How To Consistently Explain Electromagnetism With Relativity

[PAllen]

I've put off the electromagnetism thing for a bit until I understand why the electron spacing increases in their own frame. Also because I spent a lot of time with those graphics only to find they were wrong.

The thing about the rocks falling was supposed to be analogous to the electrons accelerating, but I think I messed that up. So I will rephrase it. If A and B are both stationary and both experience the same gravitational force (for example, a couple rocks sitting on the ground), will they disagree on what events are simultaneous?

No, because they are not accelerating relative to their starting position.

What is true is that if clocks spaced in the x direction start accelerating in the +x direction, then if they if they are to agree that their mutual distance doesn’t change, then the one further in the +x direction has to have less proper acceleration (and, in the original rest frame, they will get ever closer together). If, instead, they have the same proper acceleration, then they will both agree the distance between them is growing ( and in the original rest frame their distance will be constant).

Proper acceleration is what is measured by an accelerometer.

 

[Geocentricist]

No, because they are not accelerating relative to their starting position.

Okay, if two rocks floating in zero gravity are suddenly immersed in a gravitational field at the same time will they disagree that they were both immersed in the field at the same time?

What is true is that if clocks spaced in the x direction start accelerating in the +x direction, then if they if they are to agree that their mutual distance doesn’t change, then the one further in the +x direction has to have less proper acceleration (and, in the original rest frame, they will get ever slower together). If, instead, they have the same proper acceleration, then they will both agree the distance between them is growing ( and in the original rest frame their distance will be constant)

This does not help me understand. Sorry.

 

[Ibix]

Okay, if two rocks floating in zero gravity are suddenly immersed in a gravitational field at the same time will they disagree that they were both immersed in the field at the same time?

The answer to this depends on what magic you used to create a gravitational field out of nowhere, because that is not a situation you can describe in relativity. Also, you are struggling with special relativity. I strongly advise you to leave gravity out of your thinking because you need general relativity to describe that.

This does not help me understand. Sorry.

It's fairly straightforward. We've been discussing that the distance between two rockets grows in their own frames if they both undergo the same constant proper acceleration. So if they want the distance not to grow they have to undergo different proper accelerations.

 

[Geocentricist]

The answer to this depends on what magic you used to create a gravitational field out of nowhere, because that is not a situation you can describe in relativity.

The gravity field is uniform and just appears, poof! Like that.

Also, you are struggling with special relativity. I strongly advise you to leave gravity out of your thinking because you need general relativity to describe that.

A survey of opinion at CERN, according to Wikipedia, showed most theoretical physicists misunderstood Bell's paradox also. So I strongly advise you not to be condescending. I can use gravity since it's equivalent to acceleration.

It's fairly straightforward. We've been discussing that the distance between two rockets grows in their own frames if they both undergo the same constant proper acceleration. So if they want the distance not to grow they have to undergo different proper accelerations.

Yes, I understand the distance between A and B grows in either of their frames when they undergo identical acceleration. I get that, it's been repeated over and over in this thread. What I don't get is why, since if they were moving at an identical, constant velocity, it would not. How does acceleration make it any different?

 

[A.T.]

Yes, I understand the distance between A and B grows in either of their frames when they undergo identical acceleration. I get that, it's been repeated over and over in this thread. What I don't get is why, since if they were moving at an identical, constant velocity, it would not. How does acceleration make it any different?

This has also been explained over and over in this thread. Read up on accelerating frames of reference, and the effects occurring in those frames.

 

[Ibix]

The gravity field is uniform and just appears, poof! Like that.

Which, as I already said, is not a situation you can describe in relativity. It is inconsistent with Einstein's field equations. So this scenario is asking for the logical consequences of contradicting yourself. There is no answer.

I can use gravity since it's equivalent to acceleration.

This is a misstatement of the equivalence principle, which says that hovering in a gravitational field is indistinguishable (locally) from proper acceleration in flat spacetime. Your rocks would not be hovering, so would not be undergoing proper acceleration - so this scenario is not equivalent to accelerating rockets.

Yes, I understand the distance between A and B grows in either of their frames when they undergo identical acceleration. I get that, it's been repeated over and over in this thread. What I don't get is why, since if they were moving at an identical, constant velocity, it would not. How does acceleration make it any different?

I explained in #89, #96, #107, #113 and #115. Others have also answered. What did you not understand about those explanations? Please be specific. Simply repeating that you don't follow the explanations given has got you nowhere in the last 35 posts.

 

[jbriggs444]

IIf A and B are both stationary and both experience the same gravitational force (for example, a couple rocks sitting on the ground), will they disagree on what events are simultaneous?

Do they have a non-zero separation in the direction of the gravitational force? Is, for instance, one at the first floor and the other on the second floor? If so, the reference from @A.T. to gravitational time dilation is appropriate.

Note that gravitational time dilation is not a function of local gravitational acceleration. It is a function of potential.

 

[Dale]

I've put off the electromagnetism thing for a bit until I understand why the electron spacing increases in their own frame.

That has very little to do with rocks falling in gravity.

Also because I spent a lot of time with those graphics only to find they were wrong

That is because this approach is fundamentally wrong.

You are trying to draw the graphics in order to avoid the math. The correct approach is to draw graphics based on the math in order to understand the math. You have to start with the math before the graphics because the graphics are right or wrong based on if they accurately represent the math.

The graphics can help you understand the math, they cannot help you avoid the math.

 

[Geocentricist]

Which, as I already said, is not a situation you can describe in relativity. It is inconsistent with Einstein's field equations. So this scenario is asking for the logical consequences of contradicting yourself. There is no answer.

If I kick a soccer ball, does not a gravitational field suddenly (poof!) appear in the soccer ball frame?

This is a misstatement of the equivalence principle, which says that hovering in a gravitational field is indistinguishable (locally) from proper acceleration in flat spacetime. Your rocks would not be hovering, so would not be undergoing proper acceleration - so this scenario is not equivalent to accelerating rockets.

The rocks are hovering in the sense that the ground is preventing them from falling. It seems to me the situations are equivalent. They are experiencing 1G which could be described validly as either a gravitational field or an acceleration, depending on whether we use Earth's frame or the rocks' frame, no?

I explained in #89, #96, #107, #113 and #115. Others have also answered. What did you not understand about those explanations? Please be specific. Simply repeating that you don't follow the explanations given has got you nowhere in the last 35 posts.

I've been told in A's frame, B does not accelerate at the same time as A because their definition of simultaneity does not agree. But why does it not agree?

That is because this approach is fundamentally wrong.

There's nothing fundamentally wrong about my approach, since it can arrive at the correct answer as well as any mathematical formula. These are just two ways of describing the same idea. You can argue my idea is inefficient but to say it's wrong is incorrect. I enjoy doing it this way and I will be more confident that I understand it this way. As soon as I understand why electron spacing in their own frame increases, I will get back to my graphics. Or maybe before, if I give up on understanding the electron spacing thing.

 

[jbriggs444]

If I kick a soccer ball, does not a gravitational field suddenly (poof!) appear in the soccer ball frame?

First of all, the soccer ball is not a rigid object. So there is some ambiguity about when it starts moving and how fast it is moving.

Second, even if one picks a point on the ball and uses that point to define a reference frame, that reference frame is, per your scenario, accelerating. The motion of a single point can define an inertial reference frame. For an accelerating frame, picking a single point is not enough to define the frame.

[Which is to say that speaking of "the soccer ball frame" is premature -- no such frame is uniquely defined]

Third, if you have complete your definition of a particular accelerating frame, you will have had to come up with a simultaneity convention. How were you planning to make the simultaneity convention in the accelerating frame match the simultaneity convention in the inertial frame so that it would still correct to say that "poof", everything starts accelerating at once? Having adopted such a convention, what makes you sure that every point on a [Born-rigid] soccer ball will be accelerating at the same rate?

Fourth, all you have done is changed coordinates. A gravitational field in general relativity is more than just a change in coordinates. It is an invariant that is captured by a metric. You have not changed the metric -- you've just re-labelled the points on a [sub-]manifold.

 

[Ibix]

If I kick a soccer ball, does not a gravitational field suddenly (poof!) appear in the soccer ball frame?

No. If the presence or absence of a gravitational field were frame dependent I could fly by using a frame where there was no gravity. In the non-inertial frame of the ball inertial forces do appear, just as they do in the non-inertial frame of someone standing on the surface of the Earth. The use of a non-inertial frame is the similarity, not gravity.

The rocks are hovering in the sense that the ground is preventing them from falling. It seems to me the situations are equivalent. They are experiencing 1G which could be described validly as either a gravitational field or an acceleration, depending on whether we use Earth's frame or the rocks' frame, no?

You are modifying your scenario - there was no mention of a ground in your #122. In the case that there is a ground under the rocks then they are undergoing proper acceleration, but all the gravitational field is doing is making the situation more complex and removing the possibility of a global inertial frame to work in (@jbriggs444 has made this all the points so far in my post in significantly more detail).

Even in your revised form, the two rocks is a different scenario to the two rockets. They are accelerating in a Born rigid manner, which the rockets are not doing.

I've been told in A's frame, B does not accelerate at the same time as A because their definition of simultaneity does not agree. But why does it not agree?

It's a direct consequence of the two postulates of relativity. The usual demonstration is Einstein's train thought experiment, as pervect mentioned in #90.

 

[Geocentricist]

[4 reasons why kicking a soccer ball is too ambiguous]

A point-particle soccer ball (electron) is kicked (accelerated) on a soccer field (particle accelerator). Does not a gravitational field appear in the electron frame?

No. If the presence or absence of a gravitational field were frame dependent I could fly by using a frame where there was no gravity.

You could not. You'd be accelerating downwards.

You are modifying your scenario - there was no mention of a ground in your #122. In the case that there is a ground under the rocks then they are undergoing proper acceleration, but all the gravitational field is doing is making the situation more complex and removing the possibility of a global inertial frame to work in

So it's impossible to answer my question, do the two rocks agree on what events are simultaneous?

Even in your revised form, the two rocks is a different scenario to the two rockets. They are accelerating in a Born rigid manner, which the rockets are not doing.
It's a direct consequence of the two postulates of relativity. The usual demonstration is Einstein's train thought experiment, as pervect mentioned in #90.

Consider the two rocks as two electrons if it helps you answer my question.

I do not see how the increased electron-frame electron spacing follows from the two postulates of Special Relativity. Which postulate would be contradicted if the electron-frame electron spacing did not increase during the electrons' acceleration?

 

[Ibix]

I do not see how the increased electron-frame electron spacing follows from the two postulates of Special Relativity. Which postulate would be contradicted if the electron-frame electron spacing did not increase during the electrons' acceleration?

Do you understand Einstein's train thought experiment?

 

[jbriggs444]

A point-particle soccer ball (electron) is kicked (accelerated) on a soccer field (particle accelerator). Does not a gravitational field appear in the electron frame?

Again, what electron frame? A single accelerating point does not a frame define. Further, slapping the label of "gravity" on a coordinate chart does not change anything. It's still the same underlying physical reality, no matter what coordinates you use to refer to the events. All you are doing is changing coordinates.

 

[Geocentricist]

Do you understand Einstein's train thought experiment?

It seems to demonstrate the finite speed of light. What does it have to do with relativity?

A single accelerating point does not a frame define.

What information is lacking? The rate of acceleration? Direction?

 

[jbriggs444]

What information is lacking? The rate of acceleration? Direction?

Foliation (aka simultaneity convention).

For an inertial frame, there is one natural simultaneity convention. For an accelerating frame, things are not that simple.

If you do not understand Einstein's train experiment (as you do not) then you have not understood special relativity.

 

[Geocentricist]

If you do not understand Einstein's train experiment (as you do not) then you have not understood special relativity.

Enlighten me.

 

[Ibix]

It seems to demonstrate the finite speed of light.

No. It uses the finite speed of light to demonstrate that "two things happen at the same time" is not a complete sentence. You need to add "...as measured in frame S", and other frames will not agree. Please go and study the train thought experiment until you understand - or at least, accept - that. It's critical to understanding what's going on with the accelerating rockets.

What does it have to do with relativity?

Pretty much everything.

 

[jbriggs444]

Enlighten me.

Show us that you are willing to make the effort to understand it.

Edit: Look at https://en.wikipedia.org/wiki/Relativity_of_simultaneity (for instance), attempt to understand it and then ask more focused questions. "Enlighten me" does not measure up.

 

[Geocentricist]

I actually just solved my problem to my own satisfaction. Here is my reasoning. The two spaceships accelerate at the same time in S, so their separation (between midpoint of each spaceship) remains constant, while the length of each spaceship (and the string) contracts. This breaks the string.

In order to break the string in the spaceship frame where the spaceships are motionless and thus not contracted themselves, the only way is to increase the separation of the spaceships.

So now I understand the separation in the rest frame must increase in order to agree with phenomena in the S frame.

Finally I can get back to electromagnetism. How much will the separation between electrons increase if they accelerate to 0.87 c? Will it double? I want to correct my graphics.

 

[Ibix]

That explanation works as long as you are happy to ignore the acceleration phase and just consider "before and after". There are a number of complications during the acceleration.

Finally I can get back to electromagnetism. How much will the separation between electrons increase if they accelerate to 0.87 c? Will it double?

Yes. Note that this is a highly unrealistic electron drift velocity. Typical speeds are around 10^-5m/s, yielding a separation change of around one part in 10²⁶.

 

[Dale]

There's nothing fundamentally wrong about my approach, since it can arrive at the correct answer as well as any mathematical formula.

I disagree. As was pointed out earlier, you needed other people (using the mathematical formulas) to tell you the strength of each interaction. Your approach can help you understand the math, but it simply cannot substitute for the math.

You can argue my idea is inefficient but to say it's wrong is incorrect

It is not only inefficient, it is also insufficient.

But I am not the one who said your graphs were wrong, that was you. I am just telling you why: they are wrong because they are the outcome of a fundamentally flawed approach.

Another fundamental flaw of this approach is that you are attempting to “explain electromagnetism with relativity” when you don’t know relativity. How does that make sense as an approach? In order to avoid learning electromagnetism directly you are now trying to learn general relativity, but general relativity is a substantially more difficult subject.

If an advanced second grader asked you to explain multiplication tables using logarithms when they don’t know logarithms, would you not recommend a different approach to multiplication?

How much will the separation between electrons increase if they accelerate to 0.87 c? Will it double? I want to correct my graphics.

Case in point...

 

[Geocentricist]

That explanation works as long as you are happy to ignore the acceleration phase and just consider "before and after".

Awesome! That's fine since I'm not illustrating the acceleration.

As was pointed out earlier, you needed other people (using the mathematical formulas) to tell you the strength of each interaction. Your approach can help you understand the math, but it simply cannot substitute for the math.

You're right.

 

[Geocentricist]

How's this? Is this correct? Obviously didn't put as much effort as I did in the other ones.

 

[A.T.]

Is this correct?

DrGreg's diagram is better because it shows at least two electrons in each case, so you see their spacing:

For two identical currents duplicate the lower part of the loop.

For two opposite currents look at the lower and the upper part of the loop.

 

[Geocentricist]

DrGreg's diagram is not suited for my purposes since there are too many particles and also, not a simple ratio of electrons to protons in each frame. Is mine correct?

 

[A.T.]

DrGreg's diagram is not suited for my purposes since there are too many particles ...

Just enough to have at least two electrons in each case, so you see their spacing. The perfect amount.

...and also, not a simple ratio of electrons to protons in each frame.

What is a simple ratio? What non simple ratios do you see in DrGregs diagram?

Is mine correct?

It doesn't show enough particles to tell.

 

[Geocentricist]

Just enough to have at least two electrons in each case, so you see their spacing. The perfect amount.What is a simple ratio? What non simple ratios do you see in DrGregs diagram?

In one frame the ratio is 0.25 which is harder to work with than mine which is 0.5. Not a big difference but I want to keep things simple as possible!

It doesn't show enough particles to tell.

Sure it does, the ratio is all that matters and you must assume the segment I've shown is representative of the ratio of the entire wire

 

[A.T.]

In one frame the ratio is 0.25 which is harder to work with than mine which is 0.5.

The ratios are 1:1, 1:2 and 1:4. Doesn't get simpler than that, if you want to show all cases (3 ratios).

 

[Geocentricist]

The ratios are 1:1, 1:2 and 1:4. Doesn't get simpler than that, if you want to show all cases (3 ratios).

Ah you're right.

I have a question about the magnetic force. If the strength of the electric repulsion between two electrons co-moving at 87% the speed of light is 1 then is the strength of the magnetic attraction between them 0.5? And if the electrons are moving in opposite directions is the magnetic force repulsive or is it simply halved in strength and still attractive?