# What's the actual speed of electromagnetic radiation in space?

The speed of EM radiation is very slightly less than $$c$$, because space is not quite a vacuum. Say EM travels at $$(1-\varepsilon)c$$.

For example, this results in a slight delay between receiving a gravitational wave and detecting an associated EM emission from the body that caused it. For an object about 130 million light years away (GW170817) I've seen this delay quoted as everything from $$1.74$$ seconds (so $$\varepsilon\approx 4\times 10^{-16}$$) to 27 minutes (so $$\varepsilon\approx 4\times 10^{-13}$$). I'm sure these figures depend on all sorts of interesting astronomy to do with black hole mergers and gamma ray bursts, but the actual value of $$\varepsilon$$ doesn't need to know any of this.

So I'm asking here because anyone working on LIGO must surely know our best estimate for the value of $$\varepsilon$$.

• Well... space is also far from isotropic, so light may pass thru some "clouds" or it may not. So at best you'll get an estimate of $\epsilon$ in a specific direction to a specific source. I'd be more interested in the calculations of when an EM burst is released vs. the instant the two bodies merged to create the gravity wave. – Carl Witthoft Jun 10 '19 at 17:36

I believe this question was addressed in the paper , Abbot, et. al., Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A , ApJ. Lett., 848:L13, 2017 October 16.

"We use the observed time delay of ($$+1.74 \pm 0.05$$) s between GRB 170817A and GW170817 to: (i) constrain the difference between the speed of gravity and the speed of light to be between $$-3 \times 10^{-15}$$ and $$+7 \times 10^{-16}$$ times the speed of light, ..."

In Section 2.2 of the paper they discuss the uncertainty of delay between GW and GRB emission, predicted to be a few seconds. In Section 4 of the paper they compute the range of speed uncertainty quoted above. They conservatively use 26 MPc, their lower bound on the 90% credible distance interval, and for the upper bound on speed difference they assume the GW and GRB were emitted simultanously, and use the 1.74 s $$\Delta t$$. For a lower bound on speed of gravity, they assume the GRB were emitted 10 s after the GW, and a faster EM signal made up some of the difference.

I believe that X-rays were also detected several (~8-9) days later. This delay was attributed to time needed for the shock wave from the merger to interact with surrounding matter. I was unable to find any reference to signal arrival 27 minutes after GW detection in the LIGO papers.

• Thank you - that's an excellent answer. I guess if you're an experimentalist you don't rule out GW traveling slower than $c$ without experimental evidence. Personally, I'm prepared to trust Einstein's GR equations. The 27 minutes, BTW, comes from the LIGO GW170817 press release which quotes this figure as the "initial astronomer alert latency, referenced to the time of merger", but I don't know exactly what that means. – Adam Chalcraft Jun 11 '19 at 2:29
• @Adam Chalcraft, Thanks. The timeline is documented in their "Multi-Messenger Observations ..." paper. Merger occurred at 12:41:04 UTC and the GRB detection at 12:41:06 UTC. LIGO's first alert to astronomers was a GCN Notice (Gamma-ray Coordination Network) at 13:08:16 UTC, about 27 minutes later. – amateurAstro Jun 11 '19 at 14:26

Given that different frequencies of light, or energies of photons, take your pick, travel through different the same medium at different rates, e.g. red light is slowed less by a glass prism and blue is slowed more, it would seemingly take higher energy signals longer to reach the observer, be it cosmic dust, interplanetary/galactic gas, or whatever else.

The only way to calculate would be by observing a singular pulse over multiple synchronised frequencies simultaneously. Apparently with GW170817 as you mentioned there was an observed Gamma Ray Burst by the Fermi and INTEGRAL spacecraft 1.7 seconds after the LIGO detected event, but as far as I'm aware that was the only other observation instantaneously. Most other observations were telescopes directed there after being alerted by the GRB

• But was the GRB emitted simultaneously with the GW? Because a few seconds difference makes an enormous difference to the calculated value of $\varepsilon$. – Adam Chalcraft Jun 10 '19 at 16:41