Physics Help Forum Can anyone answer this relativity paradox?
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 Sep 7th 2015, 05:45 AM #101 Member   Join Date: Jul 2015 Posts: 84 Inertial reference frames So to summarise the situation on reference frames, I'm saying each point has only one inertial frame. Frames that move in relation to a visibly expanding universe give galaxies curved paths that have no reasonable explanation. To try to avoid this problem, the original description of SR's frames of reference seems to have been changed so they are purely local. This means that the curved paths can be ignored. If a path is seen to curve, the frame has to be made even smaller until, within observational error, one can pretend that the path is straight. Please can someone correct my interpretation if it is wrong. I am trying to draw conclusions from the interpretation that MBW described in post 95 and which no one has criticised. The problem though is not just one of curved paths. In a frame having a velocity of v in relation to the visible universe, galaxies are given a velocity of -v. Consider two galactic clusters lying at right angles to this velocity. Suppose the expansion means that the nearer cluster is moving away from the frame's origin at a velocity of v whilst the more distant cluster moves away at 10v. Their net directions of motion in the moving frame will differ. Hubble's symmetrical law works in the frame that is uniquely at rest, but other laws are needed to describe the asymmetric expansion that occurs in moving frames. If the tactic of localising frames is to succeed, it seems that we are not allowed to look beyond our local patch. Cosmological observations, including Hubble's law, are out of bounds otherwise inertial frames do not make sense. Again, please can someone explain where my interpretation is wrong. Personally, I cannot avoid the conclusion that the first postulate of relativity is wrong. The laws of physics are not the same in all inertial frames of reference. They only make sense in one.
Sep 7th 2015, 11:21 AM   #102
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 So to summarise the situation on reference frames, I'm saying each point has only one inertial frame.
Each point in space can have any number of inertial frames passing through it at different velocities whether gallilean or lorentz frames. It's more useful to attach inertial frames to a uniformly moving (travelling at constant velocity) observer. It's generally considered to be a better frame to make measurements and calculations in the simplest way.

 Frames that move in relation to a visibly expanding universe give galaxies curved paths that have no reasonable explanation.
Curved paths are produced by forces (normally gravity) that accelerate celestial bodies. This is true in either gallilean or lorentz frames.

 To try to avoid this problem, the original description of SR's frames of reference seems to have been changed so they are purely local. This means that the curved paths can be ignored. If a path is seen to curve, the frame has to be made even smaller until, within observational error, one can pretend that the path is straight. Please can someone correct my interpretation if it is wrong.
No, I don't think thats the reason. As I understand it the frames are made flat and small to approximate a curved plane. This is because gravity, as in a large mass, curves space time and the equations of minkowski space break down. The same problem would occur on the surface of the earth where, if you pick a large enough area, the normal rules of geometry break down. For instance parallel lines cross, the sum of the angles of a triangle no longer equal 180 degrees and so forth, because you are drawing triangles and lines on a sphere. However the earth is pretty close to flat in smaller areas and can be considered so for most surveying. Similarly, the rules of minkowski space are only true for small flat regions of flat spacetime.

 I am trying to draw conclusions from the interpretation that MBW described in post 95 and which no one has criticised. The problem though is not just one of curved paths. In a frame having a velocity of v in relation to the visible universe, galaxies are given a velocity of -v. Consider two galactic clusters lying at right angles to this velocity. Suppose the expansion means that the nearer cluster is moving away from the frame's origin at a velocity of v whilst the more distant cluster moves away at 10v. Their net directions of motion in the moving frame will differ. Hubble's symmetrical law works in the frame that is uniquely at rest, but other laws are needed to describe the asymmetric expansion that occurs in moving frames. If the tactic of localising frames is to succeed, it seems that we are not allowed to look beyond our local patch. Cosmological observations, including Hubble's law, are out of bounds otherwise inertial frames do not make sense. Again, please can someone explain where my interpretation is wrong.
Its just that you can't apply SR or minkowski space in gravitational fields. The equations expect flat space. Gravity bends space (or spacetime). Unlike SR alone, you can use minkowski diagrams to fairly easily solve some GR problems, like the twin paradox. Thats about as far as I got in studying GR. However minkowski diagrams are only valid where spacetime is relatively flat.

Last edited by kiwiheretic; Sep 7th 2015 at 11:35 AM.

Sep 7th 2015, 01:45 PM   #103
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 Originally Posted by kiwiheretic Each point in space can have any number of inertial frames passing through it at different velocities whether gallilean or lorentz frames.
This conventional relativistic interpretation differs from the one described by MBW whereby there are no inertial reference frames. I'm suggesting a non-relativistic interpretation. There is just one frame in which the laws of physics are at their simplest.

 Originally Posted by kiwiheretic Curved paths are produced by forces (normally gravity) that accelerate celestial bodies. This is true in either gallilean or lorentz frames.
Yes but only in one frame can the paths be explained by gravity and a symmetrical expansive force.

 Originally Posted by kiwiheretic Unlike SR alone, you can use minkowski diagrams to fairly easily solve some GR problems, like the twin paradox.
How about solving the triplets paradox insofar as it relates to SR. This seems to provide another way of disproving the first postulate of relativity. The symmetrical time shifts that are predicted to accumulate in each frame during periods of inertial motion do not materialise.

Sep 7th 2015, 01:59 PM   #104
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 Originally Posted by kiwiheretic Each point in space can have any number of inertial frames passing through it at different velocities whether gallilean or lorentz frames. This conventional relativistic interpretation differs from the one described by MBW whereby there are no inertial reference frames. I'm suggesting a non- relativistic interpretation. There is just one frame in which the laws of physics are at their simplest.
I am not disagreeing with MBW on that point. He was talking about reality, I was talking about the mathematical model of SR and minkowski space. There is no real inertial frames as there is no where in the universe you can completely hide from gravity. There are places, however, that its effects are negligible.

Also, when you talk about simplest, you need to answer "simplest for whom"? It depends on who is doing the measurements and which planet (or spacecraft) he is living on.

Edit: I'll have a look at the triplet paradox when I get a chance. I have done a bit of work on it but I need to dust of my drawing software package to draw out the minkowski diagrams.

Last edited by kiwiheretic; Sep 7th 2015 at 02:15 PM.

Sep 7th 2015, 03:21 PM   #105
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 Originally Posted by kiwiheretic I am not disagreeing with MBW on that point. He was talking about reality, I was talking about the mathematical model of SR and minkowski space. There is no real inertial frames as there is no where in the universe you can completely hide from gravity.
Good, we all seem to be in agreement up to the last sentence. Why do you think that a frame at rest with the visible universe would not be inertial? This frame does not need to hide from gravity.

 Originally Posted by kiwiheretic Also, when you talk about simplest, you need to answer "simplest for whom"? It depends on who is doing the measurements and which planet (or spacecraft) he is living on.
My answer is simplest for anyone trying to understand the cosmos. My guess is that when cosmologists produce simulations of the evolving universe they use the inertial frame I am talking about. This is the simplest frame for their calculations. Adjustments can then be made to suit the non-inertial frames of the Earth.

 Originally Posted by kiwiheretic Edit: I'll have a look at the triplet paradox when I get a chance. I have done a bit of work on it but I need to dust of my drawing software package to draw out the minkowski diagrams.
I am not disputing that GR/Minkowski space can make sense of this. I'm suggesting that the acceleration phases cannot explain why SR fails to predict an asymmetric time dilation. SR predicts symmetric dilations that increase with the duration of the inertial motion. I do not see how the accelerations can undo the dilation predicted in one of the frames. The accelerations do not know how long the inertial phases were.

Sep 7th 2015, 04:59 PM   #106
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 Good, we all seem to be in agreement up to the last sentence. Why do you think that a frame at rest with the visible universe would not be inertial? This frame does not need to hide from gravity.
It's not intertial if the space at that point is not flat. The presence of gravity distorts spacetime. A hypothetical inertial frame may be able to be placed there, in our thoughts, but it doesn't mean the space there is completely flat. It's like someone standing on the slope of a hill. It doesn't matter whether you jump, run, or do back flips, it doesn't change the shape of the hill.

 My answer is simplest for anyone trying to understand the cosmos. My guess is that when cosmologists produce simulations of the evolving universe they use the inertial frame I am talking about. This is the simplest frame for their calculations. Adjustments can then be made to suit the non- inertial frames of the Earth.
For the purpose of creating a simulation that is probably a reasonable approach.

 I am not disputing that GR/ Minkowski space can make sense of this. I'm suggesting that the acceleration phases cannot explain why SR fails to predict an asymmetric time dilation. SR predicts symmetric dilations that increase with the duration of the inertial motion. I do not see how the accelerations can undo the dilation predicted in one of the frames. The accelerations do not know how long the inertial phases were.
I agree, SR can't explain it. However, a minowski diagram can often offer a reasonable picture of what is happening. You have to remember the twin paradox is a bit idealised in the way its presented. For a spaceship to instaneously turn around and maintain its speed when travelling at near light speed would be an incredible acceleration and the G-forces involved would be instant death for everyone inside the ship. However, its useful for illustrating the differences between accelerating and inertial frames of reference.

However, I agree that acceleration or gravity (equivalent in effect according to Einstein) does something weird. I think what you are getting at is that you can have two twins travelling in space ships in opposite direction who accelerate in precisely the same way but in opposite directions, return to earth, and they are still the same age (although the earth has aged more than both of them). The "time dilation asymmetry" is in the perpetually inertial frame (the frame that never accelerated).

Sep 8th 2015, 03:37 AM   #107
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 Originally Posted by kiwiheretic It's not intertial if the space at that point is not flat. The presence of gravity distorts spacetime. A hypothetical inertial frame may be able to be placed there, in our thoughts, but it doesn't mean the space there is completely flat.
We are using different meanings of the word inertial. This is to be expected because I have never found a clear definition of inertial frames - even though these are the basis of the theory of SR. It seems that Copernicus, Galileo etc. did not specify how one measures whether a frame is accelerating. I'm saying that a frame is inertial if it is not accelerating with respect to the universe. Using the cosmological principle this means the visible universe. This still allows an unlimited number of inertial frames to exist with different velocities. From what I've read though, physicists go on to say that the laws of physics are at their simplest in inertial frames. It is in this sense that I say that for each point there is just one inertial frame. This is the frame that has no acceleration, rotation or velocity with respect to the visible universe. Any other frame is moving with respect to the universe so I say it has absolute motion. (In such a frame the laws of physics are complicated by the fact that they are wrong!) Our universe is our absolute benchmark. We cannot relate things to anything beyond.
However, you seem to have added a further requirement, namely that an inertial frame cannot contain gravity (or perhaps its origin cannot be subjected to gravity, which is virtually the same thing). I'm fairly sure that Galileo did not have this in mind. I don't think Einstein had this in mind either when he devised SR, nor when he spoke of the relative speed of trains and platforms etc. If inertial frames cannot contain gravity then clearly they do not exist, so I'll rephrase my question. If an inertial frame is something that (in some sense) does not accelerate and in which the laws of physics are at their simplest, do you think a frame that is at rest with the visible universe is inertial? Also, do you think there is only one such inertial frame for each point?

 Originally Posted by kiwiheretic I agree, SR can't explain it. However, a minowski diagram can often offer a reasonable picture of what is happening.
We agree that SR can't explain it, but presumably we draw different conclusions. I'm saying SR can't explain the asymmetric time dilation that results from linear motion so SR is wrong. Are you saying SR can't explain it, GR can, so SR is right?

 Sep 8th 2015, 06:22 AM #108 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,354 I have been staying out of this conversation because quite frankly any thread that grows this long is almost impossible to follow. However, I think the main point of misunderstanding here is the definition of "inertial frame." You would like to define it as "a frame is inertial if it is not accelerating with respect to the universe." The "with respect to the universe" part is immaterial, and I suspect causing confusion. A frame is inertia if it is not accelerating, and under the equivalence principal of GR it must also not be in a gravitational field. SR does not address gravity or acceleration at all, so strictly speaking if you are discussing physics with gravity present you must use the curved space concepts of GR, not the flat space limitations of SR. However, it is true that for "sufficiently small spaces" SR does a very good job of describing events. even in the presence of gravity. How small a space is "small?" One that is small enough to allow you to ignore tidal effects, or stated another way: one that is small enough that space is effectively flat. A particle physicist doing an experiment in a lab can use SR pretty reliably. A space scientist designing a GPS system consisting of satellites in orbit about the Earth can not. And clearly any discussion of cosmology must be done applying GR principles, not SR. I am also concerned that you say "for each point there is just one inertial frame." This is incorrect - there are an infinite number of inertial frames possible at every point, corresponding to frames moving at constant velocity in any possible direction. You want to talk about the one that is "stationary with respect to the visible universe," but that means nothing. We know the universe is expanding, so we know that the "visible universe" is in motion with respect to each and every point inside it. About all you can specify is that you want to consider an inertial frame that is stationary with respect to a particular observer, but of course that same frame may not be stationary with respect to another observer. The good news is that both observers can agree that the frame is indeed an inertial one. Bottom line is do not look to SR to explain the expanding universe, or Hubble's Law, or the precession of Mercury's orbit, or time dilation in the presence of gravity (or acceleration), or to resolve the twin's paradox, because none of these phenomena take place in an inertial frame. Last edited by ChipB; Sep 8th 2015 at 09:33 AM.
 Sep 8th 2015, 09:58 AM #109 Forum Admin     Join Date: Apr 2008 Location: On the dance floor, baby! Posts: 2,857 Not only very well put but also correct about the length of the thread. I say that the topic has been well dissected. Thread closed. -Dan __________________ Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup. See the forum rules here.

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