The Reality of Relativity

JesseM

How does that contradict my point? Once you make an arbitrary choice of which inertial reference frame you want to use, you can of course compare different clocks in that frame. But the choice is totally arbitrary, you could equally well have used some other inertial frame, and using the exact same laws you'd get all the same predictions about what clocks read when they meet, but different answers to how fast their respective rates are when they're apart. Do you disagree? Yes, and we could make similar corrections if we wanted to have the clocks be synchronized in an inertial frame moving at 0.99c relative to the earth, as opposed to the frame where the earth's center is at rest. Do you disagree? The question doesn't bother me, but my answer is simple: the laws governing the clocks are known to have the mathematical property of Lorentz-invariance, which insures they must behave the same way in different inertial reference frames related to each other by the Lorentz transform. I've asked you several times whether you agree that given Lorentz-invariant laws, it is logically impossible that clocks would fail to behave as predicted by relativity or that they would not work the same way in different inertial reference frames, but you've never responded. Can you please do so now?

If you want to argue that the fundamental laws of nature might not be Lorentz-invariant, or that there has to be some conceptual reason they are all Lorentz-invariant, that's fine. But so far a lot of your arguments have seemed to take for granted that clocks follow known relativistic laws in some given frame (say, the frame where two clocks are initially at rest before one accelerates in your previous example), but then you question whether these situations could really be analyzed just as well from the point of view of another inertial frame. But this is a truly incoherent line of argument, because again, if you take for granted that clocks obey the known Lorentz-invariant laws in one inertial frame, then it's logically impossible that they would fail to obey the same laws in all other inertial frames.

pervect

Let me add my $.02.

If we have an inertial observer, and someone moving via a powered orbit in a circle around the observer, the two observers are always a constant distance apart.

Because they are a constant distance apart, the travel time for a light signal will always be constant, and everyone will agree that the observer travelling in a powered orbit has a clock that is ticking slower. Constant travel time makes direct comparison of the rates of clocks possible

The obserer in a powered orbit will not have a "frame" that covers all of space-time. However, he will have a local frame that includes the inertial observer.

The observer in the powered orbit will see the inertial observer's clock as ticking faster, due to "gravitational time dilation" in his local coordinate system, as the inertial observer will always be "above" him.

So, there isn't any ambiguity here - the inertial observer thinks the accelerating observer's clock is ticking slowly, and the accelerating observer thinks the inertial obserer's clock is ticking fast.

This is perfectly consistent with the simple idea that the clock following a geodesic in flat space-time is always the clock that experiences the most time.

RandallB

I’m not lecturing on GR I’m talking about SR. And is there some list of acronyms that we should all know so we don’t wise cracks from you guys about not knowing what MTW stands for here? Tens years working on getting SR is more astonishing than having to learn acronyms of others.
Do you have an acronym for your version of relativity; LR BR YR (Lorentz, Broken, Yogi) it sure isn’t SR.

And if you think your issues in this thread are GR, you’re wrong it’s SR where you’re still having problems. Until you understand SR, how can you hope to work from an understandable vocabulary with any mentor that’s not on the same page as you with what ever version of SR you’re using?

If you’re trying to learn the correct way to understand it. Stick with SR alone first. They won’t be able to help you in GR if you don’t have SR down first.

But, if your purpose is to convince someone of your view, do it in a SR environment; in GR you’ll never be able to communicate effectively if they don’t understand your version of SR. And be clear about your purpose if this is the case; at least be fair to the mentors that are only trying to help you see SR, if that is not your intent. I really don’t thing any are looking to pick up a new view of relativity, but some may be willing to look at your augments differently if you’re actually trying to bring forward a new view of relativity.
I honestly cannot tell which you are doing.

RandallB

I took a look at the book and yes the plots should cross as they do for SR frames, where one has been accelerated to a fixed higher speed. (The SR frame work, is the best to be working with yogi on, but if you think you can help him in a truly GR environment go ahead you have 100’s of posts to go)

The issue MTW are dealing with is an accelerating frame for the moving point. And yes those lines should not cross except that they should overlap as they do at t=0.

But why Kip has a problem with seeing an overlap at g-1 I don’t understand. By simply recognizing “simultaneity” (A simple SR issue) and applying it to this accelerating frame it is clear that the “time” at this distance is in the past for this “accelerating frame”. Therefore it has a time of t<0 where the speed and this line are the same and parallel with the original stating line for the point g-0 at t=0.
Thus the correct lines will obviously progress with curves to the left that go to some limit parallel to the original horizontal line off set up somewhat.

Likewise the lines to the right represent points at “future distances” and again by “simultaneity” rule those times will be in the future. Here the speeds are higher for the accelerating frame therefore the slope needs to be progressively steeper and curving the line forward. This Projects an expectation fitting with their other graphs. But they do repeat the concern of the g-1 point again. I’m just an independent non-pro but if I ever meet Kip again and have the chance maybe I’ll bring it up to him. I’m sure the book having been so long ago he’d be allowed some revisions to his old judgments.
RB

yogi

Jesse - Do i beleive in Lorentz invarience - yes and no - how is that for a fence sitter. If you ask - do I believe in the invariance of the interval between two spacetime events in two different frames in relative uniform motion - the answer is yes until some experiment yet to be performed castrs doubt upon it - but there is no experiment that tests the transforms completely - when we take two space time points in two frames and derive the interval, the xv/c^2 term cancels - this has not been verified by experiment - so yes - I will withhold judgement at this point as to the universal validity of the transforms.

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.

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

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.

JesseM

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? 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

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

The transforms are mathematical things, not physical things -- there cannot be an experiment that tests them at all.

RandallB

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

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

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

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

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

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

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?