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The Reality of Relativity

by yogi
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yogi
#109
Jan22-06, 04:47 PM
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Randall - you are obviously going to have a difficult time undertanding the Gravity" book you borrowed - you are having a difficult time with my several statements to the effect that the resolution of the question doesn't involve anything but SR - first you accuse me of saying Relativity is Broken - title of another post - they you allege I am making a claim about GR - my reference to GR is strictly an analogy - nothing to do with it other than the fact that SR has in common with GR the fact that in some experiments things are not reciprocal.
JesseM
#110
Jan22-06, 05:19 PM
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Quote Quote by yogi
Jesse - Do i beleive in Lorentz invarience - yes and no - how is that for a fence sitter.
I don't think you understand, yogi. "Lorentz-invariance" is just a mathematical property of certain equations, deciding whether or not a given equation shows Lorentz-invariance is as straightforward as deciding whether it's a polynomial.

Let's first consider the related concept of "Galilei-invariance", which is a bit simpler mathematically. The Galilei transform for transforming between different frames in Newtonian mechanics looks like this:

[tex]x' = x - vt[/tex]
[tex]y' = y[/tex]
[tex]z' = z[/tex]
[tex]t' = t[/tex]

and

[tex]x = x' + vt'[/tex]
[tex]y = y'[/tex]
[tex]z = z'[/tex]
[tex]t = t'[/tex]

To say a certain physical equation is "Galilei-invariant" just means the form of the equation is unchanged if you make these substitutions. For example, suppose at time t you have a mass [tex]m_1[/tex] at position [tex](x_1 , y_1 , z_1)[/tex] and another mass [tex]m_2[/tex] at position [tex](x_2 , y_2 , z_2 )[/tex] in your reference frame. Then the Newtonian equation for the gravitational force between them would be:

[tex]F = \frac{G m_1 m_2}{(x_1 - x_2 )^2 + (y_1 - y_2 )^2 + (z_1 - z_2 )^2} [/tex]

Now, suppose we want to transform into a new coordinate system moving at velocity v along the x-axis of the first one. In this coordinate system, at time t' the mass [tex]m_1[/tex] has coordinates [tex](x'_1 , y'_1 , z'_1)[/tex] and the mass [tex]m_2[/tex] has coordinates [tex](x'_2 , y'_2 , z'_2 )[/tex]. Using the Galilei transformation, we can figure how the force would look in this new coordinate system, by substituting in [tex]x_1 = x'_1 + v t'[/tex], [tex]x_2 = x'_2 + v t'[/tex], [tex]y_1 = y'_1[/tex], [tex]y_2 = y'_2[/tex], and so forth. With these substitutions, the above equation becomes:

[tex]F = \frac{G m_1 m_2 }{(x'_1 + vt' - (x'_2 + vt'))^2 + (y'_1 - y'_2 )^2 + (z'_1 - z'_2 )^2}[/tex]

and you can see that this simplifies to:

[tex]F = \frac{G m_1 m_2 }{(x'_1 - x'_2 )^2 + (y'_1 - y'_2 )^2 + (z'_1 - z'_2 )^2}[/tex]

Comparing this with the original equation, you can see the equation has exactly the same form in the primed coordinate system as in the unprimed coordinate system. This is what it means to be "Galilei invariant". More generally, if you have any physical equation which computes some quantity (say, force) as a function of various space and time coordinates, like [tex]f(x,y,z,t)[/tex] [of course it may have more than one of each coordinate, like the [tex]x_1[/tex] and [tex]x_2[/tex] above, and it may be a function of additional variables as well, like [tex]m_1[/tex] and [tex]m_2[/tex] above] then for this equation to be "Galilei invariant", it must satisfy:

[tex]f(x'+vt',y',z',t') = f(x',y',z',t') [/tex]

So in the same way, if we look at the Lorentz transform:

[tex]x' = \gamma (x - vt)[/tex]
[tex]y' = y[/tex]
[tex]z' = z[/tex]
[tex]t' = \gamma (t - vx/c^2)[/tex]
where [tex]\gamma = 1/\sqrt{1 - v^2/c^2}[/tex]

and

[tex]x = \gamma (x' + vt')[/tex]
[tex]y = y'[/tex]
[tex]z = z'[/tex]
[tex]t = \gamma (t' + vx'/c^2)[/tex]

Then all that is required for an equation to be "Lorentz-invariant" is that it satisfies:

[tex]f( \gamma (x' + vt' ), y' , z', \gamma (t' + vx' /c^2 ) ) = f(x' ,y' ,z' , t')[/tex]

There may be some more sophisticated way of stating the meaning of Lorentz-invariance in terms of group theory or something, but if an equation is Lorentz-invariant, then it should certainly satisfy the condition above. Maxwell's laws of electromagnetism would satisfy it, for example. And it's pretty easy to see that if it satisfies this mathematical condition, then the equation must have the same form when you transform into a different inertial frame using the Lorentz transform. So this is enough to show beyond a shadow of a doubt that given Lorentz-invariant fundamental laws, all the fundamental laws must work the same in any inertial reference frame, and if you know the equation for a given law as expressed in some particular inertial frame (the rest frame of the center of the earth, for example) then it is a straightforward mathematical question as to whether or not this equation is Lorentz-invariant, it's not an experimental issue (the only experimental issue is whether that equation makes correct predictions in the first place). Do you disagree with any of this?
Quote Quote by yogi
Is it always permissible to shift from the frame in which the clocks were syncronized to make interrogations of the orbiting clocks? I think not.

The satellite clocks will not be seen as running at a uniform rate in another frame in motion wrt to the non-rotating earth centered reference frame.
Uh, why does this mean it's not "permissible" to shift into another frame? That's the whole point, that different frames disagree about whether a given set of clocks is running at a uniform rate. But all frames will agree on all physical questions like what two clocks will read at the moment they meet at a single location in space. You need to define what you mean by "permissible", when physicists use this term all it means is that you can use the same laws of physics in another frame and all your predictions about physical questions will still be accurate (that's why it's not 'permissible' to use the ordinary rules of SR for inertial frames in a non-inertial coordinate systems, because you would make wrong predictions if you did this). Given Lorentz-invariant laws, this is automatically going to be true for all inertial frames.

Also, the GPS clocks are programmed to adjust themselves so that they tick at a constant rate in the frame of the earth. My other point was that this is a completely arbitrary choice made by the designers, you could just as well design the orbiting GPS clocks to adjust themselves so that they tick at a constant rate in the frame of an inertial observer moving at 0.99c relative to the earth. Would you then say it is not "permissible" to analyze these clocks in the rest frame of the earth, since they would not be running at a uniform rate in the earth's frame?
pervect
#111
Jan22-06, 06:22 PM
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Quote Quote by yogi
pervect - your post 104 - I see no ambiguity either - don't know where you could have acquired the idea that i did - in fact it is what I have been trying to get across - earlier I drew an analogy to GR - the clock at the greater G potential runs faster - that clock at a lower potential runs slower - things are not reciprocal in GR nor are they in SR when only one clock has been accelerated into orbit
Fine with me. Actually I think I need to tighten this up a little bit. The round trip time for light signals between two obserers is something that can be measured - A sends a signal #1 to B, B sends a signal #2 to A on recipt of A's signal. A measures the interval on his clock between the sending of the signal #1 and the receiving of signal #2 as the "round-trip time".

If this round-trip time is always constant, we can always compare the rate of two clocks unambiguously.

We may need to demand that the round-trip time is constant for both A and B before we can compare rates, but I think it is true that if A's round trip time is constant, so is B's. I'm relying on my intuition a bit here, though.

Of course A and B don't necessarily have to agree on the value of the round-trip time (and in general they won't) - they just have to agree that it's constant.
Hurkyl
#112
Jan22-06, 06:39 PM
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but there is no experiment that tests the transforms completely
The transforms are mathematical things, not physical things -- there cannot be an experiment that tests them at all.
RandallB
#113
Jan23-06, 09:05 AM
P: 1,544
Quote Quote by yogi
The satellite clocks will not be seen as running at a uniform rate in another frame in motion wrt to the non-rotating earth centered reference frame.
This statement alone stands as a claim the Einstein’s version of relativity is broken so quit complaining.

What I’d wish you’d do tell us what your trying to do in your posts, they seem to flip from one objective to a the other.
Are you:
A) trying to convince others that the standard view of SR (and extending into GR as well) is somehow wrong or incomplete. And your 'LR-like' view or something else must be better.
OR
B) sincerely trying to learn SR completely, to filling the gaps of information about it, that leave you unable to see concepts in books you’ve had for 10 years.

For the sake of all those that are trying to respond to you, be clear on this; are you arguing a point of view; or trying to learn something. And please refrain on saying “yes & no” or “both”, do one or the other.
yogi
#114
Jan23-06, 10:38 PM
P: 1,473
I have no agenda Randall - my interest in SR goes back many years - likely before you were born - I pose questions that come to mind - if those questions lead to a different view ...one I have overlooked - great. Usually what happens on these boards is an attack - either I don't understand it or I am not qualified to question it - but for a few posters, the attitude is always one of condesention.
yogi
#115
Jan23-06, 10:43 PM
P: 1,473
If anyone thinks it is easy to synchronize GPS satellite clocks in some frame than the non-rotating earth centered system -I would like to see how you would go about doing it.
yogi
#116
Jan23-06, 10:53 PM
P: 1,473
Hurkyl - The transforms relate time and distances - they are not abstract mathematical artifact - these are physical things - my point is with you and Jesse - the mathematical relationships (LT) have been confirmed in certain experiments - but those experiments do not test the fundamental premise upon which Einstein's derivation was based - perhaps w/o complete justification, I do have a stong conviction that the spacetime interval is invarient.
yogi
#117
Jan23-06, 11:04 PM
P: 1,473
pervect - i would agree that any interrogation must depend upon the constancy of the round trip time - and since the GPS clock will always be found to be running at a uniform rate relative to the ground station - we have a convincing demonstration of the constancy of c - at least in the earth centered frame
yogi
#118
Jan23-06, 11:48 PM
P: 1,473
Jesse - your post 110 - last Paragraph: Transforming to another frame - what I have been trying to discuss was the non reciprocal reality of time dilation in certain experiments - if we have a GPS clock that was originally at the top of the tower and launched into orbit from there with no velocity correction - we have a situation where the ground clocks run consistently fast wrt to the GPS satellite clock and the GPS satellite clock always runs slow wrt to the ground clocks and we can verify this non symmetrical situation by interrogating the GPS clock with radio signals - that is the experiment. To inquire as to transforming to a frame in high speed motion wrt to the earth simply subverts the objective. Such a transformation of course is possible, but you have missed the whole point -we are now back in a situation where whatever is measured is apparent - the two frames have not been synchronized - Einstein only makes a prediction about real time dilation when one of two originally synchronized clocks is accelerated to a uniform velocity wrt the other. This is the subject of the thread - which i would like to explore further.
JesseM
#119
Jan24-06, 12:57 AM
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Quote Quote by yogi
If anyone thinks it is easy to synchronize GPS satellite clocks in some frame than the non-rotating earth centered system -I would like to see how you would go about doing it.
If the satellites can figure out their velocity relative to the center-of-earth frame and adjust their clock rates accordingly, it is trivial to figure out their velocity relative to any other inertial frame and adjust their clock rates to be constant in that frame instead. Do you doubt that if I know my velocity in earth's frame and I know the earth's velocity in frame X, I can easily figure out my velocity in frame X, and from this figure out how much my clocks would be slowed down in frame X?
JesseM
#120
Jan24-06, 01:20 AM
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Quote Quote by yogi
Jesse - your post 110 - last Paragraph: Transforming to another frame - what I have been trying to discuss was the non reciprocal reality of time dilation in certain experiments
More ill-defined terminology...what does "non-reciprocal" mean in yogi-speak? Surely you don't mean "non-reciprocal in the way the laws of physics work in different frames", do you? Please address the main part of post 110 and not the last paragraph, where I explained that "Lorentz-invariance" is simply a mathematical property of certain equations, and that given laws of physics whose equations in our own inertial frame have this property, it is automatically going to be true that the laws of physics will obey the same equations in all other inertial frames. Do you deny this or not???
Quote Quote by yogi
if we have a GPS clock that was originally at the top of the tower and launched into orbit from there with no velocity correction - we have a situation where the ground clocks run consistently fast wrt to the GPS satellite clock and the GPS satellite clock always runs slow wrt to the ground clocks and we can verify this non symmetrical situation by interrogating the GPS clock with radio signals - that is the experiment.
It is symmetric in how the laws of physics work in different inertial frames, which is all that most physicists would mean by "symmetric" in the context of special relativity. If you have your own idiosyncratic definition of "symmetrical", please present it.

Do you agree that if the GPS clock is orbiting the earth at a constant speed in the center-of-the-earth frame, that means that in other inertial frames the speed of the GPS clock is not constant? (This would be just as true in Newtonian mechanics as in relativity, of course.) Do you agree that if each inertial frame assumes the same relationship between instantaneous speed in that frame and instantaneous rate of ticking (ie that if the clock is moving at speed v in that frame it will be slowed down by a factor of [tex]\sqrt{1 - v^2/c^2}[/tex]), then different inertial frames will disagree about the relative rate of the tower clock and the orbiting clock at a given moment (with 'given moment' meaning something different in different frames too, due to different definitions of simultaneity), yet they will all make the same prediction about how far behind the orbiting clock will be at the moment it completes an orbit and reunites with the tower clock at a single point in space? Please, please give me direct answers to this question, when I ask you questions in my posts they are not meant to be rhetorical, and it's incredibly frustrating when I ask you questions that I hope will help pin down your nebulous comments and you just ignore them and comment on a single statement in my post.
Quote Quote by yogi
To inquire as to transforming to a frame in high speed motion wrt to the earth simply subverts the objective. Such a transformation of course is possible, but you have missed the whole point -we are now back in a situation where whatever is measured is apparent - the two frames have not been synchronized - Einstein only makes a prediction about real time dilation when one of two originally synchronized clocks is accelerated to a uniform velocity wrt the other. This is the subject of the thread - which i would like to explore further.
There could only be a "real time dilation" in the sense that all frames would agree on how much time elapsed on two clocks between two points in time in a case where the clocks started at the same location and ended at the same location. Einstein would certainly never say that in a case where two clocks started at separate locations and then one accelerated towards another, there is any "real" (frame-independent) truth about which clock was ticking faster or slower. Different frames would disagree about this, and there is no physical reason to prefer one frame's analysis to another. If you disagree with this, then it's important that we first see if you agree with my statements above that any laws of physics which have the mathematical property of Lorentz-invariance will automatically work the same way in all different frames, and whether you also agree that all frames will make the same prediction about all physical questions like what two clocks will read at a moment when they are at a single location in space. If you don't agree with this, then you're expressing some basic ignorance about purely mathematical issues in relativity which needs to be corrected. If you do agree with this, yet still feel that there is some other reason to "prefer" one frame's analysis of the situation to another's, you need to explain what sort of aesthetic criteria you are using here to prefer one over the other despite the fact that all will see the same laws of physics and make the same physical predictions. And if you also want to continue to defend the absurd proposition that Einstein would agree with you about preferring one frame's analysis over another's, you need to provide the quotes that you think support this interpretation.
Hurkyl
#121
Jan24-06, 08:09 AM
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Hurkyl - The transforms relate time and distances
No they don't!

The transforms relate (inertial) coordinate systems, which most certainly are "abstract mathematical artifact".

E.g., IIRC, Einstein made a big deal about showing how to construct what he called an inertial reference frame, via a hypothetical network of clocks, each of them "at rest" with a given inertial observer, and "synchronized" with his clock. I put those terms in quotes because those are also terms in need of construction.

If coordinate systems were physical things, Einstein would have just said "measure it".
RandallB
#122
Jan24-06, 09:37 AM
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Quote Quote by yogi
I have no agenda Randall - my interest in SR goes back many years - I pose questions that come to mind - if those questions lead to a different view ...one I have overlooked - great. Usually what happens on these boards is an attack - either I don't understand it or I am not qualified to question it - but for a few posters, the attitude is always one of condesention.
Fine – I’ll let your condescension towards me pass as a result of the above.

I understand I don’t have the “pro” tag, banner or ribbon of the mentors & advisors on this board - so you don’t have to take my encouragements to heart.

As to reciprocal views being relative – Based on how you pose those questions as conclusions, from the frame of reference of many trying to respond, it can often be seen as attacks on SR as they know it to be. So that part seems to be the same from both views.
Hurkyl
#123
Jan24-06, 08:25 PM
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Quote Quote by Hurkyl
No they don't!

The transforms relate (inertial) coordinate systems, which most certainly are "abstract mathematical artifact".
I guess I should qualify this...

The transforms do relate coordiante position, and coordinate time, so in some sense they can be said to relate times and distances.

But my point still stands -- coordinate position and coordinate time are derived from coordinates, which are not physical things.



Case in point: the Julian and Gregorian calendars are not the same -- they1 assign different time coordinates to events. Would you say that the transformation between these calendars is a physical thing?


1: I'm assuming any usual2 method of identifying spatial position. A calendar, by itself, is unable to assign time coordinates to almost every event!


2: Notice I said usual, and nothing such as "intrinsic" or "determined by reality" -- it's a convention we use as humans. And it's even changed over time, such as when time zones were instituted, and when calendars were changed!
pervect
#124
Jan24-06, 10:51 PM
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Quote Quote by yogi
Randall - you are obviously going to have a difficult time undertanding the Gravity" book you borrowed - you are having a difficult time with my several statements to the effect that the resolution of the question doesn't involve anything but SR - first you accuse me of saying Relativity is Broken - title of another post - they you allege I am making a claim about GR - my reference to GR is strictly an analogy - nothing to do with it other than the fact that SR has in common with GR the fact that in some experiments things are not reciprocal.
Since I've had some run-ins with RandallB in the past, I didn't and don't consider it an enjoyable use of my time to respond to his response.

Hopefully the point I wanted to make has been made, though.
yogi
#125
Jan24-06, 11:49 PM
P: 1,473
Pervect - I appreciate your comments and frequently read your posts although a cannot always make a sensible response. See Below
yogi
#126
Jan25-06, 12:19 AM
P: 1,473
Pervect - I appreciate your comments and frequently read your posts although often cannot make a worthwhile response.

I do recall at one time in another thread you made a statement that the time discrepancy is physically explainable - but then the direction of the thread veered off along other lines as is often the case - so i wasn't able to get back to the subject

In my previous posts on this thread I have tried to target the situation Einstein created when he combined the relationships that were obtained from observations in another frame - specifically to my way of thinking there is a quantum jump from the notion of two observers in relative motion drawing identical conclusions about lengths and clock rates in the other frame - as opposed to the idea that one of two synchronized clocks put in motion will run slower than the one that was not moved. There is a real loss of time between the clocks when they are later compared - in other words, did Einstein get the right answer for the wrong reason - or by intuition. He does not attempt to justify or even rationalize this - it works to explain the experiments - but it doesn't follow from the initial postulates of SR - in one sense it seems to require its own special postulate and - i guess what i am saying is that something is missing.


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