I Energy and reference frames

[Ivan Nikiforov]

I am interested in a question related to energy for different reference frames. Let's say we have two inertial reference frames A and B. The reference frame B moves relative to the reference frame A at a high speed at which relativistic effects are manifested. In reference frame B there is a diesel electric generator that operates and outputs a power of 2200VA, voltage 220V, current 10A. The terminals of this generator are connected using wires and sliding contacts to the reference frame A, which contains a load of 2200VA, 220V, 10A.

According to the special theory of relativity, for reference frames A and B, there is a relativity of simultaneity, that is, time slows down in the moving reference frame B. In this case, reference frames A and B are connected by an electric circuit, the processes in which occur at the speed of light, that is, at the maximum possible speed, the same for all reference frames.

Is it true that the following results are obtained? An observer in the frame of reference A (load) sees in the frame of reference B a generator that runs slower (consumes less fuel), but at the same time outputs power, voltage and current, as in normal operation. The observer in reference frame B sees in his own reference frame a normally operating generator that consumes a normal amount of fuel and outputs normal power, voltage and current. After returning to the frame of reference A, this observer discovers that the generator, which worked for him for 1 day, supplied energy to the frame of reference A for 2 days. Are these correct?

 

[PeroK]

In this case, reference frames A and B are connected by an electric circuit, ...

Reference frames are not physical objects that can be connected by an electric circuit! A reference is essentially a system of coordinates that assigns time and space coordinates to every event.

 

[Ibix]

First of all, you are misusing the term "reference frame". Reference frames are just coordinate systems - they can't be connected by circuits because they're just ideas. You can connect objects that are at rest in different frames, which is what you appear to be trying to describe.

Second, the relativity of simultaneity is not the same as "time slows down". It is a related effect, but it means that clocks that show the same time according to one frame of reference may not do so according to another.

To answer your actual question, I suspect that your setup is contradictory. You have a generator that produces some amount of power as measured in its own rest trame, and a load that consumes that amount of power in its own reference frame. With special relativity in play, the two devices see each other time dilated, so don't measure the same power production/consumption as in the devices' respective rest frames. So your scenario can't work as described.

It's also not clear to me whether you're imagining the devices moving in straight lines or one orbiting the other (as in the diagram). That makes a difference to the analysis.

 

[Ivan Nikiforov]

Reference frames are not physical objects that can be connected by an electric circuit! A reference is essentially a system of coordinates that assigns time and space coordinates to every event.

I agree with you. You can change the model a bit. Let's say there is a laboratory with which the reference frame A is connected and there is an object, for example, a capsule, which moves relative to the laboratory and with which the reference frame B is connected.

 

[PeroK]

I agree with you. You can change the model a bit. Let's say there is a laboratory with which the reference frame A is connected and there is an object, for example, a capsule, which moves relative to the laboratory and with which the reference frame B is connected.

You still can't "connect" reference frames like they were physical objects.

 

[Ivan Nikiforov]

To answer your actual question, I suspect that your setup is contradictory. You have a generator that produces some amount of power as measured in its own rest trame, and a load that consumes that amount of power in its own reference frame. With special relativity in play, the two devices see each other time dilated, so don't measure the same power production/consumption as in the devices' respective rest frames. So your scenario can't work as described.

The generator is located in a moving capsule. The capsule is connected to the laboratory by means of wires and sliding contacts. The load is in the laboratory. That is, a process is obtained in which, on the one hand, there is a time dilation between the capsule and the laboratory, and on the other hand, the capsule and the laboratory are connected by an electrical circuit, in which processes occur simultaneously for the capsule and the laboratory.

 

[Ivan Nikiforov]

You still can't "connect" reference frames like they were physical objects.

Let's say the laboratory is a very long building with two rails installed on the roof. A load, such as an incandescent lamp, is connected to these rails. A capsule is flying relative to the laboratory, inside of which there is a diesel generator. Wires are stretched from the capsule to the laboratory rails, which are connected through sliding contacts. It is quite possible to create such a model in reality.

 

[Ibix]

The generator is located in a moving capsule.

But moving in a straight line, or in circles? Or something else?

That is, a process is obtained in which, on the one hand, there is a time dilation between the capsule and the laboratory,

Yes, and vice versa, although details depend on your answer to the path the capsule follows.

the capsule and the laboratory are connected by an electrical circuit, in which processes occur simultaneously for the capsule and the laboratory.

This is rather vague. What processes?

 

[Ivan Nikiforov]

But moving in a straight line, or in circles? Or something else?

Yes, and vice versa, although details depend on your answer to the path the capsule follows.

This is rather vague. What processes?

This refers to an electric current, which is known to propagate in wires at the speed of light. The speed of light is the same for all reference frames.

 

[Ibix]

This refers to an electric current, which is known to propagate in wires at the speed of light.

It doesn't - electrical signals travel at a comparable speed to light, but not at light speed.

That's not really relevant to your problem, though, which is that you have a system that produces power apparently at a different rate from which it is being consumed. Am I correct in understanding that this is your problem?

 

[Ivan Nikiforov]

It doesn't - electrical signals travel at a comparable speed to light, but not at light speed.

That's not really relevant to your problem, though, which is that you have a system that produces power apparently at a different rate from which it is being consumed. Am I correct in understanding that this is your problem?

Yes, I would like to understand the energy ratios for this case, when the generator is in a capsule and the load is in the laboratory. For the capsule, there is a time dilation, that is, the processes in the capsule and the laboratory do not occur simultaneously, while the electric current in the capsule and the laboratory flows simultaneously.

 

[Nugatory]

This refers to an electric current, which is known to propagate in wires at the speed of light.

They do not, which unnecessarily complicates the analysis.

You may find the problem easier to analyze if you put it in a different form: We have a light source with a particular fuel consumption and power output, as measured using a frame in which it is at rest. It illuminates a photocell that converts light to electrical power with 100% efficiency. The photocell and the light source are moving relative to one another.

In any case, if the photocell and light source are initially colocated and at rest relative to one another, separate by moving relative to one another, and eventually reunite: The energy received between separation and reunion will be equal to the energy emitted between separation and reunion.

 

[Ibix]

Yes, I would like to understand the energy ratios for this case, when the generator is in a capsule and the load is in the laboratory.

The first thing to think about is the changing distance between the generator and the load. That on its own means that the absorbed power is different from the emitted power. Also, you will need to factor in the different energy content of the fuel in the two frames.

 

[Ivan Nikiforov]

The first thing to think about is the changing distance between the generator and the load. That on its own means that the absorbed power is different from the emitted power. Also, you will need to factor in the different energy content of the fuel in the two frames.

The distance between the rails and the capsule does not change. How can the energy of diesel fuel change during the transition to the reference frame B? Relativistic mass increase, linear size reduction, time dilation?

 

[Ibix]

The distance between the rails and the capsule does not change

The distance between the generator and the load does, though.

How can the energy of diesel fuel change during the transition to the reference frame B?

Energy is frame dependent, even in Newtonian mechanics. It matters more often in relativity.

Relativistic mass increase

Don't use relativistic mass - outside pop sci, it's been deprecated for decades because it just causes confusion.

 

[Ivan Nikiforov]

They do not, which unnecessarily complicates the analysis.

You may find the problem easier to analyze if you put it in a different form: We have a light source with a particular fuel consumption and power output, as measured using a frame in which it is at rest. It illuminates a photocell that converts light to electrical power with 100% efficiency. The photocell and the light source are moving relative to one another.

In any case, if the photocell and light source are initially colocated and at rest relative to one another, separate by moving relative to one another, and eventually reunite: The energy received between separation and reunion will be equal to the energy emitted between separation and reunion.

Yes, your model can be used to address this issue. As for the periods between separation and reunification, I think the question is that these periods are different for different frames of reference. Of course, I need some time to think about your comment.

 

[Ivan Nikiforov]

The distance between the generator and the load does, though.

The capsule moves parallel to the rails and the distance between them does not change. The load, an incandescent lamp, is connected to the rails and such a system, in fact, is an ordinary electric line.

 

[DaveE]

This all sounds like a red shifted photon to me, but with a bunch of complex hardware. No?

 

[Ibix]

The capsule moves parallel to the rails and the distance between them does not change.

Either the load is moving relative to the generator or it isn't. In the first case the distance between the load and generator must be changing. In the other case, they're at rest in the same frame.

 

[Ibix]

This all sounds like a red shifted photon to me, but with a bunch of complex hardware. No?

You need to worry about the energy content of the fuel in the two frames too, but basically yes.

 

[Ivan Nikiforov]

This all sounds like a red shifted photon to me, but with a bunch of complex hardware. No?

Devi, forgive me, I don't quite understand what a redshifted photon means.

 

[jbriggs444]

Devi, forgive me, I don't quite understand what a redshifted photon means.

You have energy in transit in the rails. Accounting for the energy in transit may be complicated. A red shifted photon is a less complex way of accounting for energy in transit.

 

[Ivan Nikiforov]

Either the load is moving relative to the generator or it isn't. In the first case the distance between the load and generator must be changing. In the other case, they're at rest in the same frame.

The load is an incandescent lamp connected to the rails. The distance between the rails and the capsule does not change. The rails are structurally part of the load.

 

[phinds]

View attachment 356680 The load is an incandescent lamp connected to the rails. The distance between the rails and the capsule does not change. The rails are structurally part of the load.

That's not exactly irrelevant, but it's far less important than the fact that the distance between the source and the load DOES change.

 

[DaveE]

Devi, forgive me, I don't quite understand what a redshifted photon means.

https://en.wikipedia.org/wiki/Redshift

Change your generator to two groups of hydrogen atoms moving wrt each other (in any single RF). A photon is made by a pair in one group, travels and is absorbed by atoms in the other group (in any single RF).

If you observe the system in a different RF, the photon energy will appear to be different, but so will the energy of the atoms.

It's not that one lab "has" a RF and the other "has" a different one. The system is two labs with generators and loads that have some relative velocity. The system can be observed in different reference frames, with different results for the internal pieces.

 

[Ivan Nikiforov]

That's not exactly irrelevant, but it's far less important than the fact that the distance between the source and the load DOES change.

Thank you for your comment. Could you explain how this affects the amount of energy? And what are the ratios for energy in such a system?

 

[Ivan Nikiforov]

https://en.wikipedia.org/wiki/Redshift

Change your generator to two groups of hydrogen atoms moving wrt each other (in any single RF). A photon is made by a pair in one group, travels and is absorbed by atoms in the other group (in any single RF).

If you observe the system in a different RF, the photon energy will appear to be different, but so will the energy of the atoms.

It's not that one lab "has" a RF and the other "has" a different one. The system is two labs with generators and loads that have some relative velocity. The system can be observed in different reference frames, with different results for the internal pieces.

Devi, thank you for your comment. I'll need some time to think about it. Unfortunately, I'm not very good at processes involving atoms and photons. I'm just an electrical engineer.

 

[PeroK]

I'm just an electrical engineer.

So is @DaveE

 

[Ivan Nikiforov]

Thank you for your comment. Could you explain how this affects the amount of energy? And what are the ratios for energy in such a system?

Sorry, if that's how the load is presented, then the distance to it probably doesn't change.

 

[SiennaTheGr8]

You have a generator that produces some amount of power as measured in its own rest trame, and a load that consumes that amount of power in its own reference frame. With special relativity in play, the two devices see each other time dilated, so don't measure the same power production/consumption as in the devices' respective rest frames.

If I'm not mistaken, it's a little more subtle than that, since both the time and the energy transform. In general, the "coordinate power" is given by $P = \gamma^3(\vec v \cdot \vec a)m + \gamma \dot{m}$, and by time dilation and the chain rule we have $\gamma \dot{m} = dm/d\tau$ (i.e., the proper power). So in the special situation where there's power but no acceleration, the power is in fact Lorentz-invariant (the magnitude of the spacelike four-force). So, technically it might depend on the generator?

(Then there's a further subtlety, which is that for a body to lose energy without accelerating, it's got to radiate "equally" from its spatially separated extremities, and then the relativity of simultaneity complicates things.)