# Do strong magnetic fields cause time dilation?

Does a strong magnetic field cause time dilation?

If you have a strong magnetic field, and a magnetic radio active material, does the half life of the material change due to field?

• What is the motivation for the question? What makes you think there would be such an effect?
– user4552
Sep 11, 2019 at 19:14

This isn't an answer because as it stands it's hard to answer your question, but it got a bit long for a comment.

You ask whether a magnetic field causes time dilation, but since there are no magnetic monopoles (or at least we've never found any) I can't think of a situation where you could usefully separate out the effects of the magnetic field from all the other effects. Magnetic fields are generated by moving charges, so the effect on spacetime woud depend on how exactly you constructed the system of moving charges that was generating the magnetic field. This is why I don't think your question has an answer.

Can I suggest a slight modification to your question and make it Does strong electric field cause time dilation? because we can answer this. The spacetime curvature for a charged static spherical body is given by the Reissner–Nordström metric:

$$ds^2=-\bigl(1-\frac{2M}{r}+\frac{r_q^2}{r^2}\bigr)dt^2+\bigl(1-\frac{2M}{r}+\frac{r_q^2}{r^2}\bigr)^{-1}dr^2+r^2d\Omega^2$$

where:

$$r_q^2 = \frac{Q^2G}{4 \pi \epsilon_0 c^4}$$

To work out the time dilation $d\tau/dt$ we just set $dr$ and $d\Omega$ to zero and we get:

$$\left(\frac{d\tau}{dt}\right)^2 = 1-\frac{2M}{r}+\frac{r_q^2}{r^2}$$

So you can feed in the value of whatever charge you want and calculate the time dilation as a function of distance from the charged body. If you do this you'll discover something rather odd, the charge reverses the effect of the mass. The mass causes time to slow (relative to the observer at infinity) but adding charge (of either sign) makes the time speed up again.

• Note that people who like to play with Maxwell's equations with a magnetic monopole term inserted will tell you that magnetic monopoles have the exact same effect on this metric (in CGS-like units, of course) - they add a $Q_\mathrm{mag}^2/r^2$ term.
– user10851
Feb 22, 2014 at 21:08
• the last result is rather odd indeed! Is there any physical intuition as to why the charge causes the time to "speed up again"?
– glS
Oct 29, 2017 at 15:52
• the Wikipedia page referenced for the Reissner-Nordstrom metric does not have the simplified time dilation equation stated above. I am having trouble with the simplification. Anyway, it seems that the time dilation solution is a square root, so a plus or minus answer is equally correct. Thus charge could cause either speed up or slow down of time as both satisfy the equation. Jan 8, 2018 at 18:43
• It isn't really the electric field that causes time dilation, it's more like the gravitational field caused by the energy in the electric field.
– user4552
Sep 11, 2019 at 19:14

Since an electromagnetic field is associated with a non-vanishing energy-momentum tensor, which in turn is the source term of gravity in the Einstein field equations, the answer is yes - if you were able to produce a strong enough field you would eventually get a measurable gravitational time dilation as compared to a reference clock far away.

It should be noted though that the field strengths needed to produce a noticeable and measurable effect here would exceed our engineering capabilities by many orders of magnitude.