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Okay suppose there is an hypothetical particle called Nelectron which has mass = mass of electron but is electrically neutral. It has same spin and other quantum mechanical properties. Even the same size (I know we don't know electron's size but bear with me) Would they bend space-time by the same amount (w.r.t. a particular observer if they move with the same velocity w.r.t. that observer) ? I read somewhere energy is ability to do stuff. What stuff? Spinning , punching , thinking , jumping . Even existence itself! Basically does the existence of charge(not mass!) Count as energy ?

PS : Can charge exist without mass ? We know masses without charges (higgs?)

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Charge does have an effect on space-time. For example a spherically symmetric charged spacetime metric would be described by Reissner-Nordströrm metric.

The existence of charge unlike mass does not contribute to any intrinsic energy.

Can charge exist without mass ? We know masses without charges

Theoretically, an equation exists equations that describes a charged massless particle. For example, by setting the mass of the scalar field to be zero in scalar QED we create the field equations of a massless charged field. But such a particle has never been observed in any of our particle colliders. These particles theoretically should be very easy to create, the fact that they haven't been observed even by the LHC seems to point that these particles do not exist.

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  • $\begingroup$ Okay but what kind of massless are we talking here ? Rest mass , right? The charge doesn't contribute to intrinsic energy....is it related to any fundamental symmetry (breaking) or equation? $\endgroup$
    – Mikhail Tal
    Commented Mar 17, 2019 at 13:57
  • $\begingroup$ +1, but one suggestion: a charge has an electric field, and the electric field does have energy density $\sim \vec E^2(x)$. $\endgroup$
    – Chiral Anomaly
    Commented Mar 17, 2019 at 13:58
  • $\begingroup$ I am not sure I understand the question. If we set the mass =0 in the field equations we get the desired particle. $\endgroup$
    – Manvendra Somvanshi
    Commented Mar 17, 2019 at 13:59
  • $\begingroup$ @DanYand yes you are right. That is why I specifically wrote intrinsic energy. The electric filed does not contribute to the energy of the particle itself. $\endgroup$
    – Manvendra Somvanshi
    Commented Mar 17, 2019 at 14:00
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    $\begingroup$ It is unnatural for a particle/field with charge to be massless. Self-interactions will generically lead to renormalization of the particle/field's mass. $\endgroup$
    – TimRias
    Commented Mar 17, 2019 at 16:21

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