I Energy and reference frames

[Ivan Nikiforov]

Excuse me if I misunderstand something, but in this book, on page 295, it literally says the following: "Since energy manifests itself only when it changes, we can put it without prejudice to the physical meaning.:

Thus, we come to the conclusion that energy, measured by the amount of "work that a body is capable of doing," and mass, determined by momentum at a given speed, are interrelated concepts. If there is one, then there is another. Neither mass nor energy are invariant; each quantity, according to (16.42), depends on the observer's frame of reference."

 

[Ivan Nikiforov]

View attachment 356684
Excuse me if I misunderstand something, but in this book, on page 295, it literally says the following: "Since energy manifests itself only when it changes, we can put it without prejudice to the physical meaning.:
View attachment 356683
Thus, we come to the conclusion that energy, measured by the amount of "work that a body is capable of doing," and mass, determined by momentum at a given speed, are interrelated concepts. If there is one, then there is another. Neither mass nor energy are invariant; each quantity, according to (16.42), depends on the observer's frame of reference."

It seems to me that the following conclusion can be drawn from this statement. If the energy depends on the reference frame, then the energy in the capsule (reference frame B) differs from what energy an observer in the laboratory identifies in it (reference frame A). If two reference frames are connected by a process occurring at the speed of light, which is equal for all reference frames, then the energy of the reference frame B can be obtained in the reference frame A...

 

[DaveE]

then the energy in the capsule (reference frame B) differs from what energy an observer in the laboratory identifies in it (reference frame A).

yes

the energy of the reference frame B can be obtained in the reference frame A...

The energy observed in reference frame B can be obtained by observations made in reference frame A if you know the relationships between the reference frames.

Also, the total energy observed in any reference frame is invariant (the same)*.

*In a non-expanding universe.

 

[Ivan Nikiforov]

yes


The energy observed in reference frame B can be obtained by observations made in reference frame A if you know the relationships between the reference frames.

Also, the total energy observed in any reference frame is invariant (the same)*.

*In a non-expanding universe.

That's the whole question. Is it true that being in the frame of reference A, we observe one amount of energy in the frame of reference B, and on the sliding contacts coming from the system B, we measure another amount of energy?

 

[DaveE]

That's the whole question. Is it true that being in the frame of reference A, we observe one amount of energy in the frame of reference B, and on the sliding contacts coming from the system B, we measure another amount of energy?

Maybe. It is only the total energy of a closed system that is invariant.

The energy observed in reference frame B can be obtained by observations made in reference frame A if you know the relationships between the reference frames.

Also, the total energy observed in any reference frame is invariant (the same)*.

*In a non-expanding universe.

Sorry, I don't know how to say this more simply.

 

[Ivan Nikiforov]

Maybe. It is only the total energy of a closed system that is invariant.


Sorry, I don't know how to say this more simply.

Devi, thank you. I know what you're talking about.

 

[jbriggs444]

Maybe. It is only the total energy of a closed system that is invariant.

The total energy of a closed system is conserved but not invariant.

That is to say that the energy is the same, no matter when you look.
But the energy can change depending on the frame of reference you adopt.

 

[berkeman]

Devi, thank you.

LOL, it's funny how the translation software translates the @DaveE username.

 

[Ivan Nikiforov]

LOL, it's funny how the translation software translates the @DaveE username.

I'm so sorry. Maybe I should have copied and pasted @DaveE. I'm sorry if my text is incorrect due to the translator.

 

[DaveE]

The total energy of a closed system is conserved but not invariant.

That is to say that the energy is the same, no matter when you look.
But the energy can change depending on the frame of reference you adopt.

Yes thanks. I'm being sloppy again.
Real Physicists know the difference better than "just" Engineers. I still expecting to get kicked out of PF any day now for have forgotten all of my physics classes, of which there weren't that many anyway .

 

[Ivan Nikiforov]

The total energy of a closed system is conserved but not invariant.

That is to say that the energy is the same, no matter when you look.
But the energy can change depending on the frame of reference you adopt.

Thank you. I would like to understand the relations for energy depending on the frame of reference. By the way, a separate question is whether the system in question is closed, due to the fact that time is heterogeneous?

 

[DaveE]

LOL, it's funny how the translation software translates the @DaveE username.

I'm so sorry. Maybe I should have copied and pasted @DaveE. I'm sorry if my text is incorrect due to the translator.

No, it's fine. I kind of like it better in a way. Dave, Mike, Chris, Mary, Scott, Lisa... they're all pretty boring names to native English speakers.

 

[Dale]

Oh wow, this is a long thread. I guess I will make it a bit longer.

1) energy is conserved in every frame.
2) different frames will disagree about the total amount of energy.
3) circuit theory is non-relativistic, so you have to use Maxwell’s equations instead.
4) this problem is not well enough specified to solve it using Maxwell’s equations, but without substantial simplification or numerical methods it would be difficult to solve.
5) nevertheless, Poynting’s theorem holds in all frames so regardless of the details we know that point 1) holds

 

[Ivan Nikiforov]

Oh wow, this is a long thread. I guess I will make it a bit longer.

1) energy is conserved in every frame.
2) different frames will disagree about the total amount of energy.
3) circuit theory is non-relativistic, so you have to use Maxwell’s equations instead.
4) this problem is not well enough specified to solve it using Maxwell’s equations, but without substantial simplification or numerical methods it would be difficult to solve.
5) nevertheless, Poynting’s theorem holds in all frames so regardless of the details we know that point 1) holds

Dale, thank you for your comment and for joining the discussion. Your opinion is very important. Please tell me if the following statement is true: Is it true that, being in the frame of reference A, we observe one amount of energy in the frame of reference B, and on the sliding contacts coming from the system B, we measure a different amount of energy? How exactly do we understand that the total sum of energies will be different in different reference frames? Is there perhaps an example?

 

[PeroK]

Dale, thank you for your comment and for joining the discussion. Your opinion is very important. Please tell me if the following statement is true: Is it true that, being in the frame of reference A, we observe one amount of energy in the frame of reference B, and on the sliding contacts coming from the system B, we measure a different amount of energy? How exactly do we understand that the total sum of energies will be different in different reference frames? Is there perhaps an example?

Imagine a car of mass $m$ accelerating from rest to speed $v$. In the original rest frame it gains kinetic energy of $\frac 1 2 mv^2$. In the final rest frame, it started with a speed of $v$ and decelerated to rest. In that frame it lost kinetic energy of $\frac 1 2 mv^2$.

And, in a frame moving at $v/2$, the car started at speed $v/2$ and ended at speed $v/2$, so it neither gained nor lost kinetic energy.

As you can see from this example, your difficulties understanding energy and reference frames are fundamental and are not directly related to special relativity.

 

[Ivan Nikiforov]

Imagine a car of mass $m$ accelerating from rest to speed $v$. In the original rest frame it gains kinetic energy of $\frac 1 2 mv^2$. In the final rest frame, it started with a speed of $v$ and decelerated to rest. In that frame it lost kinetic energy of $\frac 1 2 mv^2$.

And, in a frame moving at $v/2$, the car started at speed $v/2$ and ended at speed $v/2$, so it neither gained nor lost kinetic energy.

As you can see from this example, your difficulties understanding energy and reference frames are fundamental and are not directly related to special relativity.

Thanks for the comment. I'll think about it.

 

[pervect]

I have not worked this particular problem, but I do have a problem that I worked that illustrates some of the point (already made) that circuit theory is not relativistic.

The thread is called "boosting a current loop".

https://www.physicsforums.com/threa...rrent-density-and-charge-distribution.631446/

It illustrates how Kirchoff's current law does not work without modifications. And it serves as an inspiration for the suggestion I will give as to how to formulate your problem in a relativistic manner.

I have not worked your particular problem - it's an interesting one, but I'm much slower (and more error prone) to work out problems nowadays so it's unlikely I will even make the attempt. But I can suggest how I might approach it in a relativistic manner.

There are two quantities of interest here, current and voltage, of which you need the relativistic versions. As other posters have mentioned, circuit theory is not relativistic so you'll have to put that aside for a bit.

The relativistic version of current is the "four-current density", see https://en.wikipedia.org/wiki/Four-current. This describes how charge and current densities transform relativistically. You will also need to include the efffects of relativistic length contraction in your problem formulation.

The relativistic model for voltage would be the "Electromagnetic 4-potential", https://en.wikipedia.org/wiki/Electromagnetic_four-potential. This will transform between the frames via the Lorentz transform. Taking the appropriate gradient as described in the will give you the E and B field in a given frame. There are some other approaches you could use, but I would think that the 4-current and the 4-potential would be enough, conceptually. I could be wrong.

Because this isn't circuit theory, you will need to keep tract of the magnetic fields as well as the electric fields.

I think that what I'd suggest as the first shot would be to imagine a transmission line with a sliding "resistor". This solves the problem of dealing with the magnetic fields. Ohm's law is not relativistic, so avoid it. One might consider finding a relativistic version of Ohm's law, but I am not going to pursue that route.

The goal is to write the 4-current vector through the sliding "resistor", in the lab frame, which I would define to be of such a magnitude that it did not cause any reflected waves in the transmission line. I am assuming here some knowledge of transmission line theory and how they need to be terminated to avoid reflections and standing waves. Describing this in detail would be too much of a digression from my thought processes and the actual problem.

If we know the voltage in the lab frame, and the impedance of the transmission line, we know the current in the lab frame, from which we can compute the appropriate relativistic generalizations.

If all this is worked out, one should then be able to confirm that the problem setup satisfies Maxwell's equations.

Given this lab-frame solution, it should then be reasonably simple to convert to the moving frame, and to keep tract of all the power in each frame and confirm that it is conserved. I'd expect the power to be frame dependent, but I have not done any of the actual work, I've just thought a bit about how to set it up.

 

[Dale]

Is it true that, being in the frame of reference A, we observe one amount of energy in the frame of reference B, and on the sliding contacts coming from the system B, we measure a different amount of energy?

The situation you described is too difficult for me to analyze and answer this explicitly. However, it certainly would be possible for other more simplified scenarios.

How exactly do we understand that the total sum of energies will be different in different reference frames? Is there perhaps an example?

Yes. The best examples are very simple ones, like an infinite sheet of charge or current oriented perpendicular to the direction of travel. These geometries change the problem into a 1+1D problem.

 

[Ivan Nikiforov]

I have not worked this particular problem, but I do have a problem that I worked that illustrates some of the point (already made) that circuit theory is not relativistic.

The thread is called "boosting a current loop".

https://www.physicsforums.com/threa...rrent-density-and-charge-distribution.631446/

It illustrates how Kirchoff's current law does not work without modifications. And it serves as an inspiration for the suggestion I will give as to how to formulate your problem in a relativistic manner.

I have not worked your particular problem - it's an interesting one, but I'm much slower (and more error prone) to work out problems nowadays so it's unlikely I will even make the attempt. But I can suggest how I might approach it in a relativistic manner.

There are two quantities of interest here, current and voltage, of which you need the relativistic versions. As other posters have mentioned, circuit theory is not relativistic so you'll have to put that aside for a bit.

The relativistic version of current is the "four-current density", see https://en.wikipedia.org/wiki/Four-current. This describes how charge and current densities transform relativistically. You will also need to include the efffects of relativistic length contraction in your problem formulation.

The relativistic model for voltage would be the "Electromagnetic 4-potential", https://en.wikipedia.org/wiki/Electromagnetic_four-potential. This will transform between the frames via the Lorentz transform. Taking the appropriate gradient as described in the will give you the E and B field in a given frame. There are some other approaches you could use, but I would think that the 4-current and the 4-potential would be enough, conceptually. I could be wrong.

Because this isn't circuit theory, you will need to keep tract of the magnetic fields as well as the electric fields.

I think that what I'd suggest as the first shot would be to imagine a transmission line with a sliding "resistor". This solves the problem of dealing with the magnetic fields. Ohm's law is not relativistic, so avoid it. One might consider finding a relativistic version of Ohm's law, but I am not going to pursue that route.

The goal is to write the 4-current vector through the sliding "resistor", in the lab frame, which I would define to be of such a magnitude that it did not cause any reflected waves in the transmission line. I am assuming here some knowledge of transmission line theory and how they need to be terminated to avoid reflections and standing waves. Describing this in detail would be too much of a digression from my thought processes and the actual problem.

If we know the voltage in the lab frame, and the impedance of the transmission line, we know the current in the lab frame, from which we can compute the appropriate relativistic generalizations.

If all this is worked out, one should then be able to confirm that the problem setup satisfies Maxwell's equations.

Given this lab-frame solution, it should then be reasonably simple to convert to the moving frame, and to keep tract of all the power in each frame and confirm that it is conserved. I'd expect the power to be frame dependent, but I have not done any of the actual work, I've just thought a bit about how to set it up.

Thanks for the comment. Your thoughts are very interesting. I will carefully consider your arguments.

 

[pervect]

There's a discussion of the parallel plate transmission line I found online at https://ws.engr.illinois.edu/sitemanager/getfile.asp?id=153. But I'm too rusty to run the numbers, the source was helpful though.

What I am thinking, is that the voltage seen in the frame of the "moving resistor" is lower than the voltage in the lab frame. *ONE* of the effects of using the full relativistic solution is that the "moving resistor" along the transmission line is cutting through magnetic field lines generated by the currents in the transmission line which generates an induced voltage, similar to how a wire moving through a magnetic field generates a voltage in a general. Because the wire is moving very quickly, this effect is rather large.

But it's really more complicated than that, and a proper analysis (which I haven't done) is needed to be sure. It would, for example, be wrong to say that you add this induced voltage to the lab voltage. The relativistic transformation laws don't work like that.

An alternative to using the electromagnetic 4-potential I suggested earlier is to consider how the electromagnetic fields transform as per

https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity#E_and_B_fields

(If you don't trust Wiki on this, Griffith's book on E&M should cover this also). But I think the 4-potential approach would be less error prone for me personally, no cross products to get the sign wrong on :). Also, it's much more like the circuit theory concept of voltage.

I'm too rusty to work this out properly, but those are my thoughts on how to formulate the problem in a way it can be solved.

 

[pervect]

I was thinking about this more, and there is unfortunately the idea of matching the resistor to the impedance of the line is going to fail badly. The idea works when the resistor is at the end of the transmission line, terminating it - but if it's sliding along the line, the resistor will be in parallel with the rest of the line, creating a mismatch. I am thinking now that what is needed in an attempt to save the approach is to make the resistance "high". Then we ignore the disturbing effect the resistor has on the line. Unfortunately, that loses the idea of the generator power all flowing through the line to the resistor :(.

We can also just try dealing with the reflections in the line, I suppose. But I think these problems illustrate how the idea of a "wire" is idealized and also non-relativistic - it conducts energy with infinite speed and you don't have to worry about effects like capacitance and inductance. The real word equivalent is going to exhibit much more complex behaviors, consistent with the idea that energy propagates through fields that propagate (in a vacuum) at the speed of light.

 

[jartsa]

Oh wow, this is a long thread. I guess I will make it a bit longer.

1) energy is conserved in every frame.
2) different frames will disagree about the total amount of energy.
3) circuit theory is non-relativistic, so you have to use Maxwell’s equations instead.
4) this problem is not well enough specified to solve it using Maxwell’s equations, but without substantial simplification or numerical methods it would be difficult to solve.
5) nevertheless, Poynting’s theorem holds in all frames so regardless of the details we know that point 1) holds

So why not use conservation of energy in lab frame?

Electric energy of a moving charged capacitor goes from one place to other place, the amount of energy does not change.

Can we make a simplifying decision that the moving thing is not a rocket, meaning that its velocity does not change?

 

[Ivan Nikiforov]

I was thinking about this more, and there is unfortunately the idea of matching the resistor to the impedance of the line is going to fail badly. The idea works when the resistor is at the end of the transmission line, terminating it - but if it's sliding along the line, the resistor will be in parallel with the rest of the line, creating a mismatch. I am thinking now that what is needed in an attempt to save the approach is to make the resistance "high". Then we ignore the disturbing effect the resistor has on the line. Unfortunately, that loses the idea of the generator power all flowing through the line to the resistor :(.

We can also just try dealing with the reflections in the line, I suppose. But I think these problems illustrate how the idea of a "wire" is idealized and also non-relativistic - it conducts energy with infinite speed and you don't have to worry about effects like capacitance and inductance. The real word equivalent is going to exhibit much more complex behaviors, consistent with the idea that energy propagates through fields that propagate (in a vacuum) at the speed of light.

Thanks for the comment. It will take me quite a lot of time to comprehend the information and materials on the links that you provided. I will definitely do it. But for now, I can say the following. It seems to me that in the model I specified, there is no need to move the load. The load is attached to long rails and is a single unit. Electric current in rails travels at the speed of light in metal. I also don't quite understand the presence of wave processes and related impedances. It is assumed that a direct current flows in the electrical circuit, and it begins to flow even before the capsule starts moving.

 

[Ivan Nikiforov]

Can we make a simplifying decision that the moving thing is not a rocket, meaning that its velocity does not change?

It seems to me that it is impossible to simplify the system. The essence of the question is to understand the energy relations for the specified system - a system in which there are two objects for which there is a relativity of simultaneity, but which are connected by a process occurring at the speed of light, the same for these two objects. In comment #12, an alternative system option was proposed - a current source to which a light source (essentially a flashlight) is connected, moves relative to a long photocell and illuminates it. I would like to understand whether the following statement is true: The flashlight with which the reference frame B is connected moves relative to the photocell with which the reference frame A is connected. The flashlight may not even know about the presence of such movement, it just shines into space and illuminates the photocell. Let's say time in frame B flows 2 times slower than in frame A. That is, in the frame of reference B, the flashlight shines for 1 hour, but at the same time it illuminates the photocell in the frame of reference A for 2 hours, since time passes faster in the frame of reference A. Is this true?

 

[Dale]

So why not use conservation of energy in lab frame?

You certainly can do that. That is point 1).

Can we make a simplifying decision that the moving thing is not a rocket, meaning that its velocity does not change?

Sure. The more simplifying assumptions you make the more easily it can be analyzed. As long as you don’t accidentally make any contradictory assumptions.

 

[Ivan Nikiforov]

This idea can be considered using the example of a human. A person, as an energy system, consumes food energy. Let's say a person eats N kilograms of food per year. One person with a supply of food N goes on a space trip on a rocket, in the frame of reference of which time slows down by 2 times compared to Earth. The second person with a supply of food N remains on the Ground. Let's say that after 1/2 year (in the rocket's frame of reference), the first person returns back. He has N/2 food reserves left. The second person has completely run out of food. That is, we have a difference in the amount of food and in the amount of energy. In the model under consideration, it is assumed to use the same process, only for the technical system. The energy difference is supposed to be obtained not after the movement is completed, but continuously, by transferring energy at the speed of light. Can it work?

 

[Dale]

I also don't quite understand the presence of wave processes and related impedances. It is assumed that a direct current flows in the electrical circuit

You are looking at two relativistically moving frames. What is normal DC energy transport in one frame becomes near-field waves in another.

The simplest example of this is a single inertial charge. In the frame where it is stationary there is an E field with a certain energy density and the Poynting vector is everywhere 0. In a frame where it is moving there is an E and a B field, both of which are changing over time. The Poynting vector is non-zero and energy moves forward, but also in and out.

In comment #12, an alternative system option was proposed - a current source to which a light source (essentially a flashlight) is connected

That is a simpler system. Especially with the additional assumption that 100% of the energy emitted by the flashlight is absorbed by the photocell, and both the light and the cell are 100% efficient with their fuel cells. It will also be easier if the pulse of light is shorter than the distance between them divided by c. Continuous is also possible, but requires a bit more effort.

Are they moving towards or away from each other?

This idea can be considered using the example of a human.

Biology is very complicated. This is the opposite of what you should be doing here

 

[jartsa]

It seems to me that it is impossible to simplify the system. The essence of the question is to understand the energy relations for the specified system - a system in which there are two objects for which there is a relativity of simultaneity, but which are connected by a process occurring at the speed of light, the same for these two objects. In comment #12, an alternative system option was proposed - a current source to which a light source (essentially a flashlight) is connected, moves relative to a long photocell and illuminates it. I would like to understand whether the following statement is true: The flashlight with which the reference frame B is connected moves relative to the photocell with which the reference frame A is connected. The flashlight may not even know about the presence of such movement, it just shines into space and illuminates the photocell. Let's say time in frame B flows 2 times slower than in frame A. That is, in the frame of reference B, the flashlight shines for 1 hour, but at the same time it illuminates the photocell in the frame of reference A for 2 hours, since time passes faster in the frame of reference A. Is this true?

Two identical flashlights glued together, so that they shine to opposite directions, is a such thing that its velocity does not change in any frame. So let's use that thing.

Let's say the thing is at rest. And we let it shine until batteries are empty. And then we change to a frame where the thing's total energy is twice of its rest energy. Now what is the energy of the light in this frame? Can I have an answer from the experts, please.

Anyway, the amount of light energy produced by the flashlights, in the frame where the flashlights were moving, is that whatever the answer is.



(I think that the answer is that the energy is twice the "normal" energy, but what do I know ; ))

 

[Ivan Nikiforov]

You are looking at two relativistically moving frames. What is normal DC energy transport in one frame becomes near-field waves in another.

The simplest example of this is a single inertial charge. In the frame where it is stationary there is an E field with a certain energy density and the Poynting vector is everywhere 0. In a frame where it is moving there is an E and a B field, both of which are changing over time. The Poynting vector is non-zero and energy moves forward, but also in and out.

Thanks for the comment. I know that a moving electric charge, in addition to an electric field, has a magnetic field. I didn't know about near-field waves. I'll try to read what it is. At the same time, for example, when describing the operation of the Faraday disk, there is no indication of the presence of near-field waves, although it is well known that the relativistic effect of the relativity of simultaneity is at the heart of the operation of the Faraday disk. Can the original model match the Faraday disk? The magnetic field of the disk is a circuit with a current in which, when moving relative to the brushes, an electric moment appears. Or can the Faraday disk not be considered as a similar system?

 

[Ivan Nikiforov]

Are they moving towards or away from each other?

It is assumed that the distance between the reference frames does not change. In a simple version, the capsule moves parallel to the long rails (the flashlight moves parallel to the long photocell). In a practical sense, it is most likely possible to move along a circle, as in a Faraday disk. In the literature, this issue is considered separately - to what extent the requirement applies to inertial reference frames in terms of uniform rectilinear motion, to motion along a circle in a Faraday disk. It is argued that for the Faraday disk, the process of electric polarization, as well as the process of electric current flowing in a closed circuit, does not contradict the provisions of the special theory of relativity.
By the way, as far as I know, relativistic time dilation has been practically proven and occurs in artificial satellites that orbit in a circular trajectory.
Therefore, if there is a relativity of simultaneity for a rotating object, in theory, there are no obstacles in transferring energy from such an object.