Special Relativity misconceptions

[cmind]

This is a work in progress. DISCLAIMER: No mathematical proof or cited sources are given here, mostly because a) mathematical proofs are too advanced for the audience and b) finding articles that talk about 100 year old well-established physics is nigh impossible. If you hold any of the following misconceptions, I strongly recommend finding an undergrad physics textbook and reading it, or just do us a favour and don't spread your wrong ideas. Here's my list of what I think are the most prevalent and/or annoying public misconceptions about special relativity. Most of these are, of course, the result of dumbed-down pop science programs on tv and the failure of our education system. 4) Scientists used to say that there was a "sound barrier" that could never be exceeded, but they were obviously wrong about that. Maybe they're wrong about the "light barrier". Bullets exceeded the sound barrier in the 19th century. No actual scientist has ever, in the history of Enlightenment, ever said that nothing can go faster than sound. Furthermore, Einstein didn't say the speed of light was a "barrier". He said it was the same for all observers. Everything else in SR follows from that postulate (among a couple of others). More on this later. 3) Accelerating to the speed of light makes your mass infinite. Not mass. Momentum. Momentum approaches infinity from the perspective of a stationary observer. Why not mass? Because in SR, mass is an invariant. An invariant is a quantity that never changes for any observer. The best known invariant is the speed of light, c. 3b) Accelerating to the speed of light requires infinite energy. Nope. From the perspective of the stationary observer, your expended energy appears to increase asymptotically. However, ship-board energy consumption is linear. 2) E=mc^2 --> atomic bombs. No. In reality, nuclear chemistry --> atomic bombs. Although it was Einstein that persuaded President FDR to create a nuclear program, and although in his letter to the president he probably did reference the equation E=mc^2, it was only meant as a sort of ex-post-facto explanation for how so much energy can come from such a small bomb. In fact, E=mc^2 would not be at all helpful for anyone trying to build a bomb. 1) You can't go faster than the speed of light. Actually, you can. There are just a few provisos. First, no one will ever observe you going faster than light. To all observers, even the stationary ones, you will only appear to be going, at best, slightly less than c. Second, for the person actually in the spaceship, they must be content to measure their speed by counting landmarks as they pass by, like stars. If you see 3 stars go by in a year of travel, and you know that stars are (sans length contraction) about 5 light years apart, then you're EFFECTIVELY* going 15c. *I say effectively because you're not actually surpassing c, technically speaking. But if you're willing to ignore time dilation, there isn't a difference as far as you're concerned. Third, time dilation. If you go home, everyone you ever knew is long since dead. Of course, if your goal was to travel into the distant future, then this is a plus! Fourth, more time dilation. Whatever destination you're trying to reach will ALSO appear to pass into the future as you approach it. So, for example, if you want to go to Alpha Centauri because in your super powerful telescope you see a naked Navi waving at you, too bad. By the time you arrive, she will have moved on. But, all that being said, suppose you have a ship that can accelerate at 1g (relative to itself) for many years at a time. At 1g acceleration, you can go anywhere in the universe in a single human lifetime, shipboard.

[Xei]

Good thread. I knew all of that basically, except I wasn't sure about 2. I'd always been confused by 2 and I actually made a thread in this forum about it a while back asking what E = mc^2 has to do with anything when really it's just the interplay of nuclear forces that releases the energy in the same way that the interplay of electrical forces releases chemical energy. Most people said I was wrong and stupid so it's nice to know that it was actually them accepting things without understanding them.

[DrunkenArse]

I may be wrong here but I'll see what people say. 3) Accelerating to the speed of light makes your mass infinite. Not mass. Momentum. Momentum approaches infinity from the perspective of a stationary observer. Why not mass? Because in SR, mass is an invariant. An invariant is a quantity that never changes for any observer. The best known invariant is the speed of light, c. This is a little misleading. There are two types of mass in SR. One of them is the "rest mass" which is the mass measured in a reference frame where the object is at rest. This is an invariant. The second is the "relativistic mass" which is the one used in the equation P=mv for momentum and that does increase without bound as v approaches c. In a reference frame where the particle is at rest, relativistic mass agrees with the rest mass. This is why there's a fundamental distinction between particles with mass and particles without mass with respect to being able to travel at the speed of light. 3b) Accelerating to the speed of light requires infinite energy. Nope. From the perspective of the stationary observer, your expended energy appears to increase asymptotically. However, ship-board energy consumption is linear. Right, but as you say later on, you never measure yourself moving at the speed of light so your energy consumption increases linearly without bound... 1) You can't go faster than the speed of light. Actually, you can. There are just a few provisos. The net effect of all of these provisos is that, effectively, you can't go faster than the speed of light. If you start on a journey, with whatever acceleration, and a photon starts at the same time, you will never catch it. That photon will reach the destination first. Maybe this is like the case of one racer taking longer to get up to speed but being able to run faster? Nope. In that case, if the race is long enough, the faster racer will eventually win. That's not the case here. No matter how fast you accelerate and how long the race is, that photon will always win. And the clock attached to that photon will measure zero time. But, all that being said, suppose you have a ship that can accelerate at 1g (relative to itself) for many years at a time. At 1g acceleration, you can go anywhere in the universe in a single human lifetime, shipboard. Not really. You're still restricted to points that are on the interior of your future light cone.

[Spartiate]

Is the existence of the speed of light and answerable question? As in why it is what it is, why not faster or slower? It's ironic how slow the speed of light is compared to the size of the universe.

[cmind]

The speed of light is directly derived from the permeability and permitivity of free space. Permitivity is measured, but permeability is actually just a variation on pi. So the speed of light is derived from the permitivity constant and pi. The permitivity itself is entirely controlled by the interactions of subatomic particles and has nothing to do with the universe at large. So in other words, the speed of light is completely unrelated to the size of the universe.

[Sornaensis]

Permittivity* Also, spart v1.0's point was that the universe is so gigantically big, yet the top speed limits travel throughout it.

[cmind]

Permittivity* Also, spart v1.0's point was that the universe is so gigantically big, yet the top speed limits travel throughout it. I originally spelled it that way, but this browser's spell checker said there was only 1 t. As to the size of the universe comment, I guess I'm failing to see the point. Yes, it's a spot of bad luck that the place is so big compared to the speed we can go. But then again, would you really want to live in a "small" universe?

[Spartiate]

would you really want to live in a "small" universe? No, a faster one .

[DrunkenArse]

A faster one would be a smaller one

[Spartiate]

How do you figure?

[DrunkenArse]

If we could travel anywhere in the universe (or even to some sizable subset of it) and come back to the planet and people that we left, then it would essentially be a small universe.

[Spartiate]

Well that's a matter of interpretation of definitions... Even if you could zip around the universe like that, the universe itself would still be the largest object that exists, so compared to everything else within the universe, it would still appear large.

[DrunkenArse]

Sure but we could imagine a universe that "went on forever" which is essentially what we have now. The universe we are considering would be small in relation to that. I agree that it's a matter of definition though.

[cmind]

A new one I just heard on the internets: "Magnetic fields travel faster than light; they're instantaneous. This didn't support Einstein's theory, so that's why he called them 'fields'." This sounds a bit too crockery to be added to the big list, but still funny. By the way, changes in magnetic fields do go at the speed of light.

[ninja9578]

PhilosopherStoned is correct in everything he said in his first post. You seem to know relativity pretty well. You can not travel faster than light, you can never get to 15c. I did the math, you are correct that at a constant 1g, a human lifetime is more than enough to reach the edge of the universe, but that's for two reasons. Time dilation, and The Lorenz transformation. At high speeds, time slows down, and the universe shrinks. What stonedphilosopher said about a photon registering a trip of zero seconds is correct, at c, time ceases to exist. He forgot to mention, that it also would have registered a trip of zero meters. Because at c, space also ceases to exist. To something traveling the speed of light, the universe, is a singularity.

[Xei]

A singularity, or a plane?

[cmind]

You can not travel faster than light, you can never get to 15c. I did the math, you are correct that at a constant 1g, a human lifetime is more than enough to reach the edge of the universe, but that's for two reasons. Time dilation, and The Lorenz transformation. Like I clearly pointed out in the OP. Did you intentionally not read certain parts?

[DrunkenArse]

It seems a little weird to discount a fairly major portion of relativity to get a result (faster than light travel) and then claim that the negation of that result is a misconception about special relativity.

[rad802]

Faster than light This explanation is of a closed universe. An open universe cannot be visualized because every point in space is saddle shaped. Einstein did not know when he penned his famous theories, that space was stretching. In fact the universe is stretching or expanding from the three dimensions we know, into a higher dimension. We can not visualize this but we can visualize two dimensions expanding into three. It would look like the skin of a balloon. The skin of the balloon is just like a sheet of paper "flatland", a two dimensional universe. If you put little dots all over it to represent the galaxies and you blow this balloon up, you will see the dots are moving away from each other just like the galaxies we observe. No matter which direction you look, you are looking into the past at a time when the universe was smaller. Now lets say this balloon has a north and south pole. If you are standing at the north pole and you look out across this two dimensional surface you will notice that the universe has no edge. If light were infinitely fast and you had a powerful enough telescope you could see the back of your head. But light takes time to travel. And so as we look out across space we don't see the surface of a sphere but a sight line spiraling in toward the center like the shell of a nautilus. Let's imagine that the universe is 5 billion light years around and the light leaving a star at the south pole travels two and a half billion years to reach us if the universe were not expanding. But because it is expanding, by the time the light reaches us six and three eighths billion light years later, the universe is now twenty billion light years around. If you graph this out on a sheet of paper, you will notice that space was stretching out so fast that it exceeded the speed of light. There is also another scenario in which space swirls faster than light. The space around a spinning black hole is being spun by the immense gravity at a rate faster than light. The following was taken from wikipedia Universal expansion The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally[15] (see Comoving distance#Uses of the proper distance for a discussion of different notions of 'velocity' in cosmology). Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10−36 seconds after the Big Bang to around 10−33 seconds), when the universe may have rapidly expanded by a factor of around (10 to the 20th) to (10 to the 30th) power.[16] There are many galaxies visible in telescopes with red shift numbers of 1.4 or higher. All of these are currently traveling away from us at greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.[17][18] However, because the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future,[19] because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in Comoving distance#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light years away, but the signal would never reach us if the event was more than 16 billion light years away.[18]

[DrunkenArse]

The more I think about it, the less I like this thread. Concerning mass/energy equivalence, I think that it's more instructive to say that it's responsible for all chemistry, including nuclear chemistry. Concerning the speed of light issue, I think that it makes more sense to point out that we are constantly moving at the speed of light. When we are "at rest", we are moving at light speed through "time". When we begin "moving" (through space), our velocity vector rotates so that we are now moving partly through space and partly through time. A massive object cannot ever rotate its velocity vector to lay on its light cone. Likewise, a massless particle can never rotate its velocity vector off of its light cone.

[ninja9578]

DISCLAIMER: No mathematical proof or cited sources are given here, mostly because a) mathematical proofs are too advanced for the audience and b) finding articles that talk about 100 year old well-established physics is nigh impossible. I disagree, I think it's because you don't understand them, most is not that complicated. Most don't even require calculus. 4) Scientists used to say that there was a "sound barrier" that could never be exceeded, but they were obviously wrong about that. Maybe they're wrong about the "light barrier". How? Gamma = 1 / (sqrt(1 - (v^2 / c^2)) v > c will make gamma = 1 / x(i) where x is a scalar How can you do a transform with an imaginary number? I'll ignore the rest, some of it was right, some of it was not right. You should read up on the difference between mass and relativistic mass though.

[sloth]

Sure but we could imagine a universe that "went on forever" which is essentially what we have now. The universe we are considering would be small in relation to that. I agree that it's a matter of definition though. I can imagine a universe that "goes on further than forever". This universe is small in relation to that.

[cmind]

I disagree, I think it's because you don't understand them, most is not that complicated. Most don't even require calculus. How? Gamma = 1 / (sqrt(1 - (v^2 / c^2)) v > c will make gamma = 1 / x(i) where x is a scalar How can you do a transform with an imaginary number? I'll ignore the rest, some of it was right, some of it was not right. You should read up on the difference between mass and relativistic mass though. You do understand that the bolded parts are the misconceptions, right? /facepalm

[ninja9578]

Oops.

[DrunkenArse]

I can imagine a universe that "goes on further than forever". This universe is small in relation to that. I could imagine a "point" that was more pointless than pointless. The post that I'm responding to is pointless in relation to that. What's your point?