Analogies for relativistic physics

[studiot]

30 minutes ago, KJW said:

I don't think so.

 

And?

 

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.

 

Why would I?

 

 

You are just playing silly games.

Goodnight.

[Killtech]

8 hours ago, swansont said:

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

That i do not. Of course a SI meter won't behave like that. However, i am mathematician and i will immediately look up the definition of a meter and recognize how it is constructed from the relativity principle and that the analog definition using sound signals instead of light actually ensures the contraction in the wind frame. Anyhow, coordinates don't care at all about such matters and can contract irrespective of what an actual rod may do. coordinates are instead just a question of preference and we can chose any we like. The ones using a principle of relativity for acoustic do show they achieve the correct result using an analog of relativistic calculus. 

A real solid state rod is electromagnetic in origin - its size ist mostly governed by the interaction of the positively charged nucleus with its electron shells via the electromagnetic force which core characteristic is the speed of light. naturally it will therefore conform to the relativity principle of light and not acoustics.

But definitions are just that - convention we choose. and we can construct something which size is governed by acoustics instead of electromagnetism and therefore conform to the relativity principle of acoustics and contracts accordingly. Admittedly such constructs do not appear very intuitive (except maybe for a bat which perceives the world around it via acoustics) but mathematically they are a perfect analogy.

The issue is that we live in a world almost entirely governed by the electromagnetic force, hence we become blind to anything past that perspective. building up the math that shows how sound can be treated very much in the same way if we chose to adjust our standard definitions, is quite important to get a different perspective on what we are actually dealing with. 

[KJW]

10 minutes ago, Killtech said:

A real solid state rod is electromagnetic in origin - its size is mostly governed by the interaction of the positively charged nucleus with its electron shells via the electromagnetic force which core characteristic is the speed of light. naturally it will therefore conform to the relativity principle of light and not acoustics.

Relativity is not about electromagnetism, it is about spacetime.

[studiot]

6 hours ago, Killtech said:

i am mathematician

But definitions are just that - convention we choose. and we can construct something which size is governed by acoustics instead of electromagnetism and therefore conform to the relativity principle of acoustics and contracts accordingly. Admittedly such constructs do not appear very intuitive (except maybe for a bat which perceives the world around it via acoustics) but mathematically they are a perfect analogy.

 

I do understand what you hoping to do so, as a mathematician, you should be able to understand my difficulty with finding such an analogy.

Einstinian relativity depends upon finding an invariant such that it will be measured the same by all (inertial) observers.
Other relationships are then mathematically adjusted to conform with this requirement.

He then developed special relativity conformities on basis of the idea the speed of light in vacuo. is such an invariant.

(Note this was not one of his original two axioms, which were simpler. He actually had to deduce this invariance from his original axioms)

Right at the outset he states that he is taking into account the then up to date experiments to find an observable variation

 

If you wish to use the speed of sound in an analogous way you need to go through the same process and declare and experimentally support your invariant.

Unfortunately experiment is not with you on this, and I do not know of any such quantity that is observer invariant in the propagation of sound.

 

So I ask you one more time.

 

What is your invariant, please supply the necessary mathematical and experimental support ?

 

7 hours ago, KJW said:

Relativity is not about electromagnetism, it is about spacetime.

So why is the paper entitled

On the electrodynamics of moving bodies ?

And why is page 1 of the paper all about Maxwell, electrodynamics and what the paper is going to do with them (which he subsequently does) ?

And why is his concluding technical statement

"These three relationships are a complete expression for the laws according to which, by the theory here advanced, the electron must move."  ?

[swansont]

10 hours ago, Killtech said:

That i do not. Of course a SI meter won't behave like that. However, i am mathematician and i will immediately look up the definition of a meter and recognize how it is constructed from the relativity principle and that the analog definition using sound signals instead of light actually ensures the contraction in the wind frame. Anyhow, coordinates don't care at all about such matters and can contract irrespective of what an actual rod may do. coordinates are instead just a question of preference and we can chose any we like. The ones using a principle of relativity for acoustic do show they achieve the correct result using an analog of relativistic calculus. 

Wait - the coordinates contract but the meter stick doesn’t? Then the coordinates are useless, since they don’t tell you where things are. The transform doesn’t actually work. It’s a mathematical exercise, meaningless for physics.

 

10 hours ago, Killtech said:

A real solid state rod is electromagnetic in origin - its size ist mostly governed by the interaction of the positively charged nucleus with its electron shells via the electromagnetic force which core characteristic is the speed of light. naturally it will therefore conform to the relativity principle of light and not acoustics.

But definitions are just that - convention we choose. and we can construct something which size is governed by acoustics instead of electromagnetism and therefore conform to the relativity principle of acoustics and contracts accordingly. Admittedly such constructs do not appear very intuitive (except maybe for a bat which perceives the world around it via acoustics) but mathematically they are a perfect analogy.

If the definition of length doesn’t tell you the length, it’s pretty useless. Different measurement methods might have varying levels of precision, but if they don’t arrive at the same result, you discard the one that’s flawed.

 

10 hours ago, Killtech said:

The issue is that we live in a world almost entirely governed by the electromagnetic force, hence we become blind to anything past that perspective. building up the math that shows how sound can be treated very much in the same way if we chose to adjust our standard definitions, is quite important to get a different perspective on what we are actually dealing with. 

But you aren’t adjusting the definition, you’re introducing a contradiction. When we redefined the second to be based on the Cs hyperfine transition, it didn’t change the length of the second. We don’t get wildly different answers for a year based on the orbit (gravity) or counting seconds.

[KJW]

7 hours ago, studiot said:

14 hours ago, KJW said:

Relativity is not about electromagnetism, it is about spacetime.

So why is the paper entitled

On the electrodynamics of moving bodies ?

And why is page 1 of the paper all about Maxwell, electrodynamics and what the paper is going to do with them (which he subsequently does) ?

And why is his concluding technical statement

"These three relationships are a complete expression for the laws according to which, by the theory here advanced, the electron must move."  ?

That was more than a hundred years ago. Relativity has moved on since Einstein. The concept of spacetime didn't even exist at the time of Einstein's paper on Special Relativity... that was Minkowski's innovation. And it was an important innovation because without it there would be no General Relativity. Relativity, both Special and especially General, is about spacetime, regardless of historical development.

[Killtech]

6 hours ago, studiot said:

I do understand what you hoping to do so, as a mathematician, you should be able to understand my difficulty with finding such an analogy.

2 hours ago, swansont said:

Wait - the coordinates contract but the meter stick doesn’t? Then the coordinates are useless, since they don’t tell you where things are. The transform doesn’t actually work. It’s a mathematical exercise, meaningless for physics.

I can understand your both hesitance, because indeed this starts off as a very physically unmotivated mathematical exercise. First and foremost, i need to establish that the math of relativity in light has can in principle be also applied to sound in an analoge way, if we were to use some unintuitive artificial measurement definitions.

The idea of this analogy is not intended to provide novel physics for sound nor make it easier to calculate. However, if we could somehow achieve it even by very artificial means, then we could potentially use sound as much easier experimentally accessible model for relativistic effects. The ultimate use case would be to do a lot of math exercise to bent sound physics artificially look like GR, just so we can study a GR solution like Alcubierre metric in the lab and get an understanding where the negative energy (in such a geometry) comes from so we get a better idea what to look for when we try to build the same but for GR.

7 hours ago, studiot said:

If you wish to use the speed of sound in an analogous way you need to go through the same process and declare and experimentally support your invariant.

3 hours ago, swansont said:

If the definition of length doesn’t tell you the length, it’s pretty useless. Different measurement methods might have varying levels of precision, but if they don’t arrive at the same result, you discard the one that’s flawed.

With the math setup, we can now start to build a rod, i.e. an experimentally viable model, that actually contracts around the speed of sound.

The first challenge is to find a construct that is analog to an atom, but instead of using the electromagnetic force to define its size, it ususes sound instead. So consider some small devices that constantly emit a loud sound. Now, we know that sound waves do interact with objects and can exchange momentum and energy with them, so in principle, if the emitters have low enough mass, their constant emission will cause them to noticeably repulse each other, and the repulsion grows stronger the closer they are.

Let's now take a large amount of these and use some external force to make them clump together in an area of space. After some time we expect an equilibrium to set in with the forces at balance and it should look like this:

i.e. we expect a lattice-like structure to form, a very artificial model of a solid state using the "force of sound" and a crude analogy for a rod build via acoustics.

Now what does happen to this grid when a wind appears? (assuming the emitters are prevented from being blown away by the wind and we use such a medium and setup where no turbulences appear). The balance of forces will change, mainly the repulsion parallel to the direction of the wind will be weakened, hence the rod will start to contract.

In fact, the contraction formula will be exactly analog to relativity - but with the speed of sound replacing light. In fact, we can now fully make use of the invariance of sound wave equation here to simplify the handling and in particular, the otherwise weird choice of coordinates now provides a description of the grid that does not change depending on the wind. 

[studiot]

3 hours ago, KJW said:

That was more than a hundred years ago. Relativity has moved on since Einstein. The concept of spacetime didn't even exist at the time of Einstein's paper on Special Relativity... that was Minkowski's innovation. And it was an important innovation because without it there would be no General Relativity. Relativity, both Special and especially General, is about spacetime, regardless of historical development.

Only one hundred years, gosh that's nothing.

Pythagoras lived a lot more than two thousand years ago yet his theorem has yet to go out of fashion.

So much so that I probably used most every day of my working life.

[swansont]

3 hours ago, Killtech said:

The idea of this analogy is not intended to provide novel physics for sound nor make it easier to calculate. However, if we could somehow achieve it even by very artificial means, then we could potentially use sound as much easier experimentally accessible model for relativistic effects

Not if the theory doesn’t match experiment. Those models go into the trash bin.

Quote

The first challenge is to find a construct that is analog to an atom, but instead of using the electromagnetic force to define its size, it ususes sound instead

The size can’t depend on the method of measurement.
 

And if the method only works for some very contrived situation, it’s not particularly useful 

44 minutes ago, studiot said:

Only one hundred years, gosh that's nothing.

Pythagoras lived a lot more than two thousand years ago yet his theorem has yet to go out of fashion.

The time isn’t the issue - it’s what we knew then vs what we knew later. I take the title of the paper to mean “here’s an interesting peculiarity about electrodynamics that turns out to have application in a more general sense”

IOW, even though it was first noticed in electrodynamics, it’s not about electrodynamics.

[Killtech]

18 hours ago, swansont said:

Not if the theory doesn’t match experiment. Those models go into the trash bin.

And it does agree with the experiment. I did the math and pointed it out to you a few times that it makes the correct predictions. Since you didn't/weren't able to pointed out any flaw in it, it stands that it is correct.

18 hours ago, swansont said:

The size can’t depend on the method of measurement.

And if the method only works for some very contrived situation, it’s not particularly useful 

In some situations a sonar puls is the best available method to measure distances, for example under water or when you are a bat. Similarly seismic waves can be used for locating interesting features within earths mantle and core. However this method does not measure a distance in meters but rather acoustic propagation time.

You do not seem to understand the difference between meter distance and an acoustic distance. They are just not the same thing! However, in mathematics the concept of a metric space / distance is significantly more general and both concepts are mathematically valid, so we can build a physical model on either of them. A conversion from one to the other is not always possible if detailed information about the medium along the path is missing.

Now note what happens to sonar ranging in when used in a strong current (i.e. by a torpedo): the signal travel time will be affected resulting in a change of measured distances. A rod (or a torpedo) which size is measured by sonar will therefore contract, because its acoustic length changes while its metric length remains the same. The relativistic theory just happens to describe this phenomenon as it has mathematically the same origin.

Therefore the experiment will indeed observe a size contraction, but size does not equal size.

[swansont]

1 minute ago, Killtech said:

And it does agree with the experiment

And yet you agree that there is no actual length contraction despite it being a part of your model. Why doesn’t that count as disagreeing with experiment?

 

[Killtech]

Just now, swansont said:

And yet you agree that there is no actual length contraction despite it being a part of your model. Why doesn’t that count as disagreeing with experiment?

Please read the whole post before responding...

[swansont]

1 minute ago, Killtech said:

Please read the whole post before responding...

You haven’t convinced me it’s not a waste of my time.

[Killtech]

On 11/18/2023 at 2:36 AM, 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.

Actually, SR in fact contradicts your assumption. Normally, there is no absolute comparison method available to really check, but there are certain exceptions when this becomes possible.

For example consider the twin paradox. Normally we are not able directly compare the age of the twins since they never meet again, hence the paradox. However, if we assume the world topology is a kind of torus then inertial frames can periodically meet allowing a direct comparison. A torus is special in that it can be a flat space, hence SR still applies.

Logic constrains that it must be uniquely determined which twin is older, yet time dilatation enforces an age difference whenever they meet. In this special scenario SR predicts that there is only one inertial frame where aging proceeds the fastest. Similar, each inertial frame can try to measure the size/circumference of the world. Lorentz contraction and logic now demands that different inertial frames must have different results and there is only one inertial frame where the world has the smallest circumference as it is not a Lorentz invariant quantity.

So no, a clocks do tick differently in inertial frames and lengths change. we are usually unable to make the proper comparison, hence chose to ignore it.

Edited November 20, 2023 by Killtech

[KJW]

27 minutes ago, Killtech said:

And it does agree with the experiment. I did the math and pointed it out to you a few times that it makes the correct predictions. Since you didn't/weren't able to pointed out any flaw in it, it stands that it is correct.

Doing the math is not the same as agreeing with experiment.

A flaw in the argument you seem to be making is that you seem to be assuming that because your modified wave equation is mathematically invariant to your modified Lorentz transformations, that it is also physically invariant as well. But if the scope of your modified wave equation is limited to frames in which the speed of the medium is zero, then it won't be physically invariant in spite of the apparent mathematical invariance.

[Killtech]

28 minutes ago, swansont said:

You haven’t convinced me it’s not a waste of my time.

That post was the argument. How am i supposed to convince you when you will simply skip any tangible argumentation with math? And the other posts you respond in a way making it obvious you haven't even read them properly. Why waste both of our time? Either you are interested in the discussion or not. It's impolite to continue a discussion disrespecting your counterpart by not bothering to listen. 

15 minutes ago, KJW said:

Doing the math is not the same as agreeing with experiment.

A flaw in the argument you seem to be making is that you seem to be assuming that because your modified wave equation is mathematically invariant to your modified Lorentz transformations, that it is also physically invariant as well. But if the scope of your modified wave equation is limited to frames in which the speed of the medium is zero, then it won't be physically invariant in spite of the apparent mathematical invariance.

You do the math to make a prediction for an experiment. Since the scenario is chosen for a well know case where we already known the outcome of the experiment, we can check if the prediction is able to reproduce the know result using a different framework.

Apparently the flaw in your argument is that you haven't read the post in question. or is it possible that latex expressions are bugged and not displayed for some members? i have a few technical issues with these forums myself.

[Bufofrog]

30 minutes ago, Killtech said:

For example consider the twin paradox. Normally we are not able directly compare the age of the twins since they never meet again, hence the paradox.

No, that's not the apparent paradox.

31 minutes ago, Killtech said:

However, if we assume the world topology is a kind of torus then inertial frames can periodically meet allowing a direct comparison.

Different inertial frames meet?  What do you mean by that?

39 minutes ago, Killtech said:

Logic constrains that it must be uniquely determined which twin is older whenever they meet. In this special scenario SR predicts that there is only one inertial frame where aging proceeds the fastest.

That's poorly worded.  Let's just say SR predicts that the traveling twin ages less.

43 minutes ago, Killtech said:

Lorentz contraction and logic now demands that different inertial frames must have different results and there is only one inertial frame where the world has the smallest circumference

What frame do you think that is?

44 minutes ago, Killtech said:

So no, a clocks do tick differently in inertial frames and lengths change. we are usually unable to make the proper comparison, hence chose to ignore it.

If you're saying at speeds much less than c, you usually ignore relativistic effects, then I agree.

[KJW]

22 minutes ago, Killtech said:

Apparently the flaw in your argument is that you haven't read the post in question. or is it possible that latex expressions are bugged and not displayed for some members? i have a few technical issues with these forums myself.

I am saying that your problem is not with the maths but with the physics.

[Killtech]

2 minutes ago, Bufofrog said:

Different inertial frames meet?  What do you mean by that?

https://arxiv.org/abs/gr-qc/0101014

3 minutes ago, KJW said:

I am saying that your problem is not with the maths but with the physics.

if the math agrees with the experiment, what more do you want?

https://www.scienceforums.net/topic/132777-analogies-for-relativistic-physics/#comment-1253247

 

[Bufofrog]

8 minutes ago, Bufofrog said:

What frame do you think that is?

So you don't have an answer to the question?

I don't want to read an entire paper and try to guess which part you think helps your position.

[Killtech]

Just now, Bufofrog said:

So you don't have an answer to the question?

I don't want to read an entire paper and try to guess which part you think helps your position.

of course i do. In this particular scenario it is possible to find a preferred frame and it is where people age the most and the circumference is minimal.

We can further analyse the frames with a Sagnac detector: send light around the circumference of the torus in both directions at the same time and measure if there is a delay between the in the arriving light signals. In this special topoligy we can use the result to measure the one way speed of light. The preferred frame is a frame where the Sagnac test yields no delay while all other will have one.

If we compare what happens in the same situation with acoustic signals in a Sagnac detector, we will find the exact same result. The preferred frame is the rest frame of the medium while inertial frames that measure delay in the arriving light effectively measure the wind speed.

[KJW]

13 minutes ago, Killtech said:

if the math agrees with the experiment, what more do you want?

https://www.scienceforums.net/topic/132777-analogies-for-relativistic-physics/#comment-1253247

But I'm saying the experiment won't agree with your maths because the acoustic wave equation is only valid for stationary media.

[Killtech]

32 minutes ago, KJW said:

But I'm saying the experiment won't agree with your maths because the acoustic wave equation is only valid for stationary media.

Of course. I haven't made any physicals assumption apart from the well established acoustic wave equation in the case of a stationary medium. Everything else in that post is merely a consequence of that. Know what? i repost it...

  

Let's start with the linear approximated acoustic wave equation \(\partial_{x}^{2}p-c_{s}^{-2}\partial_{t}^{2}p=0\) in the case of a stationary medium, where \(c_{s}=\frac{1}{3}\frac{km}{s}\) is the speed of sound in the medium we use. This is of course the version with only one spatial dimension, but for the simplicity it is enough for now. The equation should hold in the rest frame of the sonic medium.

Let's compare this model with the historic start of SR, when light in vacuum was still modelled as traveling through a luminoferious aether medium. Apart from having an equation for a longitudinal wave instead of a transversal one, the models are very similar. And indeed a wave in a medium was what inspired Lorentz approach.

However, the peeps of old found out quickly, that these type of equations are invariant under a special type of coordinate transformation, the Lorentz trafo. Coordinates are just a math tool and have not much to do with physics per se, so let's ask the question we can play an analogue trick for acoustics and in fact a trafo like \(t'=\gamma_{S}(t-vc_{s}^{-2}x)\) and \(x'=\gamma(x-vt)\) with \(\gamma_{s}^{-2}=(1-\beta_{s}^{2})\) and \(\beta_{s}=vc_{s}^{-1}\) - (note that here \(c_{s}\) is the speed of sound!!) transforms the wave equation into \(\partial_{x'}^{2}p(x',t')-c_{s}^{-2}\partial_{t'}^{2}p(x',t')=0\), i.e. sound remains invariant under these kind of coordinate changes.

In order to give a little more life to this math curiosity, let's consider @studiot simple experiment where we have one observer and a wall on the ground 1km away from each other. The observer emits a sound wave, it is reflected by the wall and an echo returns to the observer. The time is measured how long it takes to go there and back again... not the hobbit, just his sound. This setup will be discussed under two situations, in calm weather with no wind speed and in windy conditions with a speed of \(v=\frac{1}{5}\frac{km}{s}\).

For reference, let's do it classically first, that is in calm weather it takes sound \(\Delta t=c_{s}^{-1}\cdot(1km+1km)=6s\) to get back. When there is wind it's \(\Delta t=(c_{s}+v)^{-1}1km+(c_{s}-v)^{-1}1km=(\frac{15}{8}+\frac{15}{2})s=\frac{15+60}{8}=9.375s\)

Now let's do the wind case differently. Exploiting the A'rentz invariance of sound, we can start in the wind frame (rest frame of the medium) where we have the wave equation for and just transform to the ground/observer frame, right? For that we get \(\beta_{s}=vc_{s}^{-1}=\frac{3}{5}\) and \(\gamma^{-2}=(1-\frac{9}{25})=\frac{16}{\text{25}}\), thus \(\gamma_{s}=\frac{5}{4}\). Appling that ensures the equation keeps its form same as in the calm weather case. Unfortunately, there is a bit more to do, because if the distance between observer and wall in the wind frame was \(\Delta x=1km\) and moving with \(v\), then in the new coordiantes it will undo an A'rentz length contraction back into its rest frame and therefore \(\Delta x'=1\cdot\gamma_{s}=\frac{5}{4}\) and hence the signal will need a travel time of \(\Delta t'=2\Delta x'c_{s}^{-1}\). However, notice that it is given in the coordinate time \(t'\) and not \(t\) and therefore we have to transform it back, so \(\Delta t=\gamma_{s}\Delta\,t'=2\gamma_{s}^{2}c_{s}^{-1}=\frac{2\cdot25\cdot3}{16}=\frac{75}{8}=9.375s\)

Either framework produces the exact same prediction for this well know acoustic situation, with the former being known to agree with reality/experiment. 

Edited November 20, 2023 by Killtech

[Bufofrog]

14 minutes ago, Killtech said:

In this particular scenario it is possible to find a preferred frame and it is where people age the most

There is no preferred frame and what do you mean by aged the most? 

I will assume you mean ages more rapidly.  That would be your frame.  IOW in every other inertial frame individuals would age slower than you.

[Killtech]

Just now, Bufofrog said:

There is no preferred frame and what do you mean by aged the most? 

I will assume you mean ages more rapidly.  That would be your frame.  IOW in every other inertial frame individuals would age slower than you.

Normally there isn't but if you read the paper, you will find that SR in that scenario has a preferred frame. there are enough reviewed papers on this, if you don't believe me.

Yes, i meant there is one frame where one ages more rapid, more rapid then in any other inertial frame, i.e. that frame becomes uniquely special by that property and is hence considered the preferred frame.