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What is general relativity in one irreducible simple sentence? 
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#1
Feb2012, 07:28 PM

P: 159

for general relativity, all i see on the internet is a bunch of statements clustered together: "oh yeah, general relativity is pretty important and explains black holes, time dilation, and gravitational lensing"
but what is it? at a point that has more energy, time goes faster? in other words im looking for an intepretation of the einstein field equation without knowing diff eq's i think ive read a simple statement about special rel: speed of light is c in a vacuum and physical laws are the same in every inertial ref. frame. and a third question im wondering about: why does your mass increase exponentially when you get linearly closer to the speed of light? im looking for an intuitive explanation rather than just something like "well in this equation the dependent variable has a power attached to it" 


#2
Feb2012, 07:50 PM

P: 1,261

The equivalence principle: ~ 'the equivalence of inertial and gravitational mass is the same as the acceleration from a gravitational field is insensitive to the nature of the accelerated object' or The principle of general covariance: ~ 'the form of all physical laws are invariant under differentiable coordinate transformations' 


#3
Feb2012, 07:59 PM

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There is no answer to your third question what you assert is not true.



#4
Feb2012, 08:04 PM

P: 159

What is general relativity in one irreducible simple sentence?
i meant to say: why does it require exponentially more energy...wait..isnt that the same thing?



#5
Feb2012, 08:54 PM

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GR is basically about geometry. In particular, the geometry of spacetime. GR is not really about time moving faster, or slower  except insofar as one can model a curved geometry by imagining that rulers change length. Some good quotes that describe GR: "Mater tells space how to curve  space tells matter how to move". (Wheeler) "The geometry of spacetime is locally Lorentzian" (from MTW, I'm not sure which of the authors came up with that quote). You might try reading Einstein's popularization, http://www.bartleby.com/173/ 


#6
Feb2112, 10:08 AM

P: 1,261

[tex]m' = \frac{m}{\sqrt{ 1  \beta^2 } }[/tex] As [itex]\beta \rightarrow 1[/itex] (i.e. [itex]v \rightarrow c[/itex]), the 'mass' becomes unbounded, but not exponentially. I.e. the initial statement is false. 


#7
Feb2112, 11:06 AM

P: 3,187

Similarly, reasonably close to the original formulation of GR (based on Einstein's formulations and I hope, not too inaccurate): Physical laws are locally the same in all reference frames; the effect of acceleration is the same as the effect of gravity. Or, in a nutshell: you can treat a freefalling system as an inertial frame. 


#8
Feb2112, 11:09 AM

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#9
Feb2112, 04:23 PM

P: 1,011

The OP meant "exponentially" in a figurative way.
I presume that the OP did not mean "according to the exponential function". Of course, it's not better to use "layspeak", but it's even worse to give an unenlightening response, such as, "There is no answer to your third question what you assert is not true." 


#10
Feb2112, 05:21 PM

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Hi Helicobacter!
at every point, the curvature of spacetime (that's geometry) is proportional to the stressenergy tensor (that's physics)? 


#11
Feb2412, 03:49 PM

P: 3,967

Let us say we set up an experiment with twins, both initially high up. Let us say B descends over a period of 2 days at a controlled velocity to a location near the event horizon. A waits for 50 years and then descends at the same controlled rate over a period of two days to meet up with his sibling. It is perfectly possible according to the rules of GR that A has aged around 50 years and B has only aged by a couple of weeks. This experiment is designed to cancel out any time dilation due to motion as both move in exactly the same way, just at different times. I am not sure why people in this forum constantly try to dismiss gravitational time dilation and try to make out it is not a real effect. 


#12
Feb2412, 03:59 PM

P: 1,261

That is an interesting way of thinking about it markosr; but this view has some serious flaws.
Additionally, while it is a tempting question, there is no valid reference frame traveling at the speed of lightthus you cannot ask what 'time durations' are for such an observer. 


#13
Feb2412, 04:45 PM

P: 95

I think it would be pretty funny to ask this question to a bunch of string theorists. Would we get "gravity is geometry" or would we get "well, there's this flat metric, and lots of strings that perturb it, but then somehow they all pile up on top of each other and we realize the flat metric is fake, but we still take it very seriously".



#14
Feb2412, 09:51 PM

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You can regard the rulers as being affected by some mysterious "extra fields", and this distortion of rulers as causing the geometry to be curved, ala Einstein's heated slab. http://www.bartleby.com/173/24.html I have a feeling that the "heated ruler" sort of approach might be more understandable to most than the curved geometry, but I'm not aware of anyone popularizing it. The string theorists sort of do that, but they popularize it in a way that needs math that is as highlevel as the GR folks use  it's just that it's not the same math, it happens to be the math of the sort that the string theorists like. 


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