact that you show with members. I hope to learn such patience from you.

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http://youtu.be/9XjS4I4oQDY

Above is a link to the YouTube video referenced.

I don't still have copies of the original papers.., but Michio Kaku's video above was made during the gap between the original paper, the identification of the loose fiber optic connection that led to the inacurate results and the follow up experiment with a short burst beam(s) that demonstrated confirmed that the neutrinos were not FTL.

Michio Kaku is a charismatic teacher/theoretical phycist. In the first part of the video where the misunderstanding originates, he is talking theoretical implications.., which essentially amount to speculations about, what ifs and imagination. The what if, aspects of theoretical physics are seductive lay public talking points. Everyone is interested in multiple universes, faster than light warp drives, worm holes etc. The problem is, that many in the lay public, fail to recognize the difference between the theoretical and imaginative what ifs.., and what is known for certain.

When watching popularized mini presentations by well known physicists, as this one on YouTube, it would be well to stop and listen carefully, for the line that separates specualtion from knowledge.

The original OPERA results and follow up papers are all still available on the arXiv web cite. To get started just search for OPERA and Neutrino... However they are not an easy read without some background.., I.E. They are not a five minute press release or popularized YouTube video.

 

Come on. Einstein didn't prove anything. He wrote down a theory of gravity which predicts the radial remote coordinate speed of light is

dr/dt_bkkpr=1-2M_meter/r_shell [Schwarzschild coordinates]

All local measurements of the speed of light v=c [as per Id]. Within small error bar associated with any measurement limits and small local spacetime curvature. The remote observation is a global analysis which takes into account the spacetime curvature over the entire path from boundary to 2M/r. All frames in relativity theory are inertial. The geodesic path is linear in SR and non linear in GR. Nice derivation.

 

Einstein postulated the equivalence principle in 1907. In 1911 Einstein published the article On the Influence of Gravitation on the Propagation of Light in Annalen der Physik, 35. In that paper he used the equivalence principle to derive the expression c = c_0(1 + Phi/c^2) for the speed of light in a gravitational field. Phi = gravitational potential where the light is and c_0 = speed of light in vacuum as measured in the absence of a gravitational field, i.e. in an inertial frame of reference. You can call this a theorem if you’d like. If so then it can be said that Einstein proved this theorem. When someone derives an expression/result from other theorems or postulates then one is said to have proved the result of the theorem. That’s the context in which I used that term. The term "prove" arises a lot in physics. Its important to understand when its use is valid and when it isn't and what it means when its used correctly.

I myself don’t worry about what kind of speed to call that. I.e. I don't bother qualifying it with "the coordinate speed of light" since no other speed is possible. E.g. one cannot assign a proper velocity to a photon. And if there's a gravitational field present then by definition the frame is not inertial. The speed measured is not local since the speed depends on potential and when measured locally the potential is zero and c = c_0. In any case all these details are implicit in the derivation and the results.

However I see this can be confusing to people so I rephrased it.

That’s incorrect. Frame of reference in which there is a gravitational field present are not inertial frames. Theorist use such frames in their work a great deal of the time. When one of your observers is sitting on a shell around a black hole then he’s not in an inertial frame of reference.

May I assume you got that impression from Exploring Black Holes? If so then that's one of the key ideas in that textbook, so in that textbook that's what they do. However that's not true for all GR texbooks and not in all work in GR. E.g. when Robert Pound measured graviational redshift at Harvard it was done with equipment which was at rest on the surface of the earth which is a non-inertial frame of reference.

The people who use the GPS system use GR and they're not in inertial frames either.

 

Ummm... that expression is derived in that link I gave, i.e. its Eq. (10) in http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

 

This is much easier. In geometric units.

dTau ^2= (1-2M/r)dt^2 - dr^2/(1-2M/r) - r^2dphi^2 [The Schwarzschild metric setting theta at 0]

For light

dTau^2 = 0 = (1-2M/r)dt^2 - dr^2/(1-2M/r) - r^2dphi^2

Setting dphi at 0

dr/dt = +/- (1-2M/r) [light radial motion].

Setting dr at 0

rdphi/dt = +/- (1-2M/r)^1/2 [light tangential motion].

The theory of general relativity describes the natural path of matter through the gravitational field. The natural path of matter through the gravitational field is inertial. I think you believe geodesic paths through the gravitational field are not really inertial. I can't say for sure but I tend to think many folks find this harder to understand because of the initial association with Newton's theory. At rest at r_shell is an interruption in the natural path and is accelerated in the same way 'our personal natural paths' are interrupted by the surface of the earth. As soon as the object falls from r_shell the path is natural. The only other path that doesn't begin 'as falling' is one that begins with a boost. The one that Taylor and Wheeler call 'Hurling a stone into the black hole'. A derivation from E/m = (1-2M/r)dt/dTau = constant. I have a different perspective because I never formally learned Newton's theory of gravity. I learned what I needed to know doing the weak field approximations. I'm not confused by stuff that isn't part of GR. At least I don't think so.

 

Not at all. Where did you ever get an idea like that? In the first place I've never ever said or wrote anything like that and in the second place it'd be contrary to general relativity which I fully accept with no reservations. The only difference between myself and the GR community is that I adhere to GR precisley as Einstein intepreted the gravitational field and gravitational forces (aka inertial forces).

Regarding the issue of whether one always works in inertial frames in GR I sent two GR experts, i.e. Øyvind Grøn and John Stachel, the following question

John Stachel responded saying

Øyvind Grøn responded saying

I'm going to get some other opinions on this too since its something I want to give Edwin Feedback on. It's unfortunate that people take what he does in his book and assume that it's done throughout the GR community. For example; I mentioned to you before that nobody I know of (or at least very few people) except Edwin et al uses the term "shell observer" or "far away observer." But when people assume that just because he uses inertial frames exclusively in their text that everyone else does also. I find it odd too because I recall some calculations regarding what shell observers measure and they're not in freefall.

Question: I tried to say some of this in a PM to you since I don't like quoting friends in public but since you don't respond to them I can't tell whether you read them and choose not to ever respond for some unknown reason or that you've never had a reason to respond to what I've sent. May I ask why?

 

pmb

No, he did not and any real scientist knows better than to say ANYTHING is proved, that goes double for theories. Proofs can only be said to exist in math only because math is a collection of rules, it is not the real world. The speed of light is always measured as C. It does not change. What changes is the vector and frequency of the photon, the rate of time's passage and the shape of local spacetime. When it encounters a Black Hole it's speed does not change, it still continues to travel at C, it's just that all possible vectors lie within the Event Horizon, space itself is curved such that no such vectors even can exist.. Light in a vacuum has never been seen to travel at other than C. Time and Space alter to the extent and in the direction necessary for light to remain at C and a gravity field is nothing but curved spacetime. Just as light's path bends as it passes mass, it's path is bent infinitely as it enters an Event Horizon(bent by the mass)and no path outward again can exist, thus "Black" Hole. A photon experiences no time and it always travels at C, it is tied into both space and time, it is as much a property of spacetime as space and time are, it is how energy moves through spacetime. It's SPEED through spacetime is a CONSTANT of the Universe, it NEVER changes(as a scientist and in the interest of accuracy, I must say that "The speed of light in a vacuum is always measured to be the same regardless of frame or relativity between frames. No instances where this is not true have been found." Nothing has been proven, however.).

Grumpy

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Why did you ignore my response to this point to Brucep? I explained to him that he proved it in the sense of proving a (mathematical) theorem from basic postulates, not as proved in the scientific sense. Did you not see my response or did you not understand my response?

 

GR is the general theory of gravity that describes the natural path of matter through the gravitational field. Natural path = inertial motion. That's what the theory does. What you asked those 'fine physicists' is whether there is more than one choice of coordinates to do the physics in. Go back and read your comments, in post #47, that I initially responded to

" Originally Posted by pmb
That's only true in special relativity where the frame of reference is inertial. Einstein proved that wasn't the case in 1907 when he stated th equivalence principle. Later on he proved in general relativity that the speed of light varies in gravitational fields/non-inertial frames of reference. See - http://home.comcast.net/~peter.m.bro..._in_gfield.htm."
"....... gravitational fields/non-inertial frames of reference...."
The natural path is inertial motion through flat and curved spacetime. Since GR is a coordinate independent theory choice of coordinates are a convenience for doing analysis. Choosing a non inertial coordinate system for GPS 'operations' is a matter of technical [operations] convenience. The fact remains that GR is a general theory of gravity that describes the natural path [inertial path] of matter through curved spacetime. SR is the special case where the effects of gravity can generally be ignored during local experiments. It's the space tangent to every point on the spacetime manifold. The space along every segment of the natural path where the spacetime is approximately flat. This isn't something Taylor and Wheeler dreamed up for Exploring Black Holes.

 

Nope. Sorry bruce but you've made mistakes here again. Since we're ignoring things that people say then that's all I have to say.

 

You’re wrong and the proof that you’re wrong was given by Einstein in 1911 and is repeated here - http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

If you are unable to follow the derivation of that theorem then let me know and I’ll help walk you through it. Otherwise please stop peddling misinformation because others want to know what GR really predicts and what experiments really show. One experiment which confirms the changing of the speed of light in a gravitational field is the Shapiro time delay. Look it up.

If the speed of light didn’t change then Schwarzschild observers would reckon that light moving towards the event horizon would cross it rather than what really happens, i.e. light comes arbitrarily close to the event horizon but never reaches it and thus, never mind cross it. At least not according to externel observers. This fact is what I proved to you in the link above. And please don't confuse the use of the term "prove" like you and bruce did above.

Your problem here is that you’re consistently confusing the locally measured speed of light with the coordinate speed of light (cso). The cso is a very real phenomena and not something that is merely a mathematical curiosity. The cso changes from c = 3x10^8 m/s when it enters a gravitational field to the value given in the link above in the special case of a radially moving photon. I just showed you the derivation of that fact. If you choose to ignore it then that’s your business. I’m here to make sure that your confusion and the resulting misinformation that your posting doesn’t spread to the rest of the forum members. The changing of the speed of light in a gravitational field is what the entire physics community knows to be the case.

I’m just going to make sure that the rest of the people reading this thread doesn’t make the same mistake that you’re content on living with. Although I am curious as to why you ignore proof when its given to you. I can only surmise that you’re unable to follow it.

This is just more misinformation. What makes it bad is you’re still passing it as the truth when your claims have been proven wrong. The Shapiro time delay is evidence of the slowing of the speed of light in a gravitational field.

Everything I’ve just told you can be found in Gravitation and Spacetime – Third Edition by Ohanian and Ruffini, Cambridge University Press (2013). This book is so new that it’s still warm from being right off the press. Instead of living with the wrong information you have why don't you read this text and learn why what I've been teaching you is right?

On page 143 they again derive what I showed you above. Their result is in Eq. (4.45) on page 143. In geometric units the speed of light in a Schwarzschild gravitational field is given by

Eq. (4.45) dz/dt = 1 - 2GM/r

The author even states

I’m very curious as to how you’re going to misinterpret that (or will you claim that he’s wrong too?) as being consistent with your claim.