Why cannot longitudinal waves travel through space (vacuum ...

'The reason sound can't travel through a vacuum is that sound needs a medium (solid, liquid or gas with real vibrating molecules) and not because it is a longitudinal wave' How does this make sense as there are particles in space which can vibrate. Light waves travel through space hence they reach earth and they also use vibration of particle to transport energy. It seems like these two ideas are contracting themselves. Maybe the thing I don't understand is why longitudinal waves such as sound have to travel through a media.
$\begingroup$If you mean a perfect vacuum, then there is nothing to displace. However, "space" is not a vacuum. It is, as you say, filled with particles, admittedly a low density, but space is not empty. Longitudinal waves can exist in space, but not in a vacuum. Note also that sound cannot be said to exist in space for two reasons. 1.) sound is a psychophysical phenomenon that exist only in the human brain. 2) the longitudinal waves in space are have a very low frequency that no human could hear.$\endgroup$
$\begingroup$@garyp - Actually there are electrostatic ion-acoustic waves, which are a longitudinal (i.e., $\mathbf{k} \times \delta \mathbf{E} = 0$) sound wave, that oscillate near the ion plasma frequency. In the solar wind near Earth, this corresponds to ~100-1000 Hz in the plasma rest frame. In a spacecraft frame (which is basically at rest compared to the plasma), the waves can be Doppler shifted up to ~1-10 kHz. We can convert these signals directly to an audio signal. The University of Iowa has done a bunch of this for various plasma waves.$\endgroup$
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Electromagnetic waves are produced by oscillating charged particles but they do not need other particles to propagate. Indeed electromagnetic waves are solutions of the Maxwell equations with no sources, i.e. in the vacuum.
On the other hand, mechanical waves need an elastic medium to propagate, regardless of being transverse, longitudinal or mixed waves.
Regarding the particles present in deep space which could propagate sound, I suggest you to read this post.
$\begingroup$Waves whose longitudinal component, ie., component that is parallel with the direction of propagation do exist in vacuum, see any TE or TM waves in waveguides. TE waves have the H, TM waves have the E component parallel with the guide axis. The boundary conditions and not the medium of propagation decide if there are longitudinal components for EM waves.$\endgroup$
$\begingroup$@hyportnex modes of waveguides are not plane waves but superpositions thereof and the basis plane wave constituents are not directed along the waveguide. This answer still holds good for plane waves, which I think is the key point for discussion - or at least an important one. Waveguide modes can always be resolved into plane wave superpositions whereas, in contrast, mechanical waves cannot be resolved into plane wave superpositions - there's a part of the field that is fundamentally longitudinal. So the boundary conditions determine the superpositions which group together to form the ....$\endgroup$
$\begingroup$@WetSavannaAnimal_aka_Rod_Vance as you say "modes of waveguides are not plane waves", and I said that all the TE and TM waveguide modes have longitudinal components. (Admittedly I did not get in the added possibility of a true TEM mode for multi-connected cross section) And while it is true that any TE or TM mode can be construed as some superposition of multiply reflected plane waves, it is also true that the sum has longitudinal component unlike the case of acoustic waves, and that is the issue what I thought the question was about.$\endgroup$