# A problem to the theory of relativity ?

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3 hours ago, Bjarne-7 said:

You have good reason to be confused.
Remember that the "problem" is not limited to the speed of light. No matter how Bob and Alice tries to relate to distances or speeds in other gravitational environments, they encounter the same problem over and over again.
They pretty much always disagree about speeds and distances everywhere in the universe.

Imagine that Bob and Alice have measured the orbital period of Saturn's orbit.

No, my reason to be confused is what I said: Two observers seeing two different things see... well two different things! What's strange with that? As @Markus Hanke has made perfectly clear. GR tell you how different the different things appear to be provided you carefully specify the conditions.

If they see the same thing, how come, if they are apart? @swansont said that.

There are other inconsistencies or unspecified conditions: How do they synch their clocks 14 billion years ago? You didn't say or wrote a diagram. @studiot pointed it out.

You're spreading all your argument with "they see", "they measure" and the like. That's not good enough, not in relativity, never mind special or general, as a good read of Einstein's original papers or a good modern relativity book --Ray D'Inverno's book is a nice example-- makes clear from the beginning. Something like this:

The diagonal lines are photons going from one observer to the other, telling each other exactly where and when they "saw" something or actually "seeing" something. That's what "see" means in relativity. The non-diagonal lines are inertial observers or objects moving at v<c.

By the way, how do two distant observers "see" the same photon? Because then it's just one photon we're talking about, and two distant observers somehow catch the  same photon.

Now it's Saturn's orbit. You seem to keep moving the goalposts.

You have to state your problem clearly, and try not to change the conditions, unles it is to refine the statement of the same problem. Stating the problem clearly is part of the art of doing physics.

So I'm still confused. It was many years ago that I understood there is no blame for being confused during a physics class. The real problem is being confused and not being able to tell why.

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3 hours ago, joigus said:

No, my reason to be confused is what I said: Two observers seeing two different things see... well two different things! What's strange with that? As @Markus Hanke has made perfectly clear. GR tell you how different the different things appear to be provided you carefully specify the conditions.

If they see the same thing, how come, if they are apart? @swansont said that.

There are other inconsistencies or unspecified conditions: How do they synch their clocks 14 billion years ago? You didn't say or wrote a diagram. @studiot pointed it out.

You're spreading all your argument with "they see", "they measure" and the like. That's not good enough, not in relativity, never mind special or general, as a good read of Einstein's original papers or a good modern relativity book --Ray D'Inverno's book is a nice example-- makes clear from the beginning. Something like this:

The diagonal lines are photons going from one observer to the other, telling each other exactly where and when they "saw" something or actually "seeing" something. That's what "see" means in relativity. The non-diagonal lines are inertial observers or objects moving at v<c.

By the way, how do two distant observers "see" the same photon? Because then it's just one photon we're talking about, and two distant observers somehow catch the  same photon.

Now it's Saturn's orbit. You seem to keep moving the goalposts.

You have to state your problem clearly, and try not to change the conditions, unles it is to refine the statement of the same problem. Stating the problem clearly is part of the art of doing physics.

So I'm still confused. It was many years ago that I understood there is no blame for being confused during a physics class. The real problem is being confused and not being able to tell why.

There are no unknown factor(s) in the thought experiment(s) described.

We can easily imagine that a time measurement starts and ends simultaneously, it is technically possible.

In the first thought experiment, doubts arose about "simultaneity", - yes, - hence it is easier to simplify the experiment rather than arguing into a dead end. .

Saturn's orbital period can be directly observed by both Bob and Alice.

It doesn't move the goalposts, no not at all, - but simply simplifies the very same principle point.

We can also boil it down even more by referring to PETER who lives infinitely far away (in vacuum) where there is no gravity at all.

Peter is the only one who meets the conditions to be able to define his 1 meter ruler to be = the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second

If the ruler is an invariant, all other observers (whom we assume live in gravitational fields) will not agree with Peter's definition applies from them.

In other words, all universal beings (who can do a little math) can provide mathematical proof that all other rulers (comparable to Peter's rules) deviate from PETER's definition of 1 meter.

As you can see now, we've excluded everything but 1 meter rulers, which is what it's all about.

Now here comes the other side of same coint, if all universal beings agree to the possibility that rulers must be a proportional relativistic variable, - then now the definition of 1 meter is suddenly universal. – It’s a choose we have.

Edith

The decisive point is still the same, how can the world's best rulers agree with each other at the factory and as soon they are brought to Bob and Alice's apartment they disagree.

Edited by Bjarne-7
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11 minutes ago, Bjarne-7 said:

If the ruler is an invariant,

The ruler's length?

Invariant under what? Rotations? It is.

Lorentz transformations? It is not.

General coordinate transformations? (Thereby including gravitational fields, either static or dynamic) It is not.

You see. It's not as simple as something is or is not invariant. It takes a little preliminary work to even say what you mean.

At least to me. Other people have the priceless ability to grasp the inner logic of fuzzy statements. Not me.

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1 hour ago, Bjarne-7 said:

The decisive point is still the same, how can the world's best rulers agree with each other at the factory and as soon they are brought to Bob and Alice's apartment they disagree.

Because rulers from a factory don’t generally agree to a part in 10^15. Or anything close to that.

And Alice and Bob live in different apartments

I recall a discussion with a Nobel prize winner who was visiting (two of my colleagues had been postdocs in his lab) about the issues that will arise once measurement precision reaches a certain level. Like having to specify whether an electron’s mass measurement was made at the bottom of a mountain or the top. We do this with time already, because we can do the measurements with sufficient precision.

17 hours ago, joigus said:

Well they would agree on the speed of light, wouldn't they? They would disagree on the frequencies and wave numbers, or IOW, the number of cycles a particular physical interval contains.

I was thinking of what happens near a BH. Light can travel (orbit) but time dilation becomes infinite as seen by a distant observer

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21 minutes ago, joigus said:

The ruler's length?

Invariant under what? Rotations? It is.

Lorentz transformations? It is not.

General coordinate transformations? (Thereby including gravitational fields, either static or dynamic) It is not.

You see. It's not as simple as something is or is not invariant. It takes a little preliminary work to even say what you mean.

At least to me. Other people have the priceless ability to grasp the inner logic of fuzzy statements. Not me.

With a bit of advanced math, you can calculate that time passes differently at different distances to the center of a gravitational field. In other words, you are comparing different relativistic views of "reality" with each other. This is exactly what you also do with simple math by comparing the length of 1 meter in Bob's apartment with the length of 1 meter in Alice's apartment.

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8 minutes ago, Bjarne-7 said:

With a bit of advanced math, you can calculate that time passes differently at different distances to the center of a gravitational field.

Oh, lay it on me, please.

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1 hour ago, Bjarne-7 said:

We can easily imagine that a time measurement starts and ends simultaneously, it is technically possible.

Yes it is exactly zero.

By the way

How did we move from a discussion about time

to a discussion about distance ?

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35 minutes ago, studiot said:

How did we move from a discussion about time

to a discussion about distance ?

It is possible as I showed in my post-11.

But perhaps it is easier for some to relate to when there is speed included.

1 hour ago, swansont said:

Because rulers from a factory don’t generally agree to a part in 10^15. Or anything close to that.

It is only something we pretend for purely pedagogical reasons.

1 hour ago, swansont said:

I recall a discussion with a Nobel prize winner who was visiting (two of my colleagues had been postdocs in his lab) about the issues that will arise once measurement precision reaches a certain level. Like having to specify whether an electron’s mass measurement was made at the bottom of a mountain or the top. We do this with time already, because we can do the measurements with sufficient precision.

Do you know, - can we also measure the ruler precise enough to know if these are any deviation from the vacuum definition?

1 hour ago, swansont said:

I was thinking of what happens near a BH. Light can travel (orbit) but time dilation becomes infinite as seen by a distant observer

I've been thinking the same thing. The light must cease to move as seen from a outside perspective, which means that the photon must cease to exist. From the point of view of the event horizon, it will move quite normally. It is a contradiction. You are probably also familiar with the BH paradox

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23 minutes ago, Bjarne-7 said:

It is only something we pretend for purely pedagogical reasons.

If you built multiple atomic clocks in one location and then sent some to a location at a different elevation, the ones at a higher elevation will run at a higher frequency. This isn’t a pedagogical exercise. I’ve done it. (Some clocks near sea level, the others at more than 1 km higher in elevation. The latter ran more than 10^-13 faster at the final location)

ETA: A ruler will curve in a gravitational field, but directly measuring that isn’t something we can currently do

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6 minutes ago, swansont said:

If you built multiple atomic clocks in one location and then sent some to a location at a different elevation, the ones at a higher elevation will run at a higher frequency. This isn’t a pedagogical exercise. I’ve done it. (Some clocks near sea level, the others at more than 1 km higher in elevation. The latter ran more than 10^-13 faster at the final location)

Right, and no surprises I guess

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In relativity, we frequently see discussions of quantities that are different in different frames of reference. Less often do we see discussions of quantities that remain the same in different frames of reference (other than the speed of light in a vacuum). I think this leads to confusion about the nature of relativity. I think it is important to note that all observers measuring the same quantity will always obtain the same value regardless of their frame of reference. This means that regardless of the picture relativity seems to paint, relativity does present a truly consistent picture of reality. When it is said that observers in different frames of reference obtain different values for a given measurement, it is because they are actually measuring different things. For example, length contraction is the result of observers in different frames of reference measuring the proper distance between different points in spacetime. The measured width of a river will depend on whether it is measured perpendicularly across or obliquely across, and the same is true for the world-strip of a rod in spacetime. In the case of time dilation, one is comparing the proper time between one pair of points in spacetime with the proper time between another pair of points in spacetime, with some notion of simultaneity between the pairs of points justifying the comparison. But it is when one believes that the different measurements are the same measurement that one can have a confused picture of relativity.

Edited by KJW
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21 minutes ago, KJW said:

But it is when one believes that the different measurements are the same measurement that one can have a confused picture of relativity.

That is not the case in this debate, here it is not necessary to measure, but only to compare 1 meter, almost exactly the same way you (using calculation) can compare 1 second

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2 hours ago, swansont said:

I was thinking of what happens near a BH. Light can travel (orbit) but time dilation becomes infinite as seen by a distant observer

For example, in Schwarzschild coordinates, the rate at which light propagates at the event horizon is zero, but still the local speed of light at the horizon is c. Obviously both things can't be referred to as "the speed of light" and be used interchangeably. I used "rate" instead of "speed" because I don't think the latter is the right word to use here.

What's the correct term for what you're describing (or for what Bjarne-7 is having a problem with?). I wouldn't use "speed of light" when talking about curved spaces unless whatever d/t that's referred to is the same as the local speed of light over d. Anything else I think needs to be described more specifically than just "speed of light."

Edited by md65536
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44 minutes ago, md65536 said:

For example, in Schwarzschild coordinates, the rate at which light propagates at the event horizon is zero, but still the local speed of light at the horizon is c. Obviously both things can't be referred to as "the speed of light" and be used interchangeably. I used "rate" instead of "speed" because I don't think the latter is the right word to use here.

Perhaps it’s terminology, but they don’t agree about the speed of light propagation in some other frame (and these are not inertial frames) even though locally they will measure it as c.

The problem as framed doesn’t seem to point to any flaw in relativity.

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1 hour ago, Bjarne-7 said:

That is not the case in this debate, here it is not necessary to measure, but only to compare 1 meter, almost exactly the same way you (using calculation) can compare 1 second

A metre is still a metre, and a second is still a second for the two observers at different elevation. Any disagreement between these two observers is the result of how these are compared, noting that the comparison is non-local. But on earth, the surrounding spacetime is approximately stationary and admits a Killing vector field, providing a natural frame of reference in which gravitational time dilation manifests itself as an apparent change in time with respect to elevation. But in spite of the naturalness of this frame of reference, it is still just some frame of reference no more special than other frames of reference in general relativity.

Edited by KJW
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19 minutes ago, KJW said:

A metre is still a metre, and a second is still a second for the two observers at different elevation. Any disagreement between these two observers is the result of how these are compared, noting that the comparison is non-local. But on earth, the surrounding spacetime is approximately stationary and admits a Killing vector field, providing a natural frame of reference in which gravitational time dilation manifests itself as an apparent change in time with respect to elevation. But in spite of the naturalness of this frame of reference, it is still just some frame of reference no more special than other frames of reference in general relativity.

Right

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3 hours ago, Bjarne-7 said:

It is possible as I showed in my post-11.

But perhaps it is easier for some to relate to when there is speed included.

The fact remains that you have made a good many claims, some of principle, some numeric and some totally irrlevant to the issue.

But I have not seen a single piece of mathematics or calculation to support them.

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1 hour ago, swansont said:

Perhaps it’s terminology, but they don’t agree about the speed of light propagation in some other frame (and these are not inertial frames) even though locally they will measure it as c.

The problem as framed doesn’t seem to point to any flaw in relativity.

I looked elsewhere and it looks like "coordinate velocity" and coordinate speed are terms that are used and understood. Yes there's no flaw in relativity here. Alice and Bob, using their different respective local coordinates, disagree on the coordinate speed of light in empty space, just as GR predicts they should.

Edited by md65536
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22 hours ago, Bjarne-7 said:

Can you disprove that he ruler is a proportional relativistic variable ?

I don’t know what ”proportional relativistic variable” is supposed to mean, but we know that measurements of distance are observer-dependent in GR, as several people here have already pointed out.

So again - where is the “problem”?

14 hours ago, Bjarne-7 said:

The light must cease to move as seen from a outside perspective, which means that the photon must cease to exist. From the point of view of the event horizon, it will move quite normally. It is a contradiction.

No, it’s not a contradiction, because in GR there’s a big difference between proper quantities and coordinate quantities. The two observers use different local notions of time, so you’re not comparing like for like.

13 hours ago, Bjarne-7 said:

That is not the case in this debate, here it is not necessary to measure, but only to compare 1 meter, almost exactly the same way you (using calculation) can compare 1 second

You compare spatial distances just like you do time separations, and you find that they are observer-dependent, as expected.

Where is the “problem”?

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12 hours ago, md65536 said:

Yes there's no flaw in relativity here. Alice and Bob, using their different respective local coordinates, disagree on the coordinate speed of light in empty space, just as GR predicts they should.

The good news is there are no conflict, also not after the meter ruler becomes a relativistic transformation factor. It is thought-provoking in itself that it is possible to "manipulate" the ruler, and that there is ample room in the theory of relativity and in our worldview for this to happen, - without there being any immediate outcry or conflict with any scientific facts.

12 hours ago, studiot said:

The fact remains that you have made a good many claims, some of principle, some numeric and some totally irrlevant to the issue.

But I have not seen a single piece of mathematics or calculation to support them.

At the end of the 18th century, people were well aware that the Lorentz Transformation had some strange consequences (time dilation and distance shortening). But it was believed that it was probably just mathematical quirks that should not be taken seriously.
But the transformation led to Einstein starting to play with thought experiments which were the starting point for the special theory of relativity in the first place, and thus the scientific community was challenged with then very strange thoughts.
In a similar way, we owe it to ourselves to seriously ask the question of whether another transformation factor was overlooked?
The equation t * v = d is of course an old classical equation. But one must remember that we know that t, - is nowadays also a relativistic variable (whereby the equation loses its classical innocence), - whereby it is legitimate to ask questions about whether "m" (the ruler) always compensates with the same factor for which t transforms (?) Or if it is just (again) mathematical quirks, -  not necessary to take serious.. ?

Yes, - my suggestion is only  a mathematically supported "conjecture" and not a definitive mathematical proof.
You can't get a more in-depth "mathematical answer" than this (today).

So all left to do is then to ask: - are there at all  "space for" another factor of transformation in the theory of relativity or not.?
Just like Einstein, you can initially try to understand the consequences of taking "a mathematical quirks" seriously.
What are the consequences of introducing yet another transformation factor?
Do you right away end up in Utopia and into conflict with well-documented "safe- knowledge"?  - No, not at all, right ?
Or on the other hand,  are there anything that points to that the consequences possible can have the potential to be able to add value to the theory of relativity that can take the theory to a deeper holistic understanding of the whole theory?  -   (which may then later indirectly lead to tangible evidence of different nature.?)

The first thought / image I get is this:
It shows that space around an astronomical object appears to be stretching towards an astronomical body, i.e. something that at least resembles an elastic property. Certainly not the intention of the image, but the thought arises: Is the "curvature" of the space in reality an elastic property?

Many more thoughts arise:
- Is the possible transformation of rulers, - caused by the tension of space  ?
- Is the variation of the relativistic tension of space (and matter), - causing clocks to tick faster / slower ?.
- Is there a an elastic connection between space and matter?   -   and hence the real cause of gravity ?
- Is gravity then still a force (as Newton claimed it to be)  ?
- Does the fabric absorb  "elastic space"?
- Is dark energy just, the oppesite, -  a disintegrating gravitational field?
Many more thoughts follow in the wake.

The key word here is "elastic space" which, in terms of understanding, actually does not deviate very much from the previous perception we have of the deformable property of space. So "merely" a "play" with expressions seems to give the theory of relativity "new properties" which may become necessary in the long run.

I don't expect any answers to any of the questions asked (right away) - but just point out that a fairly small innocent (mathematically substantiated) addition of a transformation parameter does not necessarily end in chaos, conflict and Utopia, but perhaps can have rather far-reaching consequences that may provide answers to a number of unsolved mysteries. .

Edited by Bjarne-7
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5 hours ago, Bjarne-7 said:

At the end of the 18th century, people were well aware that the Lorentz Transformation had some strange consequences (time dilation and distance shortening). But it was believed that it was probably just mathematical quirks that should not be taken seriously.

It was actually the 19th century, I know that is what you meant.

5 hours ago, Bjarne-7 said:

The equation t * v = d is of course an old classical equation. But one must remember that we know that t, - is nowadays also a relativistic variable (whereby the equation loses its classical innocence), - whereby it is legitimate to ask questions about whether "m" (the ruler) always compensates with the same factor for which t transforms (?) Or if it is just (again) mathematical quirks, -  not necessary to take serious.. ?

If you are asking if "moving rulers are shorter" is just a mathematical 'thing', the answer is no.

5 hours ago, Bjarne-7 said:

So all left to do is then to ask: - are there at all  "space for" another factor of transformation in the theory of relativity or not.?

No.  The theory of relativity passes all test so another 'factor' is not needed.

5 hours ago, Bjarne-7 said:

- Is the possible transformation of rulers, - caused by the tension of space  ?
- Is the variation of the relativistic tension of space (and matter), - causing clocks to tick faster / slower ?.
- Is there a an elastic connection between space and matter?   -   and hence the real cause of gravity ?
- Is gravity then still a force (as Newton claimed it to be)  ?
- Does the fabric absorb  "elastic space"?
- Is dark energy just, the oppesite, -  a disintegrating gravitational field?

Based on all current observation and experimentation; no, no, no, no, no, no.

5 hours ago, Bjarne-7 said:

I don't expect any answers to any of the questions asked (right away) - but just point out that a fairly small innocent (mathematically substantiated) addition of a transformation parameter does not necessarily end in chaos, conflict and Utopia, but perhaps can have rather far-reaching consequences that may provide answers to a number of unsolved mysteries. .

These unsolved mysteries are a problem that you have due to your limited knowledge of relativity.

Edited by Bufofrog
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22 hours ago, swansont said:

Because rulers from a factory don’t generally agree to a part in 10^15. Or anything close to that.

And Alice and Bob live in different apartments

I recall a discussion with a Nobel prize winner who was visiting (two of my colleagues had been postdocs in his lab) about the issues that will arise once measurement precision reaches a certain level. Like having to specify whether an electron’s mass measurement was made at the bottom of a mountain or the top. We do this with time already, because we can do the measurements with sufficient precision.

I was thinking of what happens near a BH. Light can travel (orbit) but time dilation becomes infinite as seen by a distant observer

For some reason I didn't see these comments yesterday. Thanks for the clarification.

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6 hours ago, Bjarne-7 said:

So all left to do is then to ask: - are there at all  "space for" another factor of transformation in the theory of relativity or not.?

Measurements of space and time at different places/times are related via the metric, which is the basic dynamic variable in GR. This is the entire point of the model, so you don’t need to introduce anything new. The difference to SR is that frames are no longer related via simple Lorentz transformations, so time dilation and changes in lengths do not necessarily carry the same factors, nor do they even necessarily occur together.

6 hours ago, Bjarne-7 said:

Is the "curvature" of the space in reality an elastic property?

No. Spacetime curvature behaves quite differently from elasticity in a medium; the image is just an analogy and visualisation aid.

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9 hours ago, Bjarne-7 said:

So all left to do is then to ask: - are there at all  "space for" another factor of transformation in the theory of relativity or not.?

What would this be?

Relativity has been confirmed by experiment many times, so the answer is that the effect of any new transformation must be no larger than the experimental error of the best experiments we’ve done.

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10 hours ago, Bjarne-7 said:

... The key word here is "elastic space" which, in terms of understanding, actually does not deviate very much from the previous perception we have of the deformable property of space. So "merely" a "play" with expressions seems to give the theory of relativity "new properties" which may become necessary in the long run. ...

You should talk to this guy, who had "Space must have some kind of elastic nature woven together with matter" as an important part of his theory:

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