What are the two postulates (starting assumptions) of Einstein's Special Relativity?

Mass is always conserved, and energy is always conserved The laws of physics are the same for all observers in constant motion, and the speed of light is the same for all observers regardless of relative motion Space and time are separate and absolute, and nothing can exceed the speed of light Gravity and electromagnetism are the same force, and nothing in the universe is truly at rest

A spaceship travels at 90% the speed of light. The Lorentz factor (gamma) at this speed is about 2.3. What does this mean for a clock aboard the ship compared to a clock on Earth?

The ship's clock ticks 2.3 times faster because the ship is moving quickly and covering more time The ship's clock ticks about 2.3 times more slowly — for every 2.3 years that pass on Earth, only 1 year passes on the ship The ship's clock ticks at exactly the same rate — relative motion cannot affect time The ship's clock stops completely because it is moving so close to the speed of light

Why can no object with mass reach the speed of light?

Objects would overheat and melt before reaching the speed of light There is a traffic rule in the universe forbidding speeds above c As an object accelerates toward c, its effective mass and the energy needed to accelerate it further both increase toward infinity — reaching c would require infinite energy The object would start traveling backward in time before reaching c

What does E = mc^2 actually mean in plain language?

Energy equals the mass of an object multiplied by the speed of sound squared Mass and energy are two forms of the same thing — a small amount of mass is equivalent to an enormous amount of energy because c^2 is a very large number An object moving at the speed of light has infinite mass and therefore infinite energy The energy stored in motion equals an object's mass times the speed it is traveling

GPS satellites orbit Earth at about 14,000 km/h and experience weaker gravity than at Earth's surface. Without relativistic corrections, by how much would GPS be in error each day?

About 1 millimeter per day — relativistic effects are too small to matter practically About 1 meter per day — a small but noticeable error for navigation About 10 km per day — Special Relativity causes satellite clocks to run slower (time dilation from speed), while General Relativity causes them to run faster (weaker gravity); the net effect is about 7 microseconds per day of drift that would cause ~10 km of navigation error About 1,000 km per day — making GPS completely non-functional without corrections

Cosmic ray muons are created about 15 km above Earth's surface. They have a half-life of about 1.5 microseconds and travel at 99.9% the speed of light. Classically, they should mostly decay before reaching the ground — but we detect them in large numbers. Why?

The muons absorb energy from cosmic rays that prevents them from decaying From Earth's perspective, time dilation slows down the muon's internal clock (its decay process), extending its lifetime long enough to reach the ground The muons bounce off the upper atmosphere layers and take a much shorter path Earth's magnetic field protects muons from the forces that would cause them to decay

In particle accelerators like the LHC at CERN, protons are accelerated to 99.9999991% the speed of light. Their gamma factor is about 7,500. What happens to a proton at this speed from the perspective of a physicist at rest in the lab?

The proton becomes invisible because it is moving too fast to absorb or emit light The proton turns into a photon at that speed and can no longer be detected The proton's effective mass increases 7,500 times its rest mass and time inside the proton passes 7,500 times more slowly, which is why enormous energy is needed for only small additional speed gains The proton splits into three quarks when it exceeds 99% of the speed of light

A spaceship leaves Earth at 99.9% the speed of light for a star 100 light-years away. How long does the trip take from Earth's perspective, and how long does it feel to the crew?

About 100 years from both Earth's perspective and the crew's — distance does not change About 100 years from Earth's perspective, but only about 4.5 years for the crew — time dilation (gamma = 22.4) compresses the crew's experienced time About 50 years from Earth's perspective because the ship is going so fast it shortcuts through space Both Earth observers and the crew experience 100 years because time only dilates at exactly c

Special Relativity applies to objects moving at constant velocity. Why is it called special, and what extension handles accelerating objects and gravity?

It is special because Einstein considered it his most important and personal discovery It is special because it only applies to the special case of constant velocity (inertial frames) — General Relativity, published by Einstein in 1915, extended the theory to include acceleration and gravity It is special because it requires special laboratory equipment to test and confirm It is special because only a few objects in the universe travel fast enough for it to apply

Two spaceships approach each other, each traveling at 80% the speed of light relative to Earth. A student says they must be approaching each other at 160% the speed of light. Why is this wrong?

The spaceships would collide before they could reach 160% c, so the problem is physically impossible The speed of light squared in the equation means the combined speed cannot exceed c^2 Two spaceships moving at 80% c are actually motionless in their own reference frames Velocities do not add simply at relativistic speeds — the relativistic velocity addition formula gives a combined speed of about 97.6% c, still less than c