How Special Relativity Makes Magnets Work

Magnetism seems like a pretty magical phenomenon. Rocks that attract or repel each other at a distance - that's really cool - and electric current in a wire interacts in the same way. What's even more amazing is how it works. We normally think of special relativity as having little bearing on our lives because everything happens at such low speeds that relativistic effects are negligible. But when you consider the large number of charges in a wire and the strength of the electric interaction, you can see that electromagnets function thanks to the special relativistic effect of length contraction. In a frame of reference moving with the charges, there is an electric field that creates a force on the charges. But in the lab frame, there is no electric field so it must be a magnetic field creating the force. Hence we see that a magnetic field is what an electric field becomes when an electrically charged object starts moving.

Huge thank you to Ralph at the School of Physics, University of Sydney for helping us out with all this magnetic gear. Thanks also to geology for loaning the rocks.

This video was filmed in the studio at the University of New South Wales - thanks to all the staff there for their time and support.

[Verrisin]

"You are looking slim."
"Only in your frame of reference."

- how is this not a famous quote? XD

[RationalSphere]

On my fourth viewing of this video, I realized I was looking at... a cat-ion.

[scudder]

Just saw this 7-year-old video. "A magnetic field is just an electric field viewed from another reference frame." Extraordinary!

[chessislive]

Dude wtf are you serious, I have been asking this question like millions of times too professors and teachers but noone wanted to give me an answer. This channel is sacred for me from now on

[destrometro]

Wife (While jogging): Honey, am I looking slim?
husband: Not even in my frame of reference?

[Fists]

What Schroedinger was trying to say with his cat analogy: Quantum superposition makes no sense.
What Derek learned from Shroedinger's analogy: All analogies are better with cats

[alfredowaltergutierrezmald]

"A Magnetic field is just an Electric Field viewed from a different frame of reference." Thank you for that mind-blowing definition. I always viewed Electromagnetism from a classical point of view and just started studying Special Relativity, but thanks to this video I see another connection between both theories. Thanks a lot man, you literally made my day!

[slesinski]

I’ve been teaching high school physics for 32 years, I and I’m still learning such cool things thanks to amazing videos like this one.

[triforcefiction]

Our Prof linked this video as part of his lecture. So I have to ask: Is this part of the exam?

[juliabaima]

I just want to say a BIG THANK YOU for your videos having captions in so many different languages. I started watching your videos and it was a struggle to try to understand English and Physics at the same time. When I saw that you have captions in my language I screamed of happiness! (This sounds weird but I have just realized the eager I have to learn Science) thank you, thank you! It's truly a beautiful thing that your channel is spreading knowledge to so many people all over the world. That's huge.

[abcz]

Trying to be flirty with nerds:
"You're looking slim"
"only in your frame of reference"

[LGlink-rzxc]

For those who ask themselves, why the electrons dont come closer together in the lab frame: I think its because only the electrons become contracted not the space in between. Hence, the density of charge doesn't change. When the cat moves, everything it sees is contracted, since everything (also the space between the postitiv charges) moves and the density of positive charges increases. Just my approach though

[djscurge]

6 years of Electrical Engineering curriculum which included extensive study in EM and I was never taught I'm somewhat disappointed in my university. I actually think I asked this specifically: "I understand all the effects of a magnetic field, but what IS it fundamentally?" and after some discussion of permeability and Maxwell's equations I lamented that no one in that class, professor included, actually knew. We could all describe a magnetic field by its effects and influences and even the qualities and characteristics of materials that can support a magnetic field and the methods of inducing one, but not what it actually is. Thank you so much for this video. I can now (at least more fully) answer that question "What IS a magnetic field".

[energyman]

In the case when cat is at rest and it sees electrons moving, the electrons are more densely accumulated and the positive charges are spread out. So according to this logic, even rest charge must interact with magnetic field.

[alexjames]

Why the wire has no charge in the rest frame: The electrons do initially experience length contraction as they start moving, but they repel each other and spread out to restore neutral charge. The same can't happen with the protons because they can't move freely in the material.

Why a single moving electron produces a magnetic field: The electric field caused by the electron also moves along with the electron, causing it to contract and increase its density.

[jam-trousers]

I was always told electromagnetism is a relativistic correction on a moving electric field but I’ve never actually had that explained. Thanks heaps for that.

[grzegorzbaran]

At primary school I never understood why magnets work... Now I see why it never gets explained to kids;)

[volbla]

I got it! I finally got it! I was wondering, from the stationary point of view, why the electrons don't contract and attract the positive cat. It is because from the moving cat's point of view the entire world - the positive nuclei and the wire along with it - is moving. That is why the space between the positive charges contract. Because that space itself (i.e. the wire they're in) is moving in this frame of reference.

From the stationary point of view, however, only the electrons themselves are moving. This only means that the electrons are squished down a bit and get flatter, but the space between them (again, the conducting wire) is stationary. Therefore the distance between charges remains the same and there is no change in the charge density.

I feel so happy right now.

Edit: It turns out this intepretation is not entire correct. In a simplified scenario of two co-accelerating bodies there are basically two possibilities (or more like two ends of a spectrum). If the distance between them stay *constant from the bodies' pov* it will *contract* from an observer's pov. If the distance stays *constant from an observer's pov* it will *expand* from the bodies' pov. It depends on how/when that acceleration is applied to the different bodies. Look up Bell's spaceship paradox for more info.

But the electrons in a wire seem more complicated than just some constant acceleration. Not sure how exactly it works... but i guess it does.

[tjeerdprins]

Why is the wire neutral when current flows through it? Shouldn’t the electrons experience length-contraction from our point of view? Shouldn’t a stationary cat therefore be attracted to the wire?

[sedativechunk]

"If you can't explain it simply, you don't understand it well enough." - Richard Feynman