# The Naked Scientists Forum

### Author Topic: What is Einstein's space-time curvature?  (Read 6026 times)

#### mxplxxx

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##### What is Einstein's space-time curvature?
« on: 14/05/2015 09:31:06 »
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?
« Last Edit: 15/05/2015 07:54:44 by chris »

#### David Cooper

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##### Re: Einstein's space-time curvature
« Reply #1 on: 14/05/2015 19:00:57 »
It's hard enough just trying to visualise Spacetime without trying to imagine curving it under gravity, so you're asking a lot. If you can already visualise Spacetime properly though, you should be able to do the curving bit yourself.

#### Thebox

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##### Re: Einstein's space-time curvature
« Reply #2 on: 14/05/2015 19:45:28 »
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?

I will try although it hardly makes sense.

space-time is the forth dimension, imagined as a continued line.

as - ...

A dimension that is connected to shape dimension. length, width and height, in science x,y,z

x being vertical and y being horizontal, and z width,

now if you can imagine a straight line like above, and then from point (a) to points (b) , there was also  a curved line

...........................................a
........................a.......................................a
...............a..........................................................a
........a........................................................................a
...a....................................................................................a
a..........................................................................................b

The curve is a greater distance than the straight line

if we flattened out the curve , compared to the straight line,

line.........................................................

curve...................................................................................................

now if you imagine two rockets racing, one takes the straight course and one takes the curved path, and both rockets travel at 1000 mph, the rocket taking the straight path uses less space-time to get to B.

Hence space-time curvature.

I think this is what it means.

#### PmbPhy

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##### Re: Einstein's space-time curvature
« Reply #3 on: 14/05/2015 20:23:00 »
Quote from: mxplxxx
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?
Sure. It's fairly simple. Spacetime curvature is the same thing as tidal gradients which are variations in the gravitational field. Think about four particles moving in a gravitational field all of which start from rest above the Earth's surface. Place two of the along a radial line and two of them along a circle of constant radius whose center is the center of the Earth (picture all of this in your mind). As observed from an observer who is in free fall with all four particles. One is above him, one below, and one on each side. When the entire system is allowed to be set in free-fall the one above him accelerates away from him to places higher in the field while the one below him accelerates away from him towards the ground. The particles on each side of him accelerate away from him. Each of these particles is moving away from him. That is spacetime curvature at work.

As Kip Thorne explains in his book Black Holes and Time Warps
Quote
... spacetime curvature and tidal acceleration must be precisely the same thing in different languages...

#### Thebox

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##### Re: Einstein's space-time curvature
« Reply #4 on: 14/05/2015 20:55:05 »
Quote from: mxplxxx
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?
Sure. It's fairly simple. Spacetime curvature is the same thing as tidal gradients which are variations in the gravitational field. Think about four particles moving in a gravitational field all of which start from rest above the Earth's surface. Place two of the along a radial line and two of them along a circle of constant radius whose center is the center of the Earth (picture all of this in your mind). As observed from an observer who is in free fall with all four particles. One is above him, one below, and one on each side. When the entire system is allowed to be set in free-fall the one above him accelerates away from him to places higher in the field while the one below him accelerates away from him towards the ground. The particles on each side of him accelerate away from him. Each of these particles is moving away from him. That is spacetime curvature at work.

As Kip Thorne explains in his book Black Holes and Time Warps
Quote
... spacetime curvature and tidal acceleration must be precisely the same thing in different languages...

A good explanation, I forgot to mention the effect of gravity of the moon making a bulge like curvature of the Earth's ocean.

#### codei

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##### Re: What is Einstein's space-time curvature?
« Reply #5 on: 15/05/2015 14:24:25 »
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?

I'm not sure but: space is filled with gravity (a continuous 'field' - no empty space).  In some areas gravity is stronger than in others, this variation causes variation in the way things move and in how time in measured.  These variation are called curvature in the mathematical discipline of topology( which is a slightly different meaning of curvature than is used in common parlance).

#### PmbPhy

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##### Re: What is Einstein's space-time curvature?
« Reply #6 on: 15/05/2015 16:24:54 »
Quote from: codei
I'm not sure but: space is filled with gravity (a continuous 'field' - no empty space).  In some areas gravity is stronger than in others, this variation causes variation in the way things move and in how time in measured.  These variation are called curvature in the mathematical discipline of topology( which is a slightly different meaning of curvature than is used in common parlance).
No. That is incorrect. Even in a uniform gravitational field in general relativity (GR) the spacetime is flat but the strength of the field changes with position. That is unlike the uniform field in GR.

#### mxplxxx

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##### Re: What is Einstein's space-time curvature?
« Reply #7 on: 16/05/2015 04:55:45 »
Thanks to all who replied. It would seem that the topic, like so many in physics, is one that is not widely understood. What would be really nice is a peak physics body that sits in judgement on the many and varied physics theories and publishes a believability index (possibly as score out of 100) on each along with a commentary on the theory.

#### Colin2B

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##### Re: What is Einstein's space-time curvature?
« Reply #8 on: 16/05/2015 08:22:15 »
Thanks to all who replied. It would seem that the topic, like so many in physics, is one that is not widely understood.
Physics, like many subjects, has a base of topics (about 90%) which are very well understood by physicists. The remainder of the topics are only understood by specialists working in those areas.
I emphasise "by physicists" because on a forum like this anyone is allowed to post no matter what their level of knowledge, they don't even have to be a physicist. Of the people who have posted an answer to your question I would only give any credibility to  PmbPhy. David Cooper is capable of answering, but has wisely recognised that this is a difficult concept to explain - it is in that 10% area.

What would be really nice is a peak physics body that sits in judgement on the many and varied physics theories and publishes a believability index (possibly as score out of 100) on each along with a commentary on the theory.
This does exist, but not in the form you want. Science has a process called peer review. A scientist will work on a topic, perform experiments etc until they have enough understanding to be able to write a paper, a description of the idea and how they have tested it. This is very detailed. In the new theories section of this forum you will see people posting what they consider to be a theory, these would rarely pass muster as a scientific paper because they contain only conjecture. Hardy ever do they contain sufficient data and analysis to be considered a scientific paper.
The detailed scientific papers are circulated to other scientists working in the field for review, that is effectively being 'marked' on the quality of the data and analysis. Eventually, if found to be valid a paper will be published in a reputable scientific journal and the scientist will present his ideas to conferences etc.
Although there are pitfalls to this system, in general it works well, but unless you keep up with the scientific press and are part of the research community you are unlikely to know who is a reliable source

#### mxplxxx

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##### Re: What is Einstein's space-time curvature?
« Reply #9 on: 16/05/2015 13:31:21 »
Where do you get your 90% from? The problem with physics is that is long ago stopped being physics and became mathematics. Concepts and pictures are easily understandable; mathematics, especially that developed to try and explain reality, can be extraordinarily complex. How many people really understand what string theory is all about? Given that reality is likely a type of computer, it may be best described via state machines (as per attachment which is the state machine of a hydrogen atom).

#### PmbPhy

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##### Re: What is Einstein's space-time curvature?
« Reply #10 on: 16/05/2015 17:00:30 »
Quote from: mxplxxx
Thanks to all who replied. It would seem that the topic, like so many in physics, is one that is not widely understood.
That's clearly not true. Where would you ever get such a clearly false belief from?

Quote from: mxplxxx
The problem with physics is that is long ago stopped being physics and became mathematics.
Physics has always been about man's study of nature. As physics became advanced the requirement for greater precision was required. Such a requirement can only come by using mathematics. That's why physicists say that math is the language of physics. So physics is not math. Physics merely uses math in order to be more precise. So while pictures are often helpful they are not sufficient to solve all the problems that arise in physics.

Quote from: mxplxxx
How many people really understand what string theory is all about?
As many people as there are who made it their lives task to understand.

#### PmbPhy

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##### Re: What is Einstein's space-time curvature?
« Reply #11 on: 16/05/2015 17:02:15 »
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?
If you know much about math and want a precise meaning of spacetime curvature then read the page I created for it. It all has to do with what's known as geodesic deviation. See:
http://home.comcast.net/~peter.m.brown/gr/geodesic_deviation.htm

#### jeffreyH

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##### Re: What is Einstein's space-time curvature?
« Reply #12 on: 17/05/2015 17:06:19 »
Where do you get your 90% from? The problem with physics is that is long ago stopped being physics and became mathematics. Concepts and pictures are easily understandable; mathematics, especially that developed to try and explain reality, can be extraordinarily complex. How many people really understand what string theory is all about? Given that reality is likely a type of computer, it may be best described via state machines (as per attachment which is the state machine of a hydrogen atom).

Listen to PmbPhy (Pete) and look at the link he gave you. It takes effort to understand the mathematics and how to use them. Before anyone can understand or criticize relativity they have to get to this point of understanding. Everything becomes much clearer once the effort is made to learn the mathematics. At which point you find yourself able to look at some of the things physics does not yet fully understand and start to investigate those areas. If you do not have the dedication then you have to take the explanations as read. This is often unsatisfactory the layman, being used to 'canned' explanations made specifically for the media.

#### jeffreyH

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##### Re: What is Einstein's space-time curvature?
« Reply #13 on: 17/05/2015 17:08:15 »
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?
If you know much about math and want a precise meaning of spacetime curvature then read the page I created for it. It all has to do with what's known as geodesic deviation. See:
http://home.comcast.net/~peter.m.brown/gr/geodesic_deviation.htm

Nice page Pete. I need to sit down and go through it properly though. At the moment time is not an available commodity for me.

#### codei

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##### Re: What is Einstein's space-time curvature?
« Reply #14 on: 18/05/2015 15:00:56 »

I'm not sure but: space is filled with gravity (a continuous 'field' - no empty space).  In some areas gravity is stronger than in others, this variation causes variation in the way things move and in how time in measured.  These variation are called curvature in the mathematical discipline of topology( which is a slightly different meaning of curvature than is used in common parlance).
[/quote]
No. That is incorrect. Even in a uniform gravitational field in general relativity (GR) the spacetime is flat but the strength of the field changes with position. That is unlike the uniform field in GR.
[/quote]

Not surprisingly, I don't understand...  Does the  curvature change when gravity changes?     In what way is the gravitational field "uniform"  if its strength is changing?   How does that differ from the uniform field in GR?      Anyway, thanks for any help you can provide.

#### PmbPhy

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##### Re: What is Einstein's space-time curvature?
« Reply #15 on: 18/05/2015 16:53:26 »
Quote from: codei
... space is filled with gravity (...).
That is incorrect. In fact most of space is free of gravitational fields.

Quote from: codei
Not surprisingly, I don't understand...  Does the  curvature change when gravity changes?     In what way is the gravitational field "uniform"  if its strength is changing?   How does that differ from the uniform field in GR?      Anyway, thanks for any help you can provide.
It's difficult to describe. The uniform g-field is different in GR than it is in Newtonian gravity. One of the defining properties of a uniform gravitational field is that its a spacetime with zero spacetime curvature.

The gravitational field can be obtained from an inertial frame in flat spacetime by transforming to a uniformly accelerating frame of reference. When this is done its found that the local gravitational acceleration varies with height.

It's complicated to derive it so if you'd like to follow the derivation then see:
http://home.comcast.net/~peter.m.brown/gr/uniform_field.htm

and let me know which of those articles that you'd like to read and I'll e-mail them to you.

#### jeffreyH

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##### Re: What is Einstein's space-time curvature?
« Reply #16 on: 18/05/2015 17:09:44 »
Quote from: codei
... space is filled with gravity (...).
That is incorrect. In fact most of space is free of gravitational fields.

Really? Isn't the gravitational field supposed to extend to infinity. Unless you are talking about the radial distribution of the field.

#### PmbPhy

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##### Re: What is Einstein's space-time curvature?
« Reply #17 on: 18/05/2015 18:30:38 »
Quote from: jeffreyH
Really? Isn't the gravitational field supposed to extend to infinity. Unless you are talking about the radial distribution of the field.
Anytime that you're talking about practical things one has to take into consideration what is actually measurable. The gravitational field at large distances from objects is so small that it's effectively zero. In any case you're neglecting all other sources if you think like that. Far from a single object other sources have to be taken into account and in that case they all have a tendency to average out to zero.

If this wasn't the case then the concept of an inertial frame would have no meaning.

#### Thebox

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##### Re: What is Einstein's space-time curvature?
« Reply #18 on: 18/05/2015 18:39:33 »
Quote from: jeffreyH
Really? Isn't the gravitational field supposed to extend to infinity. Unless you are talking about the radial distribution of the field.
Anytime that you're talking about practical things one has to take into consideration what is actually measurable. The gravitational field at large distances from objects is so small that it's effectively zero. In any case you're neglecting all other sources if you think like that. Far from a single object other sources have to be taken into account and in that case they all have a tendency to average out to zero.

If this wasn't the case then the concept of an inertial frame would have no meaning.

Interesting that gravity decreases in magnitude the greater the distance from source the same as light does.  I understand that gravity becomes negligible at distance,

would this be an event horizon where things could remain stationary?

#### jccc

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##### Re: What is Einstein's space-time curvature?
« Reply #19 on: 18/05/2015 19:58:41 »
Quote from: jeffreyH
Really? Isn't the gravitational field supposed to extend to infinity. Unless you are talking about the radial distribution of the field.
Anytime that you're talking about practical things one has to take into consideration what is actually measurable. The gravitational field at large distances from objects is so small that it's effectively zero. In any case you're neglecting all other sources if you think like that. Far from a single object other sources have to be taken into account and in that case they all have a tendency to average out to zero.

If this wasn't the case then the concept of an inertial frame would have no meaning.

Interesting that gravity decreases in magnitude the greater the distance from source the same as light does.  I understand that gravity becomes negligible at distance,

would this be an event horizon where things could remain stationary?

we can measure the force between charges. fe=ke x q1q2/r^2. es force.

you said you agree/understand/believe gravity is net es force of all charges within/between  bodies/matters. then you should know why fg=kg x m1m2/r^2. gravity.

as for why light decay as gravity at 1/r^2, think the mechanism of light, you will find answer.

#### JohnDuffield

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##### Re: What is Einstein's space-time curvature?
« Reply #20 on: 18/05/2015 21:11:25 »
Can someone please lucidly and non-mathematically explain Einstein's space-time curvature?
It's easier than you think. A concentration of energy, usually in the guise of a massive planet, "conditions" the surrounding space, this effect diminishing with distance. See Einstein's Leyden Address for that. Then imagine you could place optical clocks at various locations throughout an equatorial slice through the Earth and surrounding space. Clocks go slower when they're lower, so when you plot all your clock rates, what you get is a plot like this:

GNUFDL image by Johnstone, see Wikipedia

That's a depiction of Riemann curvature. It's basically a picture of curved spacetime. But note that space isn't curved. See Baez and note "not the curvature of space, but of spacetime". Curved spacetime isn't curvature of space and curvature of time. It's a curvature in your plot of measurements of motion through space over time. It's a curvature of "the metric", metric being to do with measurement. As to what you're measuring, note this on the Baez website:

"Einstein talked about the speed of light changing in his new theory.  In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position."  This difference in speeds is precisely that referred to above by ceiling and floor observers."

Those clocks I referred to are optical clocks. And they go slower when they're lower because light goes slower when it's lower. See the Shapiro quote:

"The proposed experiment was designed to verify the prediction that the speed of propagation of a light ray decreases as it passes through a region of decreasing gravitational potential."

So your plot of curved spacetime is a plot of the variable speed of light. This is known as the "coordinate" speed of light. The locally-measured speed of light is the speed that's constant, because of a tautology wherein we define the second and the metre using the motion of light. Anyway, like Einstein said, light curves because the speed of light varies with position, and this is denoted by the slope of the plot. The plot isn't flat, it's sloped. But note that if there wasn't any curvature, the plot couldn't get off the flat and level in the middle. So you need this spacetime curvature, which relates to the tidal force, to have a gravitational field, even though light curves and things fall down because of the slope.

« Last Edit: 18/05/2015 21:13:46 by JohnDuffield »

#### jeffreyH

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##### Re: What is Einstein's space-time curvature?
« Reply #21 on: 19/05/2015 14:11:50 »
Quote from: jeffreyH
Really? Isn't the gravitational field supposed to extend to infinity. Unless you are talking about the radial distribution of the field.
Anytime that you're talking about practical things one has to take into consideration what is actually measurable. The gravitational field at large distances from objects is so small that it's effectively zero. In any case you're neglecting all other sources if you think like that. Far from a single object other sources have to be taken into account and in that case they all have a tendency to average out to zero.

If this wasn't the case then the concept of an inertial frame would have no meaning.

I thought that was what you meant but had to check.

#### The Naked Scientists Forum

##### Re: What is Einstein's space-time curvature?
« Reply #21 on: 19/05/2015 14:11:50 »