# Inflation and curvature

Discussion in 'Physics & Math' started by prometheus, Jan 6, 2011.

1. ### przyksquishyValued Senior Member

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What are you talking about? I just posted two of them. I have two predictions of general relativity, in the form of metrics, both of which are solutions of the EFE. What did you think I meant?

No it's not. Yes, a metric does vaguely have something to do with measurements, in the sense that it appears in all expressions intented to predict physically measurable quantities, but what you say above doesn't exactly sum up what a metric is.

If you really believe that then why do you keep talking about the speed of light being zero there, as if that was a quantity anyone could measure?

No I haven't. The c I set to zero is an a priori constant in GR, equal to 299,792,458 m/s everywhere and at all times in the current metric system of units (effectively by definition since 1983). It's never zero.

What evidence? You haven't thrown a clock into a black hole and you couldn't retrieve it if you had.

This might be a silly question, but you *are* aware that the Kruskal metric makes exactly the same predictions as the Schwarzschild metric does in these cases, right? In particular the Kruskal solution also predicts that a clock sitting on the event horizon will freeze (because its moving at the speed of light), just like the Schwarzschild solution does. It's only clocks falling past the event horizon that don't stop.

No it's not close enough. These are two completely different situations. Like with simultaneity, the time clocks accumulate is already dependent on the path they take in special relativity. There is absolutely no reason that because a clock sitting on the event horizon freezes, that one falling past it should too.

You can't dismiss the Kruskal solution on those grounds because 1) it doesn't predict that a clock crossing the event horizon stops, and 2) you apparently believe the Schwarzschild chart does predict that and you aren't using it as an argument against the Schwarzschild chart.

Do you really need any more convincing the Schwarzschild coordinates blow up on the event horizon? That term that diverges isn't even associated with t. This one's associated with the radial coordinate.

The local speed of light? As opposed to what? Some fictional speed of light that nobody actually measures?

What are you talking about? It's been done. The Kruskal chart does effectively eliminate the infinities in the Schwarzschild metric, none of which are coordinate-independent quantities (so nothing physical is acually being changed).

Where did I ever say you could?

3. ### Guest254Valued Senior Member

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1,056
Well what a shame, I really thought that might help!

5. ### AlphaNumericFully ionizedRegistered Senior Member

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Farsight has this obsession with dismissing people who understand GR by saying "You think the metric is a real thing!! It's an abstract concept!!!" as if we think there's a metric under a rock somewhere.

It's like saying "You're using calculus!! You think a derivative is a real thing!!". No one who does calculus thinks there's a planet somewhere with little $\frac{\partial}{\partial x}$'s running around.

Farsight is arguing about things he doesn't understand. He doesn't know any beyond high school level mathematics so all he can do is try to arm wave about the qualitative stuff he's skimmed from Wikipedia. Pulling out the "The metric is not a real thing!!" is just his way of trying to make it seem like he's taking the rational side against some militant mathematician who thinks metrics are literal physical things. It's all because he can't do the mathematics and he doesn't understand how people who can think about the mathematics.

Magneto seems to have similar issues.

7. ### Guest254Valued Senior Member

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1,056
No, it's because academics spend all their energy suppressing the amazing thoughts of Farsight and people like him. Come on AlphaNumeric, get with the program!

8. ### quantum_waveContemplating the "as yet" unknownValued Senior Member

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I bet I'm on everyones ignore list. I did apologize for flaming and for not understanding what constitutes trolling. Was I out of line to post this link?
Edit: Thanks to rpenner. He pointed out that I should link to the abstract page on arXiv:
http://arxiv.org/abs/1106.3542

It seems to be appropriate to this thread and if so, can someone comment about the paper?

Last edited: Jul 2, 2011
9. ### rpennerFully WiredRegistered Senior Member

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4,833
In my opinion you were twice out of line because you should always link to the abstract page on arXiv: http://arxiv.org/abs/1106.3542
And in the second post, the link is malformed due to cut-and-paste from the forum.

"Eternal" or "Chaotic" Inflation is not about the standard Inflation model and so may be off-topic. So far as evidence, Eternal Inflation rests on shaky ground. I'm not aware of an event which does not end life on Earth which would be a demonstration of it. Since I can't speak for particle physicists, I would assume in my ignorance that particle physics does not strongly (or at all) point in the direction of Eternal Inflation.

Some things the author writes in the first paragraphs makes me think she is on shaky ground when talking about quantum mechanics and string theory.

http://en.wikipedia.org/wiki/Chaotic_inflation
http://arxiv.org/abs/hep-th/0702178 (review article)

Last edited: Jul 1, 2011
10. ### quantum_waveContemplating the "as yet" unknownValued Senior Member

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Thanks for straightening me out on that and for correcting the link.

11. ### Farsight

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IMHO she has credibility, but this is a rather speculative "multiverse" paper. The multiverse doesn't have any experimental support, so I'd say aspects of the paper lack credibility. It seems to talk about abstractions and hypotheticals as if they were real and factual. For example this excerpt...

Towards the end of the DS contracting phase, (just below the ai = 0 boundary), spacetime has contracted to its minimum size near the boundary, all the bubbles have merged, have grown to fill the whole spacetime, and thermalized.

...has me saying you don't know that these bubbles are real, spacetime is a mathematical space, and surely thermalization isn't relevant to a very early universe that can be likened to a black hole.

12. ### Farsight

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I think you meant to prove a point regardless of the crucial issue. I've been talking about non-real solutions, and you're still not understanding that the expressions don't feature c because there's an axiomatic presumption that c=1. Everything I've been saying to you is an attempt to get you to appreciate that c=1 only because we are "made of light" and thus measure the local speed of light to be the same when it isn't - gravitational time dilation is the light going slower, and when that goes infinite the light has stopped.

OK.

Because the reality underlying gravitational time dilation is a reduced speed of light, only "we are made of light" and so can't measure this reduction locally.

That definition uses the motion of light to define the second and the metre, then uses them to measure the speed of light. It's tautological.

No, but we have good evidence from optical clocks etc, and can extrapolate.

Sure. The issue comes with sweeping the future-infinity away and thinking you can cross the event horizon.

Come on przyk, remember that pair production. Make it a light clock, so light has frozen, and all electromagnetic phenomena has frozen, including the electrons etc from which the clock is made. They're frozen not just in terms of spin, but also in terms of linear motion. So that clock isn't falling past the event horizon.

Clocks just clock up local motion, in SR a fast-moving clock clocks up less because the total motion is limited to c, then in GR we've got a variable c like Einstein said. But we've still got the principle of equivalence, wherein an SR optical clock moving at c doesn't clock up any local motion, and a GR optical clock at the event horizon doesn't either. Because light has stopped. Like everything else, including the macroscopic motion of the clock.

It's the Kruskal-Szekeres metric, I'm challenging it on the grounds that it goes beyond the point where measurements stop by sweeping future infinity under the carpet.

No. But you still need convincing that you need to get to the bottom of what this blow-up is all about.

The actual speed of light. When one precise optical clock at one elevation goes slower than another at a higher elevation, it's because the light's going slower. Even though at both locations you measure the speed of light to be 299,792,458 m/s ...because you use the motion of light to define the second and the metre then use them to measure the motion of light.

That's what I'm challenging. Don't eliminate the infinity that way, see that it's really a c=0.

You didn't say it directly. But the Kruskal-Szekeres coordinate system is plotting beyond the end of time, and you can't see the problem with it.

Can we try to keep the posts shorter please and focus on one point?

13. ### quantum_waveContemplating the "as yet" unknownValued Senior Member

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Thanks to rpenner and Farsight for your comments on the Mersini paper. It is perhaps off-topic as rpenner says, especially since there is a robust discussion on this thread that doesn't need the distraction. I will refer to the rpenner and Farsight posts in my thread and leave this thread to the current debate. Thanks for the input.

14. ### AlphaNumericFully ionizedRegistered Senior Member

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And you don't see a problem with you arguing about coordinates in differential geometry when you don't know any of the relevant mathematics and have no experience working in the relevant areas of physics, on even a student level? :shrug:

15. ### przyksquishyValued Senior Member

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3,171
And you've been failing to explain why the Kruskal metric should be dismissed as "non-real". I put both the Kruskal and Schwarzschild metrics in front of you, and you couldn't explain, starting with those actual, raw, predictions of general relativity, why one should be dismissed as "non-real" and the other accepted as "real".

No, I'm not presuming anything. The Schwarzschild metric with the (constant) factor of c (and G) left in is
$\mathrm{d}s^{2} \,=\, -\, \bigl( 1 - \frac{2Gm}{rc^{2}} \bigr) c^{2} \mathrm{d}t^{2} \,+\, \bigl( 1 - \frac{2Gm}{rc^{2}} \bigr)^{-1} \,+\, r^{2} \mathrm{d} \Omega^{2} \,.$​

No, that isn't what either SR or GR is about. I've already corrected you on this several times now. Robert Close, the guy you keep quoting, is basically a century behind the times when it comes to his understanding of relativity. He's trying to solve a problem he doesn't seem to understand Einstein already solved in 1905. So he's trying to reinvent the wheel and doing it poorly at that. Once again: we will always measure an invariant c as long as we measure the speed of light using any instruments whose structure is governed by Lorentz-invariant physical laws. This does not require everything to be "made of light" or even to obey the relativistic wave equation.

If nobody will ever be able to measure it then what merit is there to saying the speed of light reduces at all?

No it doesn't. By that point the speed of light is already defined. Since it would be silly to try to measure a quantity with a defined value, using the units in which it has that defined value, nobody does it. People did however do experiments and measured an invariant speed of light before it was made invariant by definition. You seem to keep forgetting that.

Extrapolate how? Observational evidence alone only suggests that clocks at ever lower gravitational potentials will continue to slow down, but not that they'll ever stop. Observations of clocks at different altitudes doesn't necessarily imply there even is such a thing as a black hole.

So it's only meaningful to extrapolate on the basis of what general relativity predicts about clocks near black holes. But even there you've got nothing to support your case. For a clock at constant Schwarzschild radius from the black hole, both the Schwarzschild and the Kruskal metrics make identical predictions and both say that a clock sitting on the event horizon is frozen. For the Schwarzschild solution you have to take the limit $r \rightarrow 2M$ to work this out. In the Kruskal chart you can work this out directly: you get the same result as with Schwarzschild without even needing to take a limit.

But for a clock falling into the black hole the story is completely different: the Kruskal metric predicts that the clock won't stop, while the Schwarzschild metric blows up on the event horizon and can't be considered to predict anything. So the only extrapolation you can make, based on GR, about a clock falling past the event horizon is that it won't stop.

That's the whole problem: you are still assuming, without justifying anything, that anything at all freezes when crossing the event horizon in the first place.

This is something else you just keep repeating without any support. You have defined no meaningful sense in which light "stops" on the event horizon. All the justifications you give are circular: you say clocks stop on the event horizon because light has stopped, and you say light has stopped on the event horizon because clocks stop. But you've never justified either of these assertions.

I didn't say it at all, directly or indirectly. The only problems are your own unquestioned assumptions. You keep assuming the Schwarzschild coordinates have more physical significance than you've been able to justify. In this case you are assuming that the Schwarzschild coordinates actually cover all of space and time. You have no basis for assuming that, and so you have no basis for assuming that because a clock shoots off the top of the Schwarzschild chart, it's shooting beyond the "end of time".

Last edited: Jul 4, 2011
16. ### AlphaNumericFully ionizedRegistered Senior Member

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As I've already commented on, Farsight has issues grasping (or grasping other people's grasp) the role abstract concepts have in physics and mathematics. He's already accused people (not just in this thread) of thinking the metric is a real thing, like the computer infront of me is 'real', when no mathematician thinks such a thing. He's been confused by the notion of 'virtual particles', compared to usual particles, not realising its used in a different manner to "real vs make believe".

Just like some people think the 'real numbers' are more valid than the 'imaginary numbers' because obviously 'real' things exist and imaginary things don't exist Farsight struggles with such concepts, he just likes to talk about more advanced ones (though he doesn't understand even the simple ones). He's trying to tell us about coordinates and manifolds and metrics but he doesn't understand them beyond what Wikipedia and Google can tell him.

The problem is he doesn't understand the models which he's referring to.

Farsight, if you accept the SC metric description of a black hole then you must accept all which follows from it by the same methodology. Objects falling into the event horizon will continue to count time as they pass through it. Objects outside the EH won't see them count said time, they are causally disconnected (at least in one direction). The fact the object inside the EH can't communicate with an object outside the EH doesn't mean time stops.

You have got a fundamental misunderstanding of what coordinates mean in general relativity. If you don't like Kruskal coordinates then try Eddington-Finklestein coordinates, they allow a description of crossing the event horizon which is singularity free and they preserve the causal structure.

You talk about 'extrapolating' but what you really mean is you just following your gut instinct which, as I've said, has absolutely no experience with any of this sort of physics. You don't know how to do any of the relevant coordinate vector calculus or coordinate free differential geometry.

I'm certain I've recommended the book 'General Relativity' by Wald to you at some point. There's a ton of examinations of black hole space-time structures in that and it is done, in large part, in coordinate free formulations. That's how the best relativists work, they don't even make reference to a coordinate system because the coordinate system is physically irrelevant. People like the SC metric formulation because its useful for doing explicit calculations, its spherical symmetry makes the calculus easier and far from the black hole the coordinates are akin to normal spatial coordinates. However, the fact they are convenient for certain calculations (which you've never done) or illustrate a particular symmetry manifestly doesn't make them physically more valid any more than French is a more valid language to describe the world in than English or Japanese.

If you had ever been intellectually inquisitive and honest enough to open a textbook and try to learn, rather than thinking you know it all via divine knowledge, you'd have a much less myopic view of physics. Instead you cling desperately to the few concepts you think you've got your head around (like pair production) and denounce anyone who actually did read the books you didn't as thinking maths is real or wasting their time learning stuff your work has killed.

If you'd started a university undergrad course when we first crossed paths by now you could be half way through a PhD doing real research. Instead you've thrown time and money down the drain.