If you were traveling in a very high-speed spaceship away from the earth, would you notice a change in your heartbeat? would your mass or width change? would someone on earth (using a telescope) observe any such changes in you?

-- YOU would not see any change in the speed of your heartbeat, your own mass, your own height, width, or length, or the mass or measurements of your dog that who came with you in your spaceship.  Those things would all stay the same.

-- A person back on Earth, with some fantastic mysterious kind of way to watch you in your spaceship and measure all those things about you ... HE would see YOUR mass increase, your heartbeat slow down, your height and width stay the same but your length shrink in the direction you're moving, your dog's mass increase, his heartbeat slow down, and his tail shrink in the direction your spaceship is moving.

-- If YOU had similar equipment with you on the spaceship, that made it possible for YOU to look back at the person on Earth who is watching you, and make measurements of HIM, YOU would see HIS mass increase, HIS heartbeat slow down, HIS telescope and HIS body shrink along the direction that YOU're moving.

Seems weird, eh ?  How can this be ?  You AND the guy on Earth who is watching you, BOTH see the OTHER person's mass increase, see the OTHER person's heartbeat slow down, and see the OTHER person shrink along the direction of motion.  

As hard as it is to understand this or even believe it, the fact is that it has been observed and confirmed in thousands of experiments during the past 100 years.  It's even BUILT IN to the GPS satellites.  The clocks aboard each GPS satellite are built to run faster than normal, because we know that they'll slow down because of their speed in orbit.  If the clocks on the GPS satellites were built to run at the correct speed, then all the things you read on your smartphone that use GPS ... Google maps, Waze, Where Am I, Google Earth, etc. ... would all show the wrong locations, and they'd all be useless.

an obstruction