What is the time dilation less a magnetic field?

Does time dilation drop off like a gravity or does resemble a magnetic field model?

Could a smaller body with a magnetic field have more time dilation then a larger body without and to what degree?

• To talk meaningfully about time dilation you need to define both the observer and the observed. Also I think you mean "correlation" not "coalition" – Steve Linton Jun 28 at 20:09
• Relative to a clock on the ground, General Relativity says that a clock in orbit runs faster due to gravitational time dilation slowing down the ground level clock. But you also need to take into account the symmetrical time dilation due to relative speed, as predicted by Special Relativity. I'd rather not talk about magnetic fields in case I add to your confusion. ;) But basically, magnetic fields don't change the time dilation. – PM 2Ring Jun 28 at 20:48
• Most large bodies have no magnetic field to speak of, yet the time dilation due to their gravity is quite measurable. So, no, you don't need to involve magnetic fields to get time dilation. – Florin Andrei Jun 29 at 0:15
• What do you mean when you say "The range of the time dilation doesn't taper of like gravity but it does resemble the taper off of a magnetic field"? – HDE 226868 Jun 29 at 17:12
• In the weak field limit gravitational time dilation depends on differences in the gravitational potential, so for point masses it scales by $1/r$. – dmckee Jun 30 at 4:50

There is a magnetic field whenever there is a moving charge, and since "moving" is a relative term, there is at least the possibility of some observer seeing a magnetic field whenever you have any charged object at all. However, there are thought experiments which show time dilation without involving any charge.

An example in special relativity would be a beam of Z0 bosons (which are, as far as we know uncharged fundamental particles). If the beam was moving fast relative to some observer, then they would appear to decay less quickly.

A GR example is an uncharged black hole (possible in theory, but unlikely in reality – any black hole will have a bit of charge, just by chance). A clock (our bunch of Z0 bosons for example) close to the black hole will seem to run slower according to a distant observer at rest relative to the black hole. The exact degree of dilation will be affected by the charge on the black hole, but it would have to be very highly charged for the difference to be much.

• @Muze distance from what, as observed by whom? – Steve Linton Jun 29 at 17:20
• from a large body, – Muze the good Troll. Jun 29 at 17:20
• magnetic fields generally fall off as 1 / r^3 rather than 1 / r^2 for gravity. but how does time dilation fall off? – Muze the good Troll. Jun 29 at 17:24
• I asked this as a new question. – Muze the good Troll. Jun 29 at 17:35
• See en.wikipedia.org/wiki/… it's \sqrt(1 - r/R) where R is the Schwarzschild radius – Steve Linton Jun 29 at 17:35