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This question already has an answer here:

For Photons, their 'waves' are oscillating electromagnetic fields. From what I've heard, electrons are also some kind of wave. So what 'field' is exactly oscillating for electrons, which makes them a wave? It can't be the electromagnetic field, I think?

Sorry if the question is stupid.

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marked as duplicate by user10851, John Rennie, yuggib, Kyle Kanos, ACuriousMind Jul 16 '15 at 12:32

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ I know about DeBroglie waves (I'm a physics master student). My question was what exactly the wave of the electrons (and thus, for every other matter) is composed of, i.e. what 'energy field' it is. $\endgroup$ – kushy Jul 16 '15 at 1:18
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    $\begingroup$ kushy, fundamental stuff is what it is. As far as we know, the entity for which (what we identify as) electrons are the quanta is fundamental, i.e., indescribable in terms of 'more fundamental' stuff. In other words, the question of what a fundamental entity is composed off ignores the premise that the entity is fundamental. $\endgroup$ – Alfred Centauri Jul 16 '15 at 1:53
  • $\begingroup$ @Alfred Centauri Does this comment is a copy from the old Greeks about atom as the smallest an indivisible units? $\endgroup$ – HolgerFiedler Jul 16 '15 at 5:26
  • $\begingroup$ "For Photons, their 'waves' are oscillating electromagnetic fields." No. The wavefunction is not the same as the electromagnetic wave that is made up of many photons. $\endgroup$ – ACuriousMind Jul 16 '15 at 12:32
  • $\begingroup$ @ACuriousMind: Once, I have also asked the same to you & you provided me with an amazing paper which I have also linked here in my answer; hope you don't mind, sir:) $\endgroup$ – user36790 Jul 16 '15 at 14:02
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It's not a stupid question. In fact, Quantum Field Theory is the field of physics that seeks to answer exactly this question. In QFT, in addition to the electromagnetic field, there is a single electron field that extends throughout the universe. Stable ripples in the electron field constitute individual electrons. Every fundamental particle has a universe-wide field associated with it. There are quark fields, Higgs fields (which gives rise to the Higgs boson), photon fields (also known as the electromagnetic field), and so on. The larger the amplitude of a ripple at a certain location in space, the larger the probability of finding a particle there.

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  • $\begingroup$ Exactly this. From thphys.uni-heidelberg.de/~weigand/QFT1-12-13/SkriptQFT1.pdf: "an electron is the elementary excitation of the electron field" $\endgroup$ – Ben Hocking Jul 16 '15 at 5:40
  • $\begingroup$ Thanks, this is the answer I wanted! :-) Just a question out of curiosity: How are positrons described by this electron field, i.e. what kind of excitation are they, in constrast to the electrons? $\endgroup$ – kushy Jul 16 '15 at 8:11
  • $\begingroup$ Ow... My brain. $\endgroup$ – Roman Jul 16 '15 at 9:19
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The electromagnetic wave is a classical theory while matter waves are quantum mechanical. The wave aspect is a mathematical abstraction which allows us to predict future quantum states of the electron with a known probability.

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  • $\begingroup$ A precise and nice short answer, bringing it to the point $\endgroup$ – HolgerFiedler Jul 16 '15 at 5:48
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    $\begingroup$ Imho not really helpful as an answer, since it doesn't answer the actual question. Sounds more like a 08/15 textbook answer to any type of question about QM :-/ $\endgroup$ – kushy Jul 16 '15 at 8:05
  • $\begingroup$ Yeah I'm sorry I answered it quickly with little explanation. I'll do better next time, thanks for the feedback! $\endgroup$ – Alex Jul 16 '15 at 18:09
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From the famous Double-slit experiment, it is clear that electrons do behave as wave as well as particle. When it is detected by geiger counter, "click" sound appears & no matter how greatly the voltage is decreased along the cathode tube, "click" & never "half click" appears. So, electrons always arrive at lumps like bullets. However, unlike bullets the probability of detecting electron at the backstop in front of the slits is not like bullet but like interference of waves like water waves. So, electron does behave as wave.

Waves of what? Waves of probability. The quantity that varies with wave like electric field in electromagnetic wave is $\Psi(x,y,z,t) = \psi(x,y,z)e^{-(iE/\hbar)t}$, a complex entity called wavefunction. The wave associated with the electron is purely mathematical construct. It doesn't describe the space-time variation of any measurable quantity. The wave rather relates to the probabilities of observing the electron at different space locations as a function of time.

Photons do have wavefunction but it is not the classical EM waves. It needs relativistic approach & is too subtle. However, it can be expressed by means of electric & magnetic field i.e. $\psi(x) = \begin{pmatrix} \vec{E} \\ ic\vec{B} \end{pmatrix}$. You can check this paper for more info on this.

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