Electrodynamics (electricity and magnetism) is governed by Maxwell’s equations and the Lorentz force law, but that left it a little broken. It would take Albert Einstein inventing special relativity to fix it. If magnets are based on motion and motion is relative, how does that work?

Maxwell’s Equations Visualized:

The Ultimate Guide to Relativity:

Galilean Relativity:

Older Version of this Video:


Veritasium on Relativistic Electrodynamics:

Crash Course on Magnetism:



Advanced Theoretical Physics (Paperback):

Advanced Theoretical Physics (eBook):



Warden of the Asylum:

Asylum Counselors:
Matthew O’Connor

Asylum Orderlies:
Daniel Bahr, William Morton, LT MarshMan

Einsteinium Crazies:
Albert B. Cannon, Wacky, Ken Davis, Ilya Yashin, Eoin O’Sullivan

Plutonium Crazies:
JKLMN Anderson, Al Davis, Kevin MacLean

Platinum Crazies:
Stephen Blinn, Fletch, Felipe Cruz, Eugene Boone, Vittorio Monaco, Mikayla Eckel Cifrese



Einstein 1905:

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38 thoughts on “How Special Relativity Fixed Electromagnetism

  1. Clarification: We know from observation that the wire is neutral in the lab frame. You can't argue against that. That's just reality. Yes, the electrons are moving in the Lab Frame and would be length contracted. They're already contracted in the picture. They're contracted in such a way to make sure the wire stays neutral. That's why they expand when we switch to the Clone Frame and give the wire a charge density in that frame. The wire can only be (uniformly) neutral in one frame and we observe that to be the Lab Frame.

  2. Often when I type something, at the time I feel that I am pretty clear, until I look at it days later. Oh my. My previous inquiry is all backwards and messed up.
    I think I want to say this:
    If I have two alike charges and they are moving parallel and opposite each other, based on their magnetic field orientation only, wouldn't they be drawn to each other? I am under the impression that when two charges magnetic field combine, they are attracted to each other. Is this correct?

    However : ( If two alike charges are going parallel and in the same direction with each other they will repel naturally both from the stand point of magnetic field opposing each other and from Einstein's relativity there is no magnetic field and also charges being alike and stationery relative to each other, there will be repulsion).
    I really appreciate everything you do.

  3. But how about if we simply forget the electrons in the wire completely. The positive charge moving in the wire creates magnetic field and lets consider them moving out of the screen(x) if we look at it from the right hand side cross section and your frog if you will creates magnetic field counterclock wise moving towards you into the screen(o). Would this cause them to repel or attract? If it cause the positive charges to attract, would you then say that attraction due to magnetic field is not as strong as the repulsion due to electric field?
    If that be the case, in a coil of wire that we see magnetic field being created, there is also tremendous repulsion going on I suppose as well in each ring… I don't know if I am making any sense.

  4. THANK YOU VERY MUCH for the 1millionth time. i am doing electrical machines and drives and man does this help with the interaction of stators and rotors

  5. Dang good one.
    But I did rewind three times to make sure I caught everything.
    You are a breath of fresh air.
    I am getting old. I wish you talked a little slower.
    But your style is second to none.
    You are an asset to millions of people.

  6. 9:06 Of course we want more videos visualizing equations, equations are 'minimum in the range and number of signs, maximum in the energy of the signs which is thus achieved'. But don't be to haste to make video about Einstein's field equations, take as much preparation as you need for it. If you succeed to present them even close as you did with Maxwell's equations, you'll deserve to be called the king of the science videos on youtube. Actually, the king of the entire youtube, as far as I'm concerned

  7. So, if length contraction is real, and not merely some kind of mathematical or optical illusion, then, from our frame of reference, we should expect to observe massive objects that move fast enough with respect to us get length contracted below their Swartzchild radius and poof we should get a black hole for that moving object. The problem is that we do not see these black holes forming, and if they did, how would we undo them? Once the mass of an object is length contracted below its Swartzchild radius and becomes a black hole, it is not like you can simply have the mass of that object magically escape the black hole that forms around it.

  8. Moving electrons frame of reference – electrons not moving, positive charges move and contract and provide excess of positive charge. So far so good.
    Wire frame of reference – electrons moving and contracting thus providing excess of negative charge. Seems like a contradiction to me. And it is not a matter of a wire – it can be moving charges in vacuum with no wire whatsoever.
    Anyone care to explain ? How is the squirrel feeling the same effect in both frames of reference ?

  9. how to say this…
    Is special relativity that was born because of the Maxwell eqs. Legend has it, that a young Albert Einstein envisioned a though exp. in which he was traveling at the speed of light parallel to an EM wave. According to Galilean transformation he was supposed to see the EM static. i.e DE/Dt was supposed to be zero in this ref. frame. But if that would be the case the EM wave will disappeared according with Maxwell eqs. So, Einstein using intuition rather anything else decided that the fault was in classical mechanic and not in the electromagnetic theory. And the rest is physics history.

  10. What it showed at 6:07 got Thumbs Up from me. I've seen things like this before, but the other version didn't sufficiently explain the charge density increase shown at 6:07.

  11. I don't think we would have to bring in Einstein's relativity if we just define v as the velocity of the squirrel relative to the moving charge. In that case, in both frames of reference the moving charge is always the positive part of the wire. I bet the math would agree as well.

  12. My physics professor did a similar example regarding the velocity required for two protons to travel in parallel lines balancing their electric repulsion with their magnetic force. Turns out that velocity is c so in other words Fe>FB. Einstein’s paper was supposedly titled by addressing this problem in which a moving reference frame along side the protons at the same velocity would only have a force of electric repulsion. The ambiguity between what actually happens required special relativity. Fascinating stuff. I have yet to enter that section in my physics course yet but a part of me finds this more fascinating then building stuff as a civil engineer. Perhaps ill look into the lucrative careers of physics majors because i believe i have more of a passion for this kinda stuff. Science is rad

  13. Electromagnetism itself was fine. It was classical mechanics that needed to be "fixed" (I think "expanded" is the better term here).

  14. Einstein saves the day again. [thug life intensifies]
    Can you do more videos on tensors? I'm really interested. It could be on your "what the HECK is…" playlist.

    P.S : that headbanging moment got me😂😂😂 another metalhead like me :))

  15. Thank you for another AMAZING video! Really helps me to visualize the behavior of electric and magnetic fields! Well done!

  16. Sorry for these dumb questions:

    How is it that a non linear function like length contraction creates the linear Lorentz one?

    According to the explanation of the video there isnt attraction among the electrons of a cathodic rays beam, right?

    Thanks! The video is great

  17. There are many videos on yt trying to exlain this, and I think this is the first one that succeed. Even your first attempt, including follow-up video, wasn't successful enough.

  18. But reference frame of squirrel, electrons are stationary. But current is passing and electrons are moving, how is squirrel being repelled?

  19. I see a lot of people are confused by "why is the distance between the electrons contracted in a specific way to keep neutrality", I can explain. Look at 2 people on the z axis at locations 0 and d, they are static. Now they start running with velocity v in the z direction. The static (lab) observer records now their locations as 0+vt and d+vt, so the distance between them in the lab frame is still d. Certainly a co-runner will measure a bigger distance between them: γd, and relative to this, d is shorter. But the important point to emphasise is that in the lab frame the distance between them is d if they stand still or run. In addition, for the current in the wire, it is better to describe the wire as fed be a current source and not a voltage source, i.e. charges are not added, but only put in motion.

  20. It still amazes me how, once in a blue moon, a genius like Einstein is born. Someone who understands things that nobody else does, and changes our understanding of the universe. His theories of general and special relativity are still mind boggling to 99% of us. Yet they've been proven multiple times. In ways he could never do when he was alive.

  21. hey nick, it was like seeing the electromagnetism as a intelligent force. eventhough i cant figure out the math of it still it makes a great realisation of the properties discovered. also the historical perspective is awesome.thanks

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