# Special Relativity as a source of Power?

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1. Oct 7, 2014

### candybish

Hey guys,

I've recently learned that magnetism is an electric field viewed from a different frame of reference and that the mathematics of electrodynamics describes this. However something raised my eyebrow which I wasn't quite clear on.

If energy is put into a net flow of electrons, the energy is conserved within the electrons until it dissipates into neighboring particles via friction. However what is putting the energy into the Length Contraction creating the charge imbalances for the resulting magnetic field? To me it appears that the phenomenon of relativity is inputting energy into the length contraction causing the charge imbalance.

This shows that whenever there are net flow of electrons there is energy coming from a different source. Does this mean there may be a way to harness energy from relativity?

Thanks.

2. Oct 7, 2014

### A.T.

No, energy is conserved in Special Relativity, just like in Classical Mechanics.

3. Oct 7, 2014

### candybish

I know it must be conserved. I guess I should have clarified. Correct me if I'm wrong but Energy from Length Contraction is converted to the rate of change in charge, causing the change in magnetic field to occur. However, where is the energy from length contraction coming from? It was not from the movement of the electrons. From what I understand it came from the phenomenon of relativity. Do we know where that energy from relativity came from? Regardless if we know or not, doesn't it still mean relativity is a source of energy?

4. Oct 7, 2014

### Drakkith

Staff Emeritus
The energy required to accelerate the electrons and keep the current flowing comes from the circuit's power source.

5. Oct 7, 2014

### Drakkith

Staff Emeritus
I don't recommend looking at it as "putting energy into length contraction". Length contraction is a frame dependent phenomenon and it's difficult to determine the energy of an object by looking at length contraction alone. Instead, understand that energy is required to accelerate objects and in the case of an electric circuit energy is required to keep the current flowing. The acceleration of an object and the flow of electric current is not frame dependent, meaning all observers will agree that an acceleration is taking place or that current is flowing in a circuit.

In any case, the circuit gets energy from its power source.

6. Oct 7, 2014

### pervect

Staff Emeritus
I think the idea that "energy is being put into length contraction" in the first place is most likely based on a false idea of how the electric and magnetic fields transform relativisticaly.

Because the electric field in the direction of motion is unchanged, the force between charges does not increase even though the charges are closer together.

See http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity for a non-tensor explanation of how the E and B fields transform relativisticaly.

This is making me wonder about something else actually, but at the moment I have to run, alas, no time to get into it.

7. Oct 7, 2014

### candybish

I agree with that 100%. The electrons are flowing thanks to the power source of the circuit. What confuses me is the Length Contraction is what is creating the magnetic field. There is no energy in a magnetic field. But there IS energy in a change in magnetic field. So as soon as a change in magnetic field occurs from the Length Contraction then that HAS to mean the change in magnetic field must have obtained its energy from somewhere. Therefore from what I understand, there has to be energy within Length Contraction.

Although the Length does not contraction does not occur to you while you are in the frame but that is irrelevant because you are contracting from a another frame of reference and vice versa. It's still causing a physical effect being the change in magnetic field.

8. Oct 7, 2014

### candybish

I'm in a class right now but I will look into this. Thanks.

9. Oct 7, 2014

### jartsa

Let's consider accelerating two electrons using an electron gun. Acceleration takes place along the line connecting the electrons.

If electrons come out of the gun closer to each other than originally, then we might say that some "extra" energy was used, because electrons close to each other have more energy than electrons far away from each other.

10. Oct 7, 2014

### Drakkith

Staff Emeritus
I've given some considerable thought to this thread, and in the end I decided that whether you say the energy is stored in the length contraction or whether you say it's stored in the magnetic field makes little difference for most cases since length contraction occurs at the same time as the magnetic field. The one area I'm unsure about is in the case of EM waves. EM waves involve changing magnetic and electric fields, yet there are no length contracted particles around to generate them.

11. Oct 7, 2014

### Staff: Mentor

No, I don't think you understand what that means. Electrons are light and in an electric circuit they move very slowly. It takes virtually no energy to move them -- unless something is actively opposing that motion. And that thing that opposes the motion of the electrons is:
Right: that energy didn't just *poof* into existence separate from the motion of the electrons, it was put into the circuit by the generator or battery that made the electrons move. That's how conservation of energy applies.

12. Oct 13, 2014

### candybish

Okay so I looked into the wikipedia page and also some linked pages that it had to better understand everything. I've also watched this video which explains the some of the math which I found quite helpful.

However I don't understand how it is a false idea that a magnetic field is actually an electric field viewed from a different frame of reference. Unless I misinterpreted what you wrote.

Also none of the equations I saw related to the energy required to contract the length viewed from a frame. It is as if they never consider it, unless I just haven't recognized or encountered the formula or if I'm still seeing this incorrectly.

Thank you for the analogy Jartsa. However I'm unclear of how I can relate it to my question. Could you maybe clarify on the "extra" energy used and how it relates to relativity? Thanks.

I can't agree Drakkith because it seems to me that it makes all the the difference. I shoot a bullet from a gun, the energy from the gun transferred to the kinetic energy of the bullet. The bullet slows down by transferring it's energy to the air (assuming it doesn't hit anything). Same as electrons flowing in a wire, the energy given to the electrons stays within the electrons to cause it to flow until it dissipates into surrounding atoms which we can call friction.

Now consider Lenz's Law. If I give energy to electrons in a wire to flow in a certain direction relativity "occurs" at the same time. However I did not put energy into relativity, I put energy into the electrons just as I did with the bullet from the gun. Relativity as far as I know just happens, as a phenomenon. As soon as the electrons move, simultaneously length contraction occurs causing the charge imbalance. The change in field will affect electrons in a neighboring wire. HOWEVER, this energy is NOT from the electrons because the electrons are analogous to the bullet where it is not dissipating its energy through the magnetic field, it is dissipating its energy through opposing charges within the wire its flowing through. This energy comes from relativity causing the length contraction to create the charge imbalance.

The reason why we don't measure "extra energy" is thanks to Lenz's law. As soon as the electrons in a neighboring wire experience the induction, they will send out their own magnetic field that opposes the electrons I originally gave energy to. And once again this opposing magnetic field is also caused by relativity.

So in essence there would be 2 sources of energy being seen as 1. What if we find a way to separate the two sources and use length contraction in some sort of clever way to produce power. Lastly, I am not saying energy is being created by relativity, because I don't know where the energy is coming from, it may very well be conserved in a manner that is not clearly shown until relativity is understood.

13. Oct 13, 2014

### candybish

Sorry I realized this part sounds confusing and I wasn't sure how to edit my post. The last sentence in the quote above "This energy comes from..." I was referring to the energy causing the charge imbalance which creates the opposing magnetic field.

14. Oct 13, 2014

### jartsa

If the distance between the electrons, shot with the electron gun, happens to change the same way as in Lorentz-contraction, then one might say that some "extra" energy was put into the electron pair, because electrons were put closer to each other.

The "extra" energy came from the electron gun.

If an observer, observing a pair of electrons, changes his frame, he observes that the distance between the electrons Lorentz-contracts. The observer might say that some energy was used to put the electrons closer to each other.

In this case I will not speculate were the "extra" energy came from.

15. Oct 13, 2014

### Drakkith

Staff Emeritus
The distance between the electrons shot out of an electron gun does not change, it is their electric fields that are length contracted. No "extra" energy needed.

16. Oct 13, 2014

### Staff: Mentor

There is no "extra energy" so it doesn't need to come from anywhere. Energy is frame-dependent so the difference between the total energy as measured in one inertial frame and as measured in another has no physical significance.

This is also why candybish won't be able to extract energy from relativistic effects. Accelerate something so that it contracts and the total energy available in candybish's frame won't change; it's just that some of the energy used to accelerate the object will appear as kinetic energy or energy in a magnetic field in cb's frame.

(and before you succumb to the temptation to analyze the problem from the non-inertial frame of the accelerating electrons... Energy is not necessarily conserved in non-inertial frames).

17. Oct 13, 2014

### jartsa

Ok. If after the shooting of the electron pair with the electron gun you change to the rest frame of the electron pair, you will see an electron pair that has less energy than the original electron pair.

Some energy was "saved", because electrons were put further apart.

Actually this is better: An observer that is observing from the final rest frame of the electron pair observes that electrons are being put further apart by the electron gun. So electron gun kind of sucks energy from the electron pair, in that frame.

18. Oct 13, 2014

### Drakkith

Staff Emeritus
Rereading the thread, I see that it was given that the electrons were closer together than before, so yes, of course they will have a different amount of energy than before.

19. Oct 13, 2014

### Drakkith

Staff Emeritus
Candybish, I'm sorry but I really don't follow your logic in this thread. You're mixing several different concepts from both electromagnetism and special relativity without properly explaining/exploring each one.

20. Oct 13, 2014

### Staff: Mentor

What makes you think that any energy is "required to contract the length"? It is not considered because there is no such thing.

There is indeed energy in a magnetic field, and an electric field in one frame yields a magnetic field in another frame, and there is length contraction between frames. But none of that implies that energy is required for length contraction.

Energy is conserved. It is not invariant. Do you understand the distinction?

21. Oct 13, 2014

### candybish

Sure the total energy of frame A will not change but what I am trying to point out is the energy from the magnetic field produced is not from the same source as the energy of the battery pushing the electrons in frame A.

My analogy to two coils inducing each other is as follows:
Person A pushes person B with a certain force. The energy is dissipated by causing person B to fall back and then dissipate it into the ground. Person B then pushes person A back with the same amount of force.

This can look like Person A's energy was redirected back. But in reality it wasn't. Person B used his own energy to push back Person A making it seem like the energy was transferred back. However the net energy is still the same.

The push is analogous to the magnetic field. The chemical energy producing each person's push would be the energy causing the charge imbalance that creates the magnetic field.

22. Oct 13, 2014

### candybish

The way I view it is electrons flowing in a wire will witness length contraction occurring with the protons causing a "change" in magnetic field (assuming acceleration of flow). From the electron's frame, it is seeing the protons contracting together. Charge density is physically changing which is what causes the charge imbalance. Last time I checked, it takes energy to push like charges together. There is nothing that describes where the energy is coming from in order to push the charges together to increase its density. Of course I know in the frame of the protons their length did not change but that is irrelevant because it still affects the electrons in the electrons' frame.

I don't know how else to explain it. I will do more research into Lorentz transformations because I guess you guys are saying I'm missing something, maybe I'll understand it more through that.

23. Oct 14, 2014

### Drakkith

Staff Emeritus
This is simply not correct. The battery provides all of the energy available for the circuit, including that which is stored and transferred by the magnetic field.

Your analogy is wrong. In a typical transformer setup, only one side of the circuit is connected to the power source. The secondary side is connected to the load and is powered entirely by induction from the primary side. The secondary coil has zero available energy until the primary powers it.

You may also want to consider the fact that from a frame at rest with the circuit, current flow does not equal charge imbalance. This of course is obvious since only moving charged particles experience a force from the magnetic field. Stationary ones do not.

24. Oct 14, 2014

### Staff: Mentor

This is not true. The charge density is different in the lab frame and the inertial frame where the electrons are at rest, but the charge density is constant in each. The charge density is not physically changing in either frame.

It takes work (f.d) to push charges together. It does not take work for them to stay together if they start out close. In the moving frame they start out close and no work is done for length contraction.

Now, if you are talking about non inertial frames then all bets are off since energy is not even conserved in general non inertial frames and not all non inertial frames have length contraction etc.

25. Oct 14, 2014