Analogies for relativistic physics

[Killtech]

10 hours ago, KJW said:

I see two problems with this:

1: The wave equation for electromagnetism but with the speed of sound replacing the speed of light may not be the correct wave equation for describing the propagation of sound. In this wave equation there is no dependency on the velocity of the medium, whereas sound waves have a fixed velocity relative to the medium, which may differ from the velocity relative to the observer if the medium is in motion relative to the observer.

i used the well known linearized acoustic wave equation as a starting point because the equation is invariant under Lorentz transformation. The rest is going back in history, looking how special relativity developed from the Lorentz aether, back when light was still modelled as having a medium (with a possible wind effect) and replaying the same game but for acoustics instead - simply because it works just the same. And since all that is just playing around with a different representation of the original equation it is guaranteed not to be wrong. And that new representation suddenly made the question of the motion of the medium irrelevant also annoyed Lorentz. The same irritation seems to pop up when people are demonstrated that the math works the same for sound.

Here is the post where i did it explicitly: Analogies for relativistic physics - Relativity - Science Forums - so if you have any question how that is supposed to work, the simple math is there. 

10 hours ago, KJW said:

2: If the Lorentz transformation but with the speed of sound replacing the speed of light is applied to space and time coordinates, the resulting new coordinates are no longer space and time coordinates. Indeed, it is not obvious what these new coordinates represent. Note that it is Minkowskian spacetime that is invariant to Lorentz transformations, not just the electromagnetic wave equation, so that applying a Lorentz transformation to space and time coordinates results in new coordinates that are also space and time coordinates.

Imagine how much trouble it was back in the day for physicists when Lorentz coordinates were introduced the first time. Interpreting them without a precedence was a lot harder. But coordinates are coordinates, so anything goes. Let's do baby steps and confirm that they work first.

 

8 hours ago, joigus said:

So is it clear now that the sound equation is not Lorentz invariant, as v_s is not a universal constant, nor is it a Lorentz scalar, or are we still discussing that?

invariance of a given equation under a group of transformation is well defined. Any equation has a larger group it is invariant under and for the linearized acoustic wave equation, this happens to be the hyperbolic rotations of spacetime based around \(v_s\). This is a different group then the Lorentz group of SR obviously, but it has the identical structure since the only difference is that the limit speed those trafos use, that is \(v_s\) instead of \(c\). i posted an example in this thread where i did it step by step with all the math included. 

This is about the mathematical formalism of relativity. It developed from the Lorentz aether theory, where light waves were analog to sound waves and were modelled as having a medium (the luminuferious aether). We can try to do all the historic development of relativity but applying it to sound instead and see how far we can get. The question is simply if the formalism allows to hide all aspects of the medium entirely through the use of tricky coordinates. and later geometry.

Edited November 14, 2023 by Killtech

[joigus]

13 minutes ago, Killtech said:

i used the well known linearized acoustic wave equation as a starting point because the equation is invariant under Lorentz transformation. The rest is going back in history, looking how special relativity developed from the Lorentz aether, back when light was still modelled as having a medium (with a possible wind effect) and replaying the same game but for acoustics instead - simply because it works just the same. And since all that is just playing around with a different representation of the original equation it is guaranteed not to be wrong. And that new representation suddenly made the question of the motion of the medium irrelevant also annoyed Lorentz. The same irritation seems to pop up when people are demonstrated that the math works the same for sound.

Here is the post where i did it explicitly: Analogies for relativistic physics - Relativity - Science Forums - so if you have any question how that is supposed to work, the simple math is there. 

 

Imagine how much trouble it was back in the day for physicists when Lorentz coordinates were introduced the first time. Interpreting them without a precedence was a lot harder. But coordinates are coordinates, so anything goes. Let's do baby steps and first confirm that they work first.

invariance of a given equation under a group of transformation is well defined. Any equation has a larger group it is invariant under and for the linearized acoustic wave equation, this happens to be the hyperbolic rotations of spacetime based around vs . This is a different group then the Lorentz group of SR obviously, but it has the identical structure since the only difference is that the limit speed those trafos use, that is vs instead of c . i posted an example in this thread where i did it step by step with all the math included. 

This is about the mathematical formalism of relativity. It developed from the Lorentz aether theory, where light waves were analog to sound waves and were modelled as having a medium (the luminuferious aether). We can try to do all the historic development of relativity but applying it to sound instead and see how far we can get. The question is simply if the formalism allows to hide all aspects of the medium entirely through the use of tricky coordinates. and later geometry.

Einstein said:

1) The laws of physics are the same in every inertial reference system

2) The speed of light is the same in all inertial frames of reference

This gives a group of transformations that, in turn, result in a transformation of velocities that's called Einstein's transformation of velocities, which is consistent with it, as couldn't be otherwise. For systems moving in the x direction, the Einstein transformation of velocities gives,

\[ V_{x}'=\frac{V_{x}-v}{1-vV_{x}/c^{2}} \]

Now, if you feed into it a light ray moving parallel to this direction (x, called the 'boost' direction), you get,

\[ c'=\frac{c-v}{1-vc/c^{2}}=\frac{c-v}{1-v/c}=c \]

So indeed the speed of light doesn't change, consistent with Einstein's principle of relativity.

Now, what you are suggesting is a different principle of relativity. Let's call it Killtech's principle of relativity, which says,

1) The laws of physics are the same in every inertial reference system

2) The speed of sound is the same in all inertial frames of reference

That is a principle of relativity that's perfectly logically consistent. Same with the speed of 1 mile per hour, same with any other speed that you choose. That's not how Nature behaves though, so the speed of sound must change according to Einstein's transformation of velocities, and consequently it changes from reference frame to reference frame. The observation that one could have one different principle of relativity for every which velocity that one choses, and still be logically consistent is trivial, and obviously doesn't lead anywhere useful.

Is that what all this is about? Do you have some reason to suspect that sound plays a pivotal role in it all?

The speed of light is fundamental for reasons that other members have told you about.

You can do all the maths that you want, and you can rephrase it any way you want. You still got it wrong.

[Killtech]

23 hours ago, joigus said:

Now, what you are suggesting is a different principle of relativity. Let's call it Killtech's principle of relativity, which says,

1) The laws of physics are the same in every inertial reference system

2) The speed of sound is the same in all inertial frames of reference

That is a principle of relativity that's perfectly logically consistent. Same with the speed of 1 mile per hour, same with any other speed that you choose. That's not how Nature behaves though, so the speed of sound must change according to Einstein's transformation of velocities, and consequently it changes from reference frame to reference frame. The observation that one could have one different principle of relativity for every which velocity that one choses, and still be logically consistent is trivial, and obviously doesn't lead anywhere useful.

Is that what all this is about? Do you have some reason to suspect that sound plays a pivotal role in it all?

The speed of light is fundamental for reasons that other members have told you about.

You can do all the maths that you want, and you can rephrase it any way you want. You still got it wrong.

One can start by making an alternative postulate of relativity that you named after me. As you say, such a principle all by itself is all nice and self consistent, but it doesn't lead anywhere without a proper foundation in reality. And indeed it isn't immediately clear for what clocks and rods this principle actually holds true, apart from that these cannot be those we usually use - i.e. the SI standards. Einsteins theory and gedankenexperiments talk a lot about clocks and rods, yet there is nowhere a postulate/definition of what these devices are supposed to be in reality. And nature offers a wide range of possible oscillators which we can take as a basis for time measurement, yet they won't all produce an equivalent definition of time.

So instead, physicists found that the clocks and rods needed for Einsteins principle can be deducted right from the relativity principle itself. The geodesic clocks is an example of that. The problem with such definitions is that they are constructed in just such a way that they guarantee the principle to work. The definition of the SI meter makes it plain obvious for example: there is no logical way left how the speed of light could possibly deviate - irrespective of what nature does. And these definitions/concepts are in no way exclusive to light signals but can be adapted to audio signals as well. Therefore you can construct acoustics clocks and rods that measure time and space in reality consistent with the alternative acoustics relativity principle - you can measure nature in such a way that it behaves according to it.

The thing about the principle of relativity is that it is mostly math based on different references of measurement, a different representation of physics, that in some cases has its advantages over the alternative. But as predictions go, it does not make any that differ from Lorentz aether theory. It is just a question of practicability if its easier to handle the medium explicitly as a field or alternatively implicitly via coordinates or more refined via the geometry. 

[swansont]

1 hour ago, Killtech said:

Einsteins theory and gedankenexperiments talk a lot about clocks and rods, yet there is nowhere a postulate/definition of what these devices are supposed to be in reality. And nature offers a wide range of possible oscillators which we can take as a basis for time measurement, yet they won't all produce an equivalent definition of time.

Not in precision or accuracy, in reality, but one generally postulates an ideal system, and in that regard, how much would it matter? An ideal clock has whatever precision and accuracy is required.

[KJW]

On 11/15/2023 at 8:51 AM, Killtech said:

i used the well known linearized acoustic wave equation as a starting point because the equation is invariant under Lorentz transformation.

I agree that the electromagnetic wave equation with the speed of sound instead of the speed of light is invariant to Lorentz transformations with the speed of sound instead of the speed of light. But we know that sound waves do not behave like light waves, and I would like to know precisely where the properties differ. The wave equation you have given agrees with https://en.wikipedia.org/wiki/Acoustic_wave_equation, but I'm not convinced that this wave equation applies to any coordinate system other than the one in which the medium is at rest. This would break the invariance. In the case of light, the Doppler effect depends only on the relative velocity between the source and the observer, whereas in the case of sound, the Doppler effect depends not only on the relative velocity between the source and the observer but also on the relative velocity of the medium. Note that whereas both the speed of sound and the speed of light are independent of the speed of the source, only the speed of light is independent of the speed of the observer.

Elsewhere, I have said that c of relativity is not really about the speed of light but rather about the relationship between space and time. The relativistic velocity-addition formula, as measured by the Fizeau experiment, allows one to determine in principle the value of c without measuring the speed of light in a vacuum, thus highlighting the space and time aspect of c. The speed of sound cannot satisfy the space and time aspect of relativity. Only the Lorentz transformations with the speed of light are transformations between different frames of reference in which the space and time coordinates mean the same thing in both frames of reference.

Edited November 16, 2023 by KJW

[Killtech]

On 11/16/2023 at 9:47 PM, KJW said:

I agree that the electromagnetic wave equation with the speed of sound instead of the speed of light is invariant to Lorentz transformations with the speed of sound instead of the speed of light. But we know that sound waves do not behave like light waves, and I would like to know precisely where the properties differ. The wave equation you have given agrees with https://en.wikipedia.org/wiki/Acoustic_wave_equation, but I'm not convinced that this wave equation applies to any coordinate system other than the one in which the medium is at rest.

Coordinates cannot change anything about physics. if an equation is considered adequate in one coordinates, then it works in every possible coordinate. 

On 11/16/2023 at 9:47 PM, KJW said:

This would break the invariance. In the case of light, the Doppler effect depends only on the relative velocity between the source and the observer, whereas in the case of sound, the Doppler effect depends not only on the relative velocity between the source and the observer but also on the relative velocity of the medium. Note that whereas both the speed of sound and the speed of light are independent of the speed of the source, only the speed of light is independent of the speed of the observer.

Coordinates don't care about velocities or any such terminology. there are coordinates which agree with the metric and therefore for these choices a ratio of two coordinate differences may be interpreted as a velocity, but in general they can be very abstract things. Think for example generalized coordinates in Hamilton Jacobi equation. The coordinate invariance of an equation is therefore a quite abstract idea to begin with. 

On 11/16/2023 at 9:47 PM, KJW said:

The speed of sound cannot satisfy the space and time aspect of relativity. Only the Lorentz transformations with the speed of light are transformations between different frames of reference in which the space and time coordinates mean the same thing in both frames of reference.

But the analog principle of relativity does work for sound. I did the math here in this example: https://www.scienceforums.net/topic/132777-analogies-for-relativistic-physics/#comment-1253247 if you want to challenge it, then you should be able to challenge the simple math in that post. it is a very simple example to dissect and analyze the question. math is more convincing argument then hand-waving. 

Besides, no, in Einsteins SR coordinates in different inertial frame do not mean the same thing!! The term "relativity" implies there is a dependence, i.e. things change and are explicitly not the same. 1s and 1m means something else in each frame - it goes by the name of time dilatation and length contraction. even a concept like what events are simultaneous becomes relative on the frame. It is a direct results of building a metric from coordinates that mix time and space - and there is no logical contradiction in doing so, neither for light nor for sound. in Newtonian physics these concepts are absolutes, that is the same irrelevant of the frame and location, while SR has a frame dependence of time and length and GR adds a dependence of location, that is the gist of relativity.

 

[swansont]

1 minute ago, Killtech said:

Coordinates cannot change anything about physics. if an equation is considered adequate in one coordinates, then it works in every possible coordinate. 

Whether an equation works depends on agreement with experiment. The equation doesn’t work in a moving coordinate system because it doesn’t agree with experiment. Sound acquires the speed of the source if the source and medium are moving together. You can transform the equation, because that’s math, but an equation that assumes an invariant speed of propagation is wrong.

[Killtech]

12 minutes ago, swansont said:

Whether an equation works depends on agreement with experiment. The equation doesn’t work in a moving coordinate system because it doesn’t agree with experiment. Sound acquires the speed of the source if the source and medium are moving together. You can transform the equation, because that’s math, but an equation that assumes an invariant speed of propagation is wrong.

The linear acoustic wave equation works and of course it is confirmed by experiment. There is a reason we use it after all. 

but if you are tying to imply that physical predictions change depending on your choice of coordinates, oh boy, i want you to try to prove that. You can then surely explain why different coordinates still produce identical predictions in this case here: https://www.scienceforums.net/topic/132777-analogies-for-relativistic-physics/#comment-1253247 (note: there is one typo in that post towards the end, where i wrote \(\gamma_s = 5/3\) instead of  \(5/4\))

 

Edited November 18, 2023 by Killtech

[swansont]

38 minutes ago, Killtech said:

The linear acoustic wave equation works and of course it is confirmed by experiment. There is a reason we use it after all. 

but if you are tying to imply that physical predictions change depending on your choice of coordinates, oh boy, i want you to try to prove that.

A sound source is on a plane traveling 300 m/s. The sound travels 343 m/s inside the plane. An observer on the ground will measure the sound traveling at 643 m/s, or -43 m/s, depending on the direction the sound is traveling.

[KJW]

1 hour ago, Killtech said:

1s and 1m means something else in each frame - it goes by the name of time dilatation and length contraction.

No, you have misunderstood what I said. If in some inertial frame of reference, I have a clock that ticks away seconds and a rod that is one meter long, and I accelerate to some other inertial frame of reference, then the clock will still tick away seconds and the rod will still be one meter long. This is the principle of relativity in action and neither time dilation nor length contraction would make sense without it.

[Killtech]

56 minutes ago, swansont said:

A sound source is on a plane traveling 300 m/s. The sound travels 343 m/s inside the plane. An observer on the ground will measure the sound traveling at 643 m/s, or -43 m/s, depending on the direction the sound is traveling.

The assumptions of the acoustic wave equation is a homogeneous static medium, in your case the medium has two layers moving relative to each other, so you are discussing a different scenario. Coordinates don't have anything to do with that. An analogy to SR requires to have analogous conditions, hence why for the start we assume a simple medium setup, same as LAT and SR does.

In relativity the analogue of your example however already requires the use of an Alcubierre metric to achieve an analoge result with light. So this requires quite a bit of GR and a lot of more involved math. Let's go slow and first discuss the simple situations before we go there.

40 minutes ago, KJW said:

No, you have misunderstood what I said. If in some inertial frame of reference, I have a clock that ticks away seconds and a rod that is one meter long, and I accelerate to some other inertial frame of reference, then the clock will still tick away seconds and the rod will still be one meter long. This is the principle of relativity in action and neither time dilation nor length contraction would make sense without it.

yes, and now think it through. the meter and second at rest in one frame are the same as they are at rest but another frame, right? how would you know they are the same? if you put them next to each other for comparison (but still with their relative movement) they actually won't be - length contraction, remember? so you measure the proper length of each, i.e. you measure the meter in meters in its rest frame. you do that with the other meter, too. you found out that relative to itself the meter did not change... but how could it?

as you can see, the trick it to define a compare relation that makes it so.

Edited November 18, 2023 by Killtech

[swansont]

11 hours ago, Killtech said:

The assumptions of the acoustic wave equation is a homogeneous static medium, in your case the medium has two layers moving relative to each other, so you are discussing a different scenario. Coordinates don't have anything to do with that. An analogy to SR requires to have analogous conditions, hence why for the start we assume a simple medium setup, same as LAT and SR does.

IOW your equation doesn’t agree with experiment, as I said. And the frame matters.

[KJW]

12 hours ago, Killtech said:

yes, and now think it through. the meter and second at rest in one frame are the same as they are at rest but another frame, right? how would you know they are the same? if you put them next to each other for comparison (but still with their relative movement) they actually won't be - length contraction, remember? so you measure the proper length of each, i.e. you measure the meter in meters in its rest frame. you do that with the other meter, too. you found out that relative to itself the meter did not change... but how could it?

as you can see, the trick it to define a compare relation that makes it so.

One could measure the clock and the rod in both frames of reference from a third frame of reference relative to which the two frames of reference have equal speeds.

 

Edited November 18, 2023 by KJW

[studiot]

56 minutes ago, KJW said:

One could measure the clock and the rod in both frames of reference from a third frame of reference relative to which the two frames of reference have equal speeds.

 

How would that work, bearing in mind that the length contractionformula is only correct in the direction of motion and the measuring rod cannot be oriented in two different directions at once ?

[KJW]

53 minutes ago, studiot said:

How would that work, bearing in mind that the length contraction formula is only correct in the direction of motion and the measuring rod cannot be oriented in two different directions at once ?

I don't think it would be too difficult to arrange the frames of reference and the rod orientations to give the same length contraction, thereby establishing that the rod is the same length in both frames of reference. The simplest would be for the rod to be oriented parallel to the change in velocity in both frames of reference, and for the third frame of reference to be collinear to the other two frames of reference.

 

Edited November 18, 2023 by KJW

[Killtech]

1 hour ago, swansont said:

IOW your equation doesn’t agree with experiment, as I said. And the frame matters.

Nor is SR able to correctly predict the bending of light due to massive bodies. It's absurd to apply physical equation to situations that they are not suited for/do not try to model just to claim they are invalid. What you are doing here is called a strawman argument :(

For the linearized acoustic wave equation, we know quite well the domain it is valid for. So we have to limit our discussion to the case of a static perfect medium as long as we are discussing this particular case. Only there it does agree with the experiment and this is where the analogy with light also works. The generalization to a locally inhomogenes medium is more involved and requires different equations. However, similar to SR, the core framework and its terminology is setup in the easiest possible situation first and generalized to other cases later and i intend to do it the same way.

[studiot]

39 minutes ago, KJW said:

I don't think it would be too difficult to arrange the frames of reference and the rod orientations to give the same length contraction, thereby establishing that the rod is the same length in both frames of reference. The simplest would be for the rod to be oriented parallel to the change in velocity in both frames of reference, and for the third frame of reference to be collinear to the other two frames of reference.

 

You have a diagram of this arrangement ?

[KJW]

1 hour ago, studiot said:

You have a diagram of this arrangement ?

No, I don't have a diagram. I actually don't see the difficulty.

[studiot]

24 minutes ago, KJW said:

No, I don't have a diagram. I actually don't see the difficulty.

Then you haven't shown anything.

 

You are the one making the claim so you are the one who needs to substantiate that claim.

[KJW]

14 minutes ago, studiot said:

You are the one making the claim so you are the one who needs to substantiate that claim.

I did substantiate my claim. I said:

Quote

The simplest would be for the rod to be oriented parallel to the change in velocity in both frames of reference, and for the third frame of reference to be collinear to the other two frames of reference.

 

 

[swansont]

2 hours ago, Killtech said:

Nor is SR able to correctly predict the bending of light due to massive bodies. It's absurd to apply physical equation to situations that they are not suited for/do not try to model just to claim they are invalid. What you are doing here is called a strawman argument :(

SR does not claim to work under that condition. 

But I must apologize; I was recalling a claim about the speed of sound being invariant but it was in another thread, by another poster.

 

17 hours ago, Killtech said:

but if you are tying to imply that physical predictions change depending on your choice of coordinates, oh boy, i want you to try to prove that. You can then surely explain why different coordinates still produce identical predictions in this case here: https://www.scienceforums.net/topic/132777-analogies-for-relativistic-physics/#comment-1253247 (note: there is one typo in that post towards the end, where i wrote γs=5/3 instead of  5/4 )

 

Are you really claiming that a meter stick will have its length contracted to 80 cm if measured in the wind frame?

[studiot]

26 minutes ago, KJW said:

I did substantiate my claim. I said:

Quote

The simplest would be for the rod to be oriented parallel to the change in velocity in both frames of reference, and for the third frame of reference to be collinear to the other two frames of reference.

Indeed you did an thereby contradicted yourself since if there was to be a change in velocity the frames would not be inertial.

[KJW]

3 minutes ago, studiot said:

Indeed you did an thereby contradicted yourself since if there was to be a change in velocity the frames would not be inertial.

There are two inertial frames of reference in which there is no acceleration. The acceleration in going from one inertial frame to the other inertial frame does not count. Otherwise, it would be one non-inertial frame of reference.

 

[studiot]

Your specification is insufficiently detailed.

You say you have 3 colinear frames.

You say velocity, but do not specify what it is relative to, since all velocity is relative to something.

You say you don't have a diagram.  Why not ?

[KJW]

37 minutes ago, studiot said:

Your specification is insufficiently detailed.

I don't think so.

 

37 minutes ago, studiot said:

You say you have 3 colinear frames.

And?

 

37 minutes ago, studiot said:

You say velocity, but do not specify what it is relative to, since all velocity is relative to something.

Yes, I did. The velocities of the two frames are relative to the third frame. Perhaps I should have simply said the velocity relative to the third frame of the second frame is equal and opposite that of the first frame.

 

37 minutes ago, studiot said:

You say you don't have a diagram.  Why not ?

Why would I?