Using Black holes as speedometers ?

So there you are in your rocketship accelerating towards the speed of light and your speedometer breaks. Desiring to know how fast you are going, you remember having brought along a small electrically charged black hole suspended in a powerful magnetic field. After determining its mass by perturbing the magnetic field and then looking at the oscillation frequency of the hole, you realize you forgot to write down the rest mass of the hole when they loaded it into the cargo bay. In desperation you dig out a spectroscope and use it to determine the energy distribution of the Hawking radiation.
Do these two bits give you enough information to calculate your speed relative to the quantum vacuum ?

No. Relativistic mass depends on the speed relative to the reference frame. If the black hole is moving with you, there is no increase in relativistic mass.

Wow, you’ve got a portable black hole with you on the ship. Do you realize what MacGyver could with such a thing?

The black hole is moving with you, but the vacuum, which generates the virtual particle pairs responsible for the energy coming off the black hole, is not moving with you.

I forget the details, but the vacuum fluctuations have a spectrum such that, if you red shift it, it still looks the same. The vacuum does not provide a reference frame.

What you are trying to do is detect motion relative to the preferred reference frame (the one that is not moving). One of the assumptions of relativity is that a preferred reference frame does not exist. QM does not allow you to violate this assumption.

But on a thread a couple weeks ago, I thought everyone came to agree that there is a preferred at-rest reference frame, where you are at zero velocity compared to background microwave radiation. You could (?) figure your absolute velocity (or velocity relative to the background radiation) using just the spectroscope.

And you know how MacGyver used his swiss army knife to get out of all those jams? He would have never been IN a jam in the first place if he just carried a roll of black electrical tape with him. Now THAT is a miracle substance.