Entries by bcrowell

At What Velocity Does the Universe Expand and Can It Be Faster than Light?

Neither of these questions actually makes sense in the form in which it was posed. To see why, let’s start by thinking about how we know the universe is expanding. The expansion of the universe was originally discovered by Hubble, who found that the redshifts of galaxies were proportional to their distances from us. To […]

Why Is the Speed of Light the Same in All Frames of Reference?

The first thing to worry about here is that when you ask someone for a satisfying answer to a “why” question, you have to define what you think would be satisfying. If you ask Euclid why the Pythagorean theorem is true, he’ll show you a proof based on his five postulates. But it’s also possible […]

Was the Early Universe in a Disordered State?

No. The second law of thermodynamics says that entropy can only increase, so if the early universe had been in a state of maximum entropy, then the cosmos would have experienced its heat death immediately after being born. This contradicts the observation that the present universe contains burning stars, heat engines, and life. These observations […]

What Is the Steady-state Model and Why It’s No Longer Viable

[Back in 2011, I wrote a FAQ entry for physicsforums on the steady state model and why it is no longer viable. I’ve learned more about the theory since then, and it turns out that Fred Hoyle was a lot cleverer than I’d assumed. The following is an update to that FAQ that, while more […]

Why Does C Have a Particular Value, and Can It Change?

Short answer: Because c has units, its value is what it is only because of our choice of units, and there is no meaningful way to test whether it changes. These questions are more meaningful when posed in terms of the unitless fine structure constant. Nobody knows why the fine structure constant has the value […]

How Fast Do Changes in the Gravitational Field Propagate?

General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational waves travel at the speed of light. Gravitational waves have never been detected directly, but the loss of energy from the Hulse-Taylor binary pulsar has been checked to high precision against GR’s predictions of the power emitted in […]

Will All Matter Be Converted to Photons?

FAQ: In the very distant future, will all matter be converted into black holes and then photons? No. There is a misconception that a lot of laypeople seem to be picking up recently from popularizations, which is that all the matter in the universe will first be sucked into black holes, and then recycled into […]

Relativistic Work-Kinetic Energy Theorem

I was bothered for a long time by the reasons for the relativistic validity of the work-kinetic energy relation ##\Delta E=Fd##, which holds without any need for corrections. We’ve discussed this before here on PF,  but I think at this point I understand it better, so I thought I’d post a summary of my present […]

What Is the Bell Spaceship Paradox, and How Is It Resolved?

Bell describes two spaceships that start out at rest relative to each other, with an elastic string between them, one end attached to each ship, which is initially just long enough to span the distance between the ships without being stretched. The ships’ clocks are synchronized in their common initial rest frame K. At some […]