Electromagnetism and relativity

[F6FLT]

If velocity is distance/time and length/time dilation exists in certain parts of the universe, then photons would *appear* to exceed their maximum velocity when viewed from the right reference frame (eg: near a black hole).
...

Wrong. First, length dilation doesn't exist, only contraction. And for time, only dilation.

General relativity also implies the contraction of length by gravity, just like the contraction of lengths by speed in special relativity. And also the dilation of time.
This is due to the invariance of the space-time intervals between reference frames, i.e. the 4D distance between 2 events is the same (as we have the distance between 2 positions in a 3D space).
An interval being the same for all inertial observers, then if time is contracted for one, that is to say that one of the 4 dimensions, that of time, is dilated, then it is the dimensions of space which will compensate by being seen contracted.
Thus if an object A moves at the speed V with respect to an object B, all the observers will be able to calculate the same relative speed V that A has with respect to B, whether their frame of reference is attached to A, to B or to any other frame of reference.

A fortiori when V=c, everyone sees c without even having to use transforms to go from one frame of reference to another, since this limited speed is the basis of the construction of relativity and all its equations, whether it is special or general. All observers see light at the same speed c, this is the starting hypothesis.

[Hakasays]

Wrong. First, length dilation doesn't exist, only contraction. And for time, only dilation.

From an absolute POV, I would agree.
From a relativistic POV, someone in a relativistic situation (ie: near a black hole) would observe apparent length dilation and time contraction when attempting to measure the rest of the universe.

All observers see light at the same speed c, this is the starting hypothesis.

While it is true that an observer would not be able to directly measure velocities greater than C, an observer in a relativistic situation (near a black hole) could infer it by viewing the apparent velocity of light in 'normal space'.

[F6FLT]

@Hak

Explain how you expect to compare the views of observers who are not at the same gravitational potential?

Remember: "Special relativity requires that the frame of reference be inertial, i.e. without acceleration or gravity, or these negligible.

The laws of physics are the same only in all inertial reference frames, not in all reference frames.
General relativity allows by transformations to reduce the point of view of an observer subjected to gravitation to what an inertial observer would see (thus to pass to special relativity), the only method to be able to compare the reality he sees to the one another observer would see.

For such an observer there is no dilation of lengths or contraction of time.

[Hakasays]

@Hak

Explain how you expect to compare the views of observers who are not at the same gravitational potential?

See attached.  Observers not on the same gravitational potential can still communicate with each-other, they would just have to compensate for redshift/blueshift between them.

Remember: "Special relativity requires that the frame of reference be inertial, i.e. without acceleration or gravity, or these negligible.

I'm curious on the basis is for this.  Is it due to an inherent conflict in Lorentz transformation, or because it conflicts with GR?  Or invariant vs covariant SR?



At any rate, it still loops back to the same underlying principle, that energy depends on the reference frame.   If a reference frame is constant, energy will remain constant.

[F6FLT]

See attached.  Observers not on the same gravitational potential can still communicate with each-other, they would just have to compensate for redshift/blueshift between them.

Your scheme seems to be correct (I say "seems" because we often get trapped on obvious things, so I prefer to wait before giving an opinion) but I don't understand what you are trying to prove.
A and B are not observing the same thing since they are not at the same gravitational potential.
But each can see the conservation of energy in the closed system including their own frame of reference and the disc seen from it. And A and B can agree with each other on what the other sees.

I'm curious on the basis is for this.  Is it due to an inherent conflict in Lorentz transformation, or because it conflicts with GR?  Or invariant vs covariant SR?

It is due to experimental evidence.
Just one example, if you are standing on the edge of a large disk at rest, you feel no force.
If the disc is spinning, you are subject to centrifugal acceleration.
So obviously, any mechanical experiment done on a stationary disc or a rotating disc will not give the same results, since they will depend on the acceleration.
However, whether you are in a vehicle in space at a constant speed v, or at 1000 times that speed, the experiments you do there will give the same results, speed doesn't matter, nobody knows who is moving, it's only relative, unlike acceleration.

[Hakasays]

Your scheme seems to be correct (I say "seems" because we often get trapped on obvious things, so I prefer to wait before giving an opinion) but I don't understand what you are trying to prove.
A and B are not observing the same thing since they are not at the same gravitational potential.
But each can see the conservation of energy in the closed system including their own frame of reference and the disc seen from it. And A and B can agree with each other on what the other sees.

The attempt is to first build a solid framework to model and understand how waves and electricity behave at galactic scales, IMO using standard transmission line formulas and characteristic impedance.   If we can establish 'As above, So below', then we can use galactic thought-experiments as equivalent analogies for small-scale circuits.

The end-goal is to articulate conceptually and mathematically what happens to a given signal/photon/electron if the region of space it's traveling through changes with respect to time.   I'm not aware of any serious attempts to do this since Steinmetz.

[Allcanadian]

Hakasays

See attached.  Observers not on the same gravitational potential can still communicate with each-other, they would just have to compensate for redshift/blueshift between them.

There is a simpler more plausible explanation to explain what we measure than GR and variable time. In fact many teenagers probably understand it better than most older people including some physicists.

Imagine your playing a newer high definition video game programmed to run at over 120 frames/second. Your playing the game with a good computer running at 120 frames/sec while the other person with a bad internet connection can only get 20 frames/sec. To you the game seems to run in real time however to the other person it seems much slower so you can run circles around them and win every time. It doesn't mean time has changed or is variable it means the frame rate or rate of oscillation gives the appearance of different rates of change.

So in some sense reality could be like a video game and velocity or gravity could change the rate of oscillation in matter like a slower/faster frame rate giving the appearance that time is changing when it's not. For example, the human eye can only see between 30 and 60 frames/sec so if something moved much faster than that we could not perceive it. Like our video game something could be oscillating at a much higher rate than we can sense right in front of our nose yet be invisible to us.

I get it, variable time sets the mind racing with all kinds of wacky possibilities however at the end of the day the theory just doesn't work. It opens up a train wreck of contradictions and impossibilities no rational person should be buying into in my opinion...

AC

[F6FLT]

...It doesn't mean time has changed or is variable it means the frame rate or rate of oscillation gives the appearance of different rates of change.
...

How do you explain that the life time of radioactive particles depends on their speed according to the equations of relativity ?
How do you explain mercury perihelion ?
How do you explain the blue shift ?
How do you explain the magnetic field ?
...

A ridiculous explanation for each particular case when relativity alone answers to all of them?!

This thread is dedicated to relativity and its link to electromagnetism, not to its contestation, even less when it is by simplistic comparisons with anything, devoid of any mathematical formalism and unable to quantify anything.

[Hakasays]

I think AllCanadian's point was that time is not a dimension that can be measured directly; it always has to be measured in reference to space.
Distance/Time.

It's why Time dilation and Length contraction are equivalent, because at a fundamental level I don't believe we can tell (yet) if it is time or space that is changing (or a combination of both).

[Allcanadian]

moved my response to new thread "problems with electromagnetism and relativity".

[F6FLT]

I think AllCanadian's point was that time is not a dimension that can be measured directly; it always has to be measured in reference to space.
...

This is the problem, a mistake. On the one hand an atomic clock does not refer to space, on the other hand it is because the speed of the photon is a limit and the same in all reference frames, that we logically deduce that time and space are linked.

In the same way that the distance between 2 points (x,y) and (x'=x+Δx, y'=y+Δy) in a 2D space is d = √( Δx²+Δy² ), i.e. d²= Δx² + Δy², we note that the spacetime interval between 2 events in a 4D space (squared) is s² = Δx² + Δy² + Δz² - c²Δt² . ct is chosen instead of t in the fourth coordinate by convention, which does not change the principle because c is constant, and the sign allows to distinguish the space coordinates from the time coordinates.

To simplify we take Δl² = Δx²+Δy²+Δz², where Δl is the spatial distance separating the events, hence s² = Δl² - c²Δt².
The interval between the 2 same events seen from another frame of reference will be s'²= Δl'² - c²Δt'², and as this interval is an invariant between frames of reference, we have Δl² - c²Δt² = Δl'² - c²Δt'².
Therefore if an observer in one reference frame sees a contraction of lengths, for example l'<l then he will see t'>t so that s=s'. Space and time are completely related. This is a corollary of the Lorentz transforms. This is also why we say that it is the geometry that is modified, and not that it is a physical effect.

An object seen shorter because it is at velocity v has always the same length in its own reference frame: physically, locally, nothing has changed. On the other hand, if the object is an electron current, then the field seen by the observer will depend on the observer and therefore locally will not be the same and will not have the same effects, even if seen from the charge at constant velocity, it is still isotropic.
The relativistic effects are therefore not only changes of appearance depending on the observer, they are also real effects locally to the observer.

[Hakasays]

(edit: moved space/time sidebar to the other thread)


Found an interesting online comment regarding the 'impedance of space-time':

https://physics.stackexchange.com/questions/239132/gravitational-waves-impedance

Spacetime is a very stiff elastic medium which is capable of propagating gravitational waves. The impedance of spacetime is
Zs=c3/G=4×10³⁵kg/s.
This impedance appears in two books on gravitational waves. The most recent is titled "Advanced Gravitational Wave Detectors" edited by Blair, Howell, et al (page 52). The gravitational wave designated GW150914 had measured intensity of about 20 mw/m2 at 200 Hz. If this was a 200 Hz sound wave, it would be very loud. However, the large impedance of spacetime meant that the displacment of spacetime (ΔL/L) was only about 1 part in 10²¹.

[F6FLT]

(edit: moved space/time sidebar to the other thread)


Found an interesting online comment regarding the 'impedance of space-time':

https://physics.stackexchange.com/questions/239132/gravitational-waves-impedance

...However, the large impedance of spacetime meant that the displacment of spacetime (ΔL/L) was only about 1 part in 10²¹.

This is why it is so difficult to detect them, and why Robert Baker failed to use HFGW in communication, he was several orders of magnitude wrong on the intensity he was supposed to produce or detect.

[Hakasays]

This is why it is so difficult to detect them (gravity waves), and why Robert Baker failed to use HFGW in communication, he was several orders of magnitude wrong on the intensity he was supposed to produce or detect.

What interests me is how the 'gravity waves' might relate to electro-magnetic principles.   Either we find a simple Lorentzian mechanic that ties a gravity wave to a well-known process (like perhaps displacement currents), or otherwise we find gravitational impedance is completely distinct and more-or-less isolated from EM theory.

Both cases are interesting IMO, and both have some potentially useful ramifications (even if they only as thought-experiments with current technology).



Anyway, going back to the impedance mechanism https://www.overunityresearch.com/index.php?topic=4370.msg101723#msg101723
I think if we are to try to understand+explain signal propagation on extremely large (galactic) and small (sub-atomic) scales, I still think characteristic impedance presents the simplest and most straightforward way to do so.

[F6FLT]

 
I see a lot of reluctance to use relativity, although it is the best we have for the representation of the macroscopic universe.

So I will try to explain in simple terms why, starting from a basic observation, the constancy of the speed of light for all observers, we easily arrive at special relativity and the Lorentz transforms.

Let us take a point (x,y,z) in space. From the origin (0,0,0), let's send a light signal toward this point. The distance to travel is :
d = √(x²+y²+z²). To simplify let us write d²=x²+y²+z².
The light covers this distance d at speed c in a time t, we will have d=ct so c²t² = x²+y²+z² or x²+y²+z²-c²t² = 0.

Let us suppose that for another observer, an observer being either a human or a measuring device or an electrical charge feeling effects...  the point is seen in (x',y',z') relatively to (0,0,0).
As the speed of light does not depend on the observer, it will see: c²t'² = x'²+y'²+z'² or x'²+y'²+z'²-c²t'² = 0.

Therefore (1) x²+y²+z²-c²t² = x'²+y'²+z'²-c²t'².       s = √(x²+y²+z²-c²t²) is called a space-time interval, i.e. a "distance" between 2 points in a 4D space, and its value is the same for all observers.

In a 4D space, we note (x,y,z,-ct) the coordinate of an event, which is the spatial coordinates of a point to which we add -ct, the temporal coordinate, made homogeneous with the others since in this form, multiplied by c, it is in fact like a fourth spatial coordinate, this changing only the form because c is a constant.

An event is to 4D space what a position is to 3D space, and the space-time interval s, "distance" between 2 events, the same for everyone, is to 4D space what a distance between 2 positions is to 3D space.
If you have understood this invariance of the space-time interval in a 4D universe, you know everything about special relativity, the rest being only logical consequences..



One of these consequences are the Lorentz transforms, allowing to express in one observer, what another sees. So now that everything is clear and straightforward, let's check it.

Let us consider only the x-axis, so y=z=0, with a fixed observer at the origin (0,0), and another one moving on this axis at the speed v.
Then according to (1) x²-c²t² = x'²-c²t'² where (x,t) is seen by the fixed observer and (x',t') by the moving observer. The mobile observer moving at the speed v, the fixed observer will see it at the distance x=vt, and x'=0 because x' is the position of the mobile observer seen by itself.
It thus remains: x²-c²t² = -c²t'² => (vt)²-c²t² = -c²t'² => v²/c².t² - t² = - t'² => t² = t'²/(1-v²/c²) =>
t = t'/√(1-v²/c²)
We find the Lorentz transform for the time dilation. Indeed v/c < 1, so 1/√(1-v²/c²) > 1 so t > t' : the time which passes for the fixed observer is longer than the one to which the mobile observer is subjected.

I let you do the same calculation exercise for the contraction of lengths.


These questions concern the space and time coordinates, i.e. the geometry.
Everything we express depends on them, electric and magnetic fields, potentials, fluxes, the movement of charges... and energy!
If the reference frame is not implicit and you do not specify it, you are wrong.
If you believe that a moving electric charge will see the same fields as you, you are wrong.
If you mix quantities measured from different reference frames, you are wrong.
If you neglect relativistic effects without justifying it, you are wrong...
Relativity is just common sense drawing inevitable conclusions from the facts. It applies everywhere. We are really in a 4D space.
The 19th century ideas of absolute time are no longer valid, those who still have them must absolutely update their brains!

[Hakasays]

The 19th century ideas of absolute time are no longer valid, those who still have them must absolutely update their brains!

Good insight overall, and I think even many in the 21st century will have problems dealing with relative time as well.
Try solving Kirchhoff's laws when one half of the circuit is near a black hole

Anything that incorporates velocity is dealing with X/time, is subject to this contraction/dilation, which means a lot of 'constants' are only constant within a single reference frame.

Even things like 'C' become distorted (distance over time), to the point that it's often more useful to use the term 'light-seconds' rather than 'velocity'.  I know Steinmetz shifted that way in his lectures.

What does it mean if electric current is defined as "Coulombs-per-second" and the value of 'second' is changing?

[F6FLT]

Good insight overall, and I think even many in the 21st century will have problems dealing with relative time as well.
Try solving Kirchhoff's laws when one half of the circuit is near a black hole

Misinterpretation.
I talked about SR, not GR. In this framework there is no problem with time.

Anything that incorporates velocity is dealing with X/time, is subject to this contraction/dilation, which means a lot of 'constants' are only constant within a single reference frame.

Which ones?
( Dimensionless constants are not concerned, and others may have dimensions whose relativistic effects cancel out. ).

What does it mean if electric current is defined as "Coulombs-per-second" and the value of 'second' is changing?

It sounds like you are starting to realize the problem. The current measured in one reference frame will not be the same as measured from another. And if you move at the speed of the charges in vacuum, the current is zero.
But the effects are the same, the facts remain, if there is a force on a charge, it will be seen from all reference frames.

Example (Wikipedia):
"An observer measures a charge at rest in frame F. The observer will detect a static electric field. As the charge is stationary in this frame, there is no electric current, so the observer does not observe any magnetic field.
The other observer in frame F′ moves at velocity v relative to F and the charge. This observer sees a different electric field because the charge moves at velocity -v in their rest frame. The motion of the charge corresponds to an electric current, and thus the observer in frame F′ also sees a magnetic field."

Those who believe that the magnetic field is something existing in space independently of the observer, i.e. almost the entire "FE community", are completely wrong.

[Hakasays]

Misinterpretation.
I talked about SR, not GR. In this framework there is no problem with time.

Which ones?
( Dimensionless constants are not concerned, and others may have dimensions whose relativistic effects cancel out. ).

It sounds like you are starting to realize the problem. The current measured in one reference frame will not be the same as measured from another. And if you move at the speed of the charges in vacuum, the current is zero.
But the effects are the same, the facts remain, if there is a force on a charge, it will be seen from all reference frames.

Example (Wikipedia):
"An observer measures a charge at rest in frame F. The observer will detect a static electric field. As the charge is stationary in this frame, there is no electric current, so the observer does not observe any magnetic field.
The other observer in frame F′ moves at velocity v relative to F and the charge. This observer sees a different electric field because the charge moves at velocity -v in their rest frame. The motion of the charge corresponds to an electric current, and thus the observer in frame F′ also sees a magnetic field."

Those who believe that the magnetic field is something existing in space independently of the observer, i.e. almost the entire "FE community", are completely wrong.

The problem I'm paraphrasing is that if we are to dispose of the idea of 'absolute time' as you say, then we must also dispose/modify all of the formulas that depend on it.

Those tweaks probably open up a lot of possibilites that may not be immediately evident.

[F6FLT]

The problem I'm paraphrasing is that if we are to dispose of the idea of 'absolute time' as you say, then we must also dispose/modify all of the formulas that depend on it.

Those tweaks probably open up a lot of possibilites that may not be immediately evident.

It is not that they should be modified, it is that their domain of validity should be restricted: they should not be believed to apply everywhere. This is what has been done with Newtonian mechanics, it is still valid but not for everything. Beyond that, we must take relativity.

(sorry, I had to restore your post having clicked "modify" instead of "quote", hence the "Last edit" mention above)

[Hakasays]

It is not that they should be modified, it is that their domain of validity should be restricted: they should not be believed to apply everywhere. This is what has been done with Newtonian mechanics, it is still valid but not for everything. Beyond that, we must take relativity.

I agree, but also this 'domain of validity' has a big degree of subjectivity to it.  One could argue that a single molecule could even apply (due to the relativistic effect of the nucleus to an electron at various distance)

[F6FLT]

I agree, but also this 'domain of validity' has a big degree of subjectivity to it. 
...

It's just the opposite. The domain of validity is limited when the measurements do not correspond anymore to the theoretical predictions (Mercury's perihelion, life span of radioactive particles varying with the speed... the measurements do not correspond anymore with the Newtonian mechanics).
Based on the difference between theory and measurements, the domain of validity is therefore objective.

[Hakasays]

Ah I see, you mean 'domain' in the scientific sense, rather than the metrical sense

[F6FLT]

h I see, you mean 'domain' in the scientific sense, rather than the metrical sense

Yes, for example one cannot apply Newtonian mechanics in the field of speeds close to light.
The high speeds are out of the domain (field) of validity of this mechanics.

(I made a mistake again when answering. It only happens with your posts. Would you have cast a bad spell on me? )

[F6FLT]

In the thread "New generator from a spatial gradient of the vector potential and current", where we have seen that a charge at constant speed cannot be influenced by a gradient of the vector potential, the idea came to study the possibility of new effects when charges are accelerated in a vector potential.

Following a discussion elsewhere with a special relativity enthusiast, and verification of little known but astonishing academic theses, the relativity of accelerations between charges has fantastic consequences.

It is well known that an accelerating charge radiates. This is the principle of a radio antenna.
What is less known is that a static charge radiates when seen by an accelerating charge, a question of relativity. The laws of physics are indeed the same in all reference frames, even accelerated.
So if we make a charge oscillate, it could detect static fields with the same efficiency as a static charge in an antenna is sensitive to the field coming from a distant emission.

I don't know the consequences for energy, I'll see that in a second time, but for radio it seems to open remarkable perspectives, and as I know that there are several radio amateurs here, it will surely interest them.

I have indeed made the connection with W Beaty's "energy sucking antennas" ("http://www.amasci.com/tesla/tesceive.html" ). Not everything in his text seems correct, but the § "Transmit in order to receive" is clear to me. The industry is now doing research in this direction, to make small smartphone antennas work efficiently, by re-injecting energy into them through negative impedance, a technique known as "non foster matching antenna". The method has been known since the so-called "reaction" tube receivers, except that from this 1910s technique, to today's non-foster matching, via Beaty or this NASA patent that I find very enlightening ( https://patents.google.com/patent/US5296866A/en ), nobody understands or deals with the common physics issue behind it that relativity unifies.

I am working on the subject. As a proof of principle I am considering using the injection of a signal with a different frequency than the one received by an antenna. With a negative impedance, the signal is obviously re-injected at the same frequency, which poses problems of stability. However, the explanation by relativity allows to consider that the effect can also be obtained with different frequencies, which will be much easier to handle thanks to the filtering and tuned circuits. The method should lead to the emergence of signals with sum or difference frequencies of the received and emitted frequencies, and the local acceleration should considerably boost the received signal, we are talking in tens of dB and with SNR improvement.

Not being a math whiz, I have initiated myself to Wolfram's "Mathematica" to confirm it. I am currently trying to find by Lorentz transforms of accelerated reference frame (yes, it is possible) what an accelerated charge oscillating at a frequency F2 sees from another accelerated distant charge, oscillating at F1 and which produces a 4-vector potential A at the position of the first one. It is very complicated, long and tedious, just to know what one has to provide to Mathematica so that it makes the calculation. If my hypothesis is confirmed, I will set up the experiment. After confirmation (or not), it will be time to see the possibility of an interest in extracting energy, in particular through scalar or magnetic potential couplings between oscillating circuits.

[Cortazar]

Hi F6FLT
  Is it possible to share what relativity forums are those your are talking about ?
Regards
Cortazar