What is general relativity in one irreducible simple sentence?

[Helicobacter]

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 I am looking for an intepretation of the einstein field equation without knowing diff eq's


i think I've 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 I am 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"

 

[zhermes]

for general relativity, all i see on the internet is a bunch of statements clustered together

That's usually what both the interweb, and explanations in general are.

but what is it?
...
i think I've 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.

Okay. Well based on that model, I guess the best answer would be either:
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'

and a third question I am wondering about: why does your mass increase exponentially when you get linearly closer to the speed of light?

Why do you say the mass increases exponentially?

 

[HallsofIvy]

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

 

[Helicobacter]

i meant to say: why does it require exponentially more energy...wait..isnt that the same thing?

 

[pervect]

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 I am looking for an intepretation of the einstein field equation without knowing diff eq's

It might be too advanced if you don't have at least calculus, but http://math.ucr.edu/home/baez/einstein/ is pretty good.

GR is basically about geometry. In particular, the geometry of space-time. 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 space-time 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/

 

[zhermes]

i meant to say: why does it require exponentially more energy...wait..isnt that the same thing?

(First, its somewhat poor-form to talk about 'mass increasing', but using that type of language...)
$$m' = \frac{m}{\sqrt{ 1 - \beta^2 } }$$
As $\beta \rightarrow 1$ (i.e. $v \rightarrow c$), the 'mass' becomes unbounded, but not exponentially. I.e. the initial statement is false.

 

[harrylin]

for general relativity [..]

i think I've 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.
[..]

Ok, that's reasonably close to Einstein's original formulation of SR.
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 free-falling system as an inertial frame.

 

[markosr]

and a third question I am 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"

As previous posters have already stated... it's not linear / exponential; rather mass approaches infinity as speed approaches c. Anyhow, my favourite intuitive explanation is that speed of light is in fact an infinite speed. You can see that is very much true if you are the one traveling at light speed, you can travel any distance in an infinite small amount of time. You can go to M33 (2 millions lys away) in a second of your time... if you live to tell about it due to very large accelerations involved. :)

 

[kmarinas86]

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."

 

[tiny-tim]

Hi Helicobacter!

… in other words I am looking for an intepretation of the einstein field equation without knowing diff eq's

Since you know Einstein's field equations, what's wrong with the simple description:

at every point, the curvature of space-time (that's geometry) is proportional to the stress-energy tensor (that's physics)?

 

[yuiop]

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.

This throwaway line makes me sad and I could not let it go unchallenged. One notable feature of GR is that time dilation is not reciprocal as it is in SR. While in SR, A might think B's clock is ticking slower and B thinks A's clock is ticking slower, in GR both observers agree which clock is ticking slower. If for example A is high up and B is low down close to an event horizon, then A will say B's clock is ticking slower, and B will agree that A's clock is ticking faster. This is not just an optical effect due to signal travel times. Clocks low down in a gravity field really do tick slower.

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.

 

[zhermes]

That is an interesting way of thinking about it markosr; but this view has some serious flaws.

Anyhow, my favourite intuitive explanation is that speed of light is in fact an infinite speed. You can see that is very much true if you are the one traveling at light speed, you can travel any distance in an infinite small amount of time. You can go to M33 (2 millions lys away) in a second of your time... if you live to tell about it due to very large accelerations involved. :)

The speed of light is very much a finite speed. That's how we can use lasers to measure distances (or times w/ a known distance); that's why gravity/electromagnetism doesn't respond instantly, and thus why waves are able to exist in both cases.

Additionally, while it is a tempting question, there is no valid reference frame traveling at the speed of light---thus you cannot ask what 'time durations' are for such an observer.

 

[Sam Gralla]

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".

 

[pervect]

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".

If you use the rulers that we actually use, which are derived from ones made out of atoms, basically, then you'l find that space-time geometry is curved, no question about it.

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 high-level 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.