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Author Topic: What is the relationship between gravity and special relativity?  (Read 2893 times)

Offline Pmb

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I recently got into a discussion with some people that I know about the speed of light in special relativity. There was a lot of confusion due to the change in definitions and perceptoions of "gravitational field" from Einstein's times to our own time.

Here's the problem: most modern textbooks and journal articles refer to physics in flat spacetime as falling under the auspice of Special Relativity. Mind you, this includes physics in an accelerating (i.e. non-inertial) frame of reference in flat spacetime. Where Einstein referred to this as there existing a "real" gravitational field in this accelerating frame being produced by a change of coodinates, modern literature refers to this as being a "pseudo" or "apparent" gravitational field. However, in such a frame of reference

(1) The speed of light is a function of position
(2) The gravitational potential is non-zero
(3) The gravitational force on particles is non-zero

This seems to cause a great deal of confusion. Sometimes people even get angry about it. I've never really understood that. Why get angry?? It's not like you're hurting someone or stating a falsehood. These are actual facts which can be shown mathematically are referenced in the physics literature. I don't know why people get so pissed off when they run into something they do disagree with. Why? I never understood this! I was merely explaining the physics and yet was charged with "causing a scuffle" (forget about where and with whom I got into such a discussion. You wouldn't know them.)

What do you think? Is a gravitational potential in special relativity something that would confuse you given what I've explained? Have you ever gotten angry with someone in a physics debate? As much as I don't understand it I myself have gotten angry with people. But its because the other person is clueless and behaving and talking as it I have no idea what I'm talking about.  Perhaps that's the reason. Have you experienced this? What's the best way to get out of such an agrument? Before you reply "Well just stop posting" let me tell you about the effect that has on people. Laymen quite often seem to think that the last post which has a response, an "explanation" to which you didn't respond because you simply stopped posting, causes a lot of people to think that you just saw your errror and didn't repond because you knew the other person was right, i.e. you "saw the error of your ways." and terminated your part in the discussion. When this keeps happeing its quite possible (I know this from actual experience) that others who merely follow along will then start thinking that you're clueless or you don't know physics better than so and so and because of this start to harass you or insult you.

Strange but true. I've experienced it in a forum called "Ask Dr. Neutrino". Back then is when I first came upon a the mass debate. One of the moderators was a particle physicist. Particle physicists think they run relativity merely because they are currently the majority of the users. That's no way to think. It led to tons of misinformation. There were in fact many modern textbooks and journal articles which contained discussions and definitions that he claimed don't exis anywhere in the world and that I was the only one in the world using it. Late on when statistics were taken it turned out that in certain senses the opposite was true (i.e. in the time period of the discussion the majority of textbooks published in that time period used relativistic mass rather than proper mass, contrary to his claim). I.e. he was clueless and didn't know it. Mainly because he never looked in the new textbooks and took a survey!

What do you think aboiut all this?
« Last Edit: 05/02/2013 22:41:29 by chris »


 

Offline Ethos_

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Re: Gravity in special relativity
« Reply #1 on: 02/02/2013 04:35:38 »


What do you think aboiut all this?
It's very common for some individuals to think they have a lock on the truth about reality. If they would only look back a very few years in history, the evidence is abundant that scientific foundations have changed considerably over time. There is a quote from John S. Mill: "The more things change, the more they remain the same."

It's very difficult to convince anyone when they are absolutely sure about their facts. We should all remember Mr. Mill's quote when we are totally convinced about our assumed facts. I love the search for new information about the cosmos but am truly convinced that what we know for sure today will be turned on it's head tomorrow.

I do understand where you are coming from my friend, but we all need to remember that it's the search that satisfies the scientific spirit. When people are so convinced they can't view things from a different perspective, they have short-changed themselves. But those who keep an open mind are more inclined to recognize the truth when it appears.
 

Offline Pmb

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Re: Gravity in special relativity
« Reply #2 on: 02/02/2013 05:41:13 »
Quote from: Ethos
I do understand where you are coming from my friend, but we all need to remember that it's the search that satisfies the scientific spirit. When people are so convinced they can't view things from a different perspective, they have short-changed themselves. But those who keep an open mind are more inclined to recognize the truth when it appears.
Thanks Ethos. I appreciate being understood. What irritated me was that they claimed I was causing confusion where in fact they were ignorant of the correct physics. But this I donít mean absolute truth in the nature of the phenomena but as it is currently understood in the relativity literature. Being accused of causing confuse when I know it as fact is really irritating. It would be like claiming that the derivative of f(x) = sin(x) is really cosh(x) and if I thought differently then I donít know what Iím talking about. Lol!

Itís good that I backed off to cool down. When I came back to it I had fresh eyes and saw where his errors lay. Itís nice to be able to quote Einstein and give a reference to precisely what I was talking about. The problem was that I even provided a derivation of the fact that the speed of light varies in the presence of gravity, It was ignored. Sheesh!
 

Offline Phractality

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Re: Gravity in special relativity
« Reply #3 on: 02/02/2013 07:16:19 »
The problem was that I even provided a derivation of the fact that the speed of light varies in the presence of gravity, It was ignored. Sheesh!

You seem to be missing the fact that the speed of light, in meters per second, is constant by definition. That which is defined as a constant can't possibly vary, regardless of gravity. The definitions of meter, second and speed of light are inexorably tied to one another.

Those definitions are also tied to a particular electromagnetic emission from a cesium atom. The definitions make no distinction about where the cesium atom is. It can be in the middle of a cosmic void or at the event horizon of a black hole; either way its wavelength and frequency in meters and seconds are exactly the same by definition.

If you want to invent new units of distance and time which yield a variable speed of light, you may do so. I'd try to do it myself, but I am not a mathematician, so I'd be doomed to fail. Actually, I would prefer units of distance and time which represent a flat space-time continuum, even in the vicinity of a black hole. This would not alter the fact that the space-time continuum represented by a 4D grid of meters and seconds is warped. It would just give you a different way to look at that warp.
 

Offline Pmb

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Re: Gravity in special relativity
« Reply #4 on: 02/02/2013 07:48:20 »
Quote from: Phractality
You seem to be missing the fact that the speed of light, in meters per second, is constant by definition.
I donít know where you got that idea from but itís quite wrong. In an inertial frame of reference its invariant by postulate. That is we always observe that the speed of light will always be the same no matter from what inertial frame of reference that we measure it from. This does not apply to non-inertial frames of reference

Quote from: Phractality
That which is defined as a constant can't possibly vary, regardless of gravity. The definitions of meter, second and speed of light are inexorably tied to one another.
Iím sorry but thatís the furthest thing from the truth. Want proof? Then see the derivation at http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

Albert Einstein first proved this fact. Let me refer you to the original work. See On the Influence of Gravitation on the Propagation of Light by Albert Einstein, Annalen der Physik, 35, 1911 section 3 Equation #3. Einstein writes
Quote
If we call the velocity of light at the origin of coordinates c0 then the velocity of light c at a place with the gravitational potential Phi will be given by the relation

(3) c = c0(1 + Phi/c2)

The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity.
Iím extremely curious where you got the idea otherwise. Do you recall where you got that notion from?

Quote
Those definitions are also tied to a particular electromagnetic emission from a cesium atom. The definitions make no distinction about where the cesium atom is. It can be in the middle of a cosmic void or at the event horizon of a black hole; either way its wavelength and frequency in meters and seconds are exactly the same by definition.
Youíre confused. When its said that the speed of light is defined as such what it really means is that when we go into the lab ďin an inertial frame of referenceĒ and use our clocks and rods to make a measurement of the speed of light then we demand that the value of our measurements of ďdistance traveledĒ/Ētime traveledĒ comes out to be that special value. So what we have to do is change the lengths of our meter sticks or slow down or speed up our clocks in order to make it come out just right. It doesnít mean that we can automatically require that nature behaves in a certain way just because we arrogant scientists define it to be that way.

Suppose I were to go outside and run at my top speed. Can I automatically claim that ďmy top speed is 300 miles per hour as measured by all cars passing by?Ē The answer is no. But what I can do is to make a measurement using clocks and rods and label those clocks and rods with units such that my top speed is 300 miles per hour. However that doesnít mean that when a scientist in a car moving relative to me will also measure me to be running at 300 miles per hour. Especially if heís going the same speed I am.
 

Offline yor_on

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Re: Gravity in special relativity
« Reply #5 on: 02/02/2013 19:46:27 »
"most modern textbooks and journal articles refer to physics in flat spacetime as falling under the auspice of Special Relativity. Mind you, this includes physics in an accelerating (i.e. non-inertial) frame of reference in flat spacetime. Where Einstein referred to this as there existing a "real" gravitational field in this accelerating frame being produced by a change of coordinates, modern literature refers to this as being a "pseudo" or "apparent" gravitational field." sounds correct to me Pete.

What Einstein defined it as that is. The trick to remember is how we defined physics experimentally, what you measure is what you get. Your measurements must define your reality, if you say they don't? Well, then you're a theorist and also looking for something 'hiding' behind the apparent 'screen of reality'.

When it comes to 'c' though I define it as a 'constant', not saying we can define a speed, as that always need to build on first defining what 'unmovable' or at least 'unmoving' relative my measurement.
==

Damn that keyboard :)
« Last Edit: 02/02/2013 19:49:51 by yor_on »
 

lean bean

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Re: Gravity in special relativity
« Reply #6 on: 02/02/2013 22:18:23 »
The trick to remember is how we defined physics experimentally, what you measure is what you get. Your measurements must define your reality, if you say they don't? Well, then you're a theorist and also looking for something 'hiding' behind the apparent 'screen of reality'.
Back in january I said something of the same about reality and what's the so called truth
Quote
If from experiment and observation we create our reality and so our models (GR), then in what other way do you wish to explain reality if not by models?
 Observation, and so our models, suggests something about mass/energy alters spacetime in their vicinity.
Can you suggest a way of getting to the fundamental ''truth'' (whatever that means) and how we will know it is the fundamental ''truth'' and not just a very good model?
http://www.thenakedscientists.com/forum/index.php?topic=46551.msg403106#msg403106




 

Offline Pmb

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Re: Gravity in special relativity
« Reply #7 on: 02/02/2013 23:48:22 »
Quote from: Ethos
But those who keep an open mind are more inclined to recognize the truth when it appears.
This person sure wasnít one of those people with an open mind. But with what you said in mind I tried to explain things a bit more to him in PM. He didnít respond well to that so I just plopped him into the ignore list and thatís that. All forums should have that function. Perhaps Iím just getting old and am tired of the disrespect that Iím being shown by people. I mean, Iím a well educated (about two years worth of graduate work in physics) physicist whose been studying the field for close to thirty years now. Fifteen to twenty years of them in relativity, and over fourteen years experience in general relativity. Iím certainly no slouch. And frankly, yes. Iím starting to get a bit pissed off at the disrespect that Iíve been shown by some people and for no other reason other than theyíve been studying physics for five to ten years and they think they know everything and if they see me say something theyíre not familiar with I must be an idiot and if what theyíre reading confuses them then it must be I who is confusing them. I  mean these people donít even know more than algebra, start talking about the lightís frame of reference, the proper time etc. All nonsense. And they claim its all because Iím being confusing!  Well how then hell am I supposed to know who Iím talking to? I have no idea who people reading these posts are and its hard to write an explanation that everyone from all levels of knowledge and education can understand.

I gotta tell ya. Itís really frustrating! Most of the people I help to understand physics in these forums were still eggs when I started studying physics! :)   And no. This is not arrogance whatsoever.
 

Offline JP

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Re: Gravity in special relativity
« Reply #8 on: 02/02/2013 23:52:07 »
Pmb, while I can plug-and-chug in the equations, what I find I'm lacking is a physical intuition for curvature vs. flat spacetime vs. the special case of Minkowski spacetime.   Can you provide any intuition to the geometry described in the flat spacetime in your example above vs. Minkowski vs. curved space-time?  Is it akin to the fact that you can have a curve y=0, which is flat and constant vs. y=x, which is flat and non-constant vs. higher order polynomials which are always curved?
 

Offline yor_on

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Re: Gravity in special relativity
« Reply #9 on: 02/02/2013 23:59:32 »
Don't really know what's a absolute truth? Observer dependencies maybe could be one? If you look how some theorist today want to prove a propagation of light by using so called weak measurements (indirect observations deducting a propagation from) where does the archetype for that come from? I would say it comes from our classical observations of motion. Each one of us seems to me, depending on how far you want to draw your conclusions about relativistic effects, in a way very unique. We will find different measurements, all of us have it that way, as I think, even if they might be too small to be measurable.

And that goes for the universe each one of us perceive too.

So which is the correct answer here? One 'common universe' in where we all are together? Or a unique universe for each one of us measuring, communicating by light (radiation).

And it most certainly has to do with experiments, and the way we define those to define reality.
 

Offline Pmb

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Re: Gravity in special relativity
« Reply #10 on: 03/02/2013 00:18:03 »
Quote from: JP
Pmb, while I can plug-and-chug in the equations, what I find I'm lacking is a physical intuition for curvature vs. flat spacetime vs. the special case of Minkowski spacetime.   Can you provide any intuition to the geometry described in the flat spacetime in your example above vs. Minkowski vs. curved space-time?  Is it akin to the fact that you can have a curve y=0, which is flat and constant vs. y=x, which is flat and non-constant vs. higher order polynomials which are always curved?
Oooo goody! A challenge! Thanks JP!! :)

Just so that I donít leave anything out and make false assumptions I start off by assuming that you know what curvature is in all its detail. In differential geometry when we speak of curvature what weíre speaking about intrinsic curvature. Consider a cylinder. A cylinder has a curved surface in the sense that its surface cures into a dimension higher than the dimension of the manifold itself. I.e. we have a two dimensional surface (the surface of the cylinder is two dimensional) which curves into our three dimensional space. However its intrinsic curvature is still zero. If I draw a triangle on the surface of a sheet of paper and measure the sum of the interior angles Iíll always get 180 degrees. When I roll the paper into a cylinder those angles donít change. The shape of curves drawn on the surface donít change. Two lines, which are parallel when drawn on the surface, remain parallel when you roll it up into a cylinder. Now think of the surface of a sphere. Clearly the intrinsic curvature of the surface of a sphere is curved. The sum of the angles of a triangle add up to be greater than 180 degrees. Parallel lines do not remain parallel. And itís the intrinsic curvature of the surface which makes it it so damn difficult gift-wrapping a basketball. Lol!! 

Now if you take a triangle on a surface of a sphere and make it small and smaller and smaller then the interior angles get closer and closer and closer to being 180 degrees. Thatís why people on a huge massive sphere think that theyíre on a plane. The Gaussian curvature K of a sphere of radius R is K = 1/R^2. This is locally measured quantity. The more local the measurements the more accurate the measurement is (hard for us to see being people standing on the surface of a perfect sphere though). So while the curvature is still curved we can construct a locally Cartesian coordinate system in a small area on the surface. This is called a local flat frame of reference. If you use spherical coordinates then you donít have a locally flat frame. In fact thereís no unique coordinate system which covers the entire sphere

Can you see how this works now? Consider a general curved spacetime. If the spacetime is flat (like the sheet of paper) then there is no curvature to it and you canít change coordinates to take away the curvature. The curvature is a geometrical property and not an artifact of the coordinate system. Now if you have a frame of reference which is uniformly accelerating relative to this frame then what youíre doing is changing to curvilinear coordinates and in doing such things which are moving in as straight worldline in flat spacetime now become a curved worldline in flat spacetime. The object is accelerating in this frame.

Does this help?
 

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Re: Gravity in special relativity
« Reply #10 on: 03/02/2013 00:18:03 »

 

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