Relativity Facepalm

Part two: the lunacy continues

Josh and Tom had always been good friends throughout high school.  Fate however led them along different career paths.  Josh went to work in a government laboratory as an experimental physicist, while Tom ended up a mechanic.  Despite this, they resolved to maintain their friendship, and once a week would meet up at a local bar to discuss their work and other matters.

One day, Josh failed to turn up for their weekly get-together.  Tom received a text message urging him to visit Josh’s workplace to witness an important development.  Tom travelled there and made his way down to an underground laboratory where he found Josh adjusting some equipment.  Josh looked up to see him arriving.

Josh:  “Oh good, you made it.  Come in, come in.”

Tom:  “You said you had something important?”

Josh:  “Yes indeed.  There’s been an exciting development in the field of particle research.  A new subatomic particle, which has been christened a zoton, has recently been discovered.

Tom:  “I hear there are hundreds of such particles.”

Josh:  “There certainly are.  But what makes this one special is that it can be generated on-the-fly, and in precise numbers.  I’ve decided to use them for testing Relativity Theory.”

Josh then pointed to a long metal cylinder that stretched the length of his laboratory.

“See this large piece of equipment?  It’s our linear particle accelerator.  So called because it accelerates particles in a straight line.”

Tom:  “I know, you’ve shown me pictures of it.”

Josh:  “Right.  Well at this end of the accelerator I have my zoton generator.  It generates a batch of a hundred particles at a time and feeds them into the accelerator, which then accelerates them along the tube.”

“Now at the far end of the accelerator is a photographic plate.  When a zoton hits that, it a leaves a bright spot on the developed film.”

“As it happens, zotons have a half-life of one microsecond.  That’s slightly less than the time it should normally take them to reach the other end.  By sending them along the tube at a known speed, we can calculate how many should reach the other end and leave spots on the plate.  We can then compare that with the actual spot count and determine whether the effects of Relativity have taken place.”

“If the particles were moving fast enough, we’d expect a larger number of spots than what classical mechanics would predict.  That would show the particles were living longer due to time dilation, which is to say their time was running slower than ours.”

Tom:  “Amazing stuff.  So how fast are the particles moving?”

Josh:  “50 percent of light speed.”

Tom:  “And how fast is the accelerator moving?”

Josh:  “Huh?  It’s not moving.  It can’t move because it’s bolted to the floor as you can see.”

Tom:  “But aren’t we rotating through space and orbiting the Sun?  And isn’t our Solar System in orbit around the Milky Way?”

Josh:  “Okay I understand what you’re asking.  Yes we are all moving through space.  But we can ignore such motion because it applies equally to all parts of the experiment.  What we’re interested in is the relative speed between the particles and the accelerator.”

Tom:  “So what is the speed of the particles relative to the accelerator?”

Josh:  “50 percent of light speed, as I said.”

Tom:  “And what is the speed of the accelerator relative to the particles?”

Josh:  “That would also be 50 percent of light speed.”

Tom:  “In which case why can’t we say the particles are still while the accelerator is moving?”

Josh:  “It’s a matter of convenience.  Our reference frame is usually chosen based on what is larger.  In this case the accelerator is so much larger than the particles; not to mention it’s attached to the floor and then the Earth.  So it is more convenient to describe the accelerator as motionless.”

Tom:  “Conveniences are all well and good.  But I’d like to propose an experiment where the particles are standing still and the accelerator is moving toward them at 50 percent of light speed.  In this case the particles wouldn’t be experiencing time dilation and thus more would decay, leaving fewer spots on the plate.  Is that correct?”

Josh:  “Impossible to say in practise.  The accelerator weighs many tons.  It would take a huge amount of energy to launch it into space at that speed.  Probably more than we could ever make available.  We humans have never achieved such high speeds with heavy objects.”

Tom:  “I’m not asking anyone to launch it into space.  I just want to consider it as moving and the particles as being still.”

Josh:  “It makes no sense to consider the accelerator moving because it doesn’t decay and we can’t do measurements on it.  Only the particles decay, so we treat them as moving.”

Tom:  “Let me try a different angle.  Suppose a spaceship was flying overhead and in the same direction as the particles.  We’ll say it was moving at 20 percent of light speed, relative to the accelerator.”

Josh:  “Okay.”

Tom:  “So relative to the spaceship, subtracting 20 from 50, the particles are now moving 30 percent of light speed.  Is that correct?”

Josh:  “Sounds about right.”

Tom:  “In which case the particles should be experiencing less time dilation and decay more quickly.  The person aboard the spaceship would see fewer spots on the plate.  How would you account for the discrepancy?”

Josh:  “You might think that would happen.  But you’re not taking into account Length Contraction.”

Tom:  “Length Contraction?  I believe I’ve heard of that.”

Josh:  “Yes.  From the perspective of the spaceship the accelerator is contracted along its length.  Therefore the particles travel a shorter distance before hitting the screen, and the same number survive as what we would see.”

Tom:  “The accelerator is contracting?  I’m pretty sure that couldn’t happen, especially as it’s bolted to the floor.  I’d surely notice that.”

Josh:  “Actually you wouldn’t because the floor would also be contracting with the accelerator.  And you and I would be contracting with it.”

“As a matter of fact, the whole universe will contract with respect to the spaceship.”

Tom:  “The spaceship can make the universe contract?  It must have some powerful magic!”

Josh:  “Well, it’s not actually contracting as such.  That’s a perception from the point of view of the spaceship.  You could think of it like an optical illusion.”

Tom:  “If it’s just a perception or illusion, how could it possibly have an effect on a real physical outcome?”

Josh:  “We tend to describe it as an illusion when explaining it to newcomers, but that’s not quite correct.  From the perspective of the spaceship, the accelerator is genuinely contracting and that’s why it can have a real effect.”

Tom took a moment to think about this.

Tom:  “Okay, let me try another approach.  Suppose the spaceship were moving in the opposite direction, i.e. against the particles.  I’ll also say that it’s moving at the same speed of 20 percent of light, relative to the accelerator.  Does Length Contraction apply here?”

Josh:  “It certainly does.  And it will contract by the same amount because the relative speed is the same.”

Tom:  “In that case it would appear we have a problem.  Because now the speed of the particles relative to the spaceship is 70 percent of light, producing a much higher degree of time dilation and making more of them survive.”

“Not only that, but with the accelerator shrinking along its length, the number of particles surviving will be higher again.  The spaceship occupant would see far more particles on the screen than someone in the laboratory.  How could you account for the discrepancy?”

Josh:  “Well first of all, you’re not adding velocities correctly.  When adding velocities in Relativity you need to use a special formula that prevents their sum from being greater than light speed.”

Tom:  “Why do you need to use such a formula?”

Josh:  “To prevent their sum from being greater than light speed.”

“Now that should help a bit.  But it won’t be enough.  The other thing you should take into account is the Relativity of Simultaneity.”

Tom:  “Huh?”

Josh:  “What that means is when an event happens at a distance, it hasn’t yet happened locally until a later time.”

Tom:  “I don’t understand.”

Josh:  “Okay, suppose somebody was on the Moon, and you had an agreement that he would let off a flashbulb at a certain time.  You wouldn’t see that flash until about a second later.”

Tom:  “That’s true, because it takes light over a second to reach here.  But so what?”

Josh:  “Well if you didn’t see it until later, that’s like saying that it didn’t happen until you saw it.”

Tom:  “I would have thought it’s like saying that the signal took a while to get here.”

Josh:  “Well, in Relativity Theory, time and space are considered interchangeable.  An event separated by space is equivalent to an event separated by time.”

“So, getting back to our experiment, as the spaceship passes over the photographic plate at one end, and the zoton generator creates particles at the other, in fact from the spaceship’s perspective, the particles have not yet been generated.  This means the particles have more time to traverse the tube, and more should decay before hitting the plate.”

Tom:  “So will combining all these considerations produce the required outcome?”

Josh:  “We won’t know until we do the calculations.”

Tom:  “And what if the calculations show a discrepancy?”

Josh:  “Then it’s probably due to Length Expansion.”

Tom:  “Length Expansion?  I’m pretty sure I’ve never heard of that.”

Josh:  “It’s a relative term.  When we look up at the spaceship we see it contracting along its length.  So compared to it, we are length-expanded.”

Tom:  “Wow, this relativity stuff sure is weird!”

Josh:  “I know.  It’s always a difficult subject for beginners.  You need to abandon your intuitive notions of space and time in order to understand it.”

Tom:  “One thing I can’t understand is why you didn’t include those considerations when the spaceship was moving in the other direction.”

Josh:  “Because we didn’t need to.  Simple length-contraction was sufficient on its own.”

Tom:  “There are so many Relativity formulas to consider.  How do I know which ones to use in a given situation?”

Josh:  “The ones that give you the correct answer.”

Tom:  “Relativity sure is confusing.”

Josh:  “That’s why you should probably leave it to the experts.”

“Anyway, I need to be getting back to my work.  Glad I could be of help.  Please drop by again if you have more questions about Relativity.”

Tom:  “Somehow I don’t think I will.”