Question regarding relativity and "infinite" speed - WTF?!

[MattusMaximus]

Howdy all,

I am engaged in a discussion on another message board over at the Christian and Atheist forums (you have to sign up to see the thread, sorry), and I'm wrangling with a chap who seems to be pushing some kind of nonsense to me about relativity. This fellow, Mitch McKain, does seem to understand some relativity, but he seems to be explaining things in a really weird way that doesn't make sense to me.

So, I wanted to come check with some of you to see if anyone here can translate just what the hell he's talking about, because from what I know of relativity (though I'm no expert) this just seems like word salad to me...

In the OP he states the following:

The fact is that the speed of light in our universe is an infinite speed. It takes an infinite amount of energy to get to that speed, but at that speed you could go anywere (all the way accross the universe) in no time at all. The problem is that it is space-time you are traveling and you cannot travel space alone, so although you could go the 100,000 light years accross the galaxy in no time at all (with enough energy), you MUST travel 100,000 years into the future at the same time. If you didn't then there would be reversals of causality itself. This is what you get when you try to talk about going faster than an infinite speed -- it means getting to your destination before you even left which just doesn't make any sense at all -- except when you want to make fun SF books and movies.

That first line is what is troubling me. So I challenged him on it, and he responded thusly...

The fact is that the speed of light in our universe is like an infinite speed. No it is not an infinite velocity. It is 299,792,458 m/s. That is indeed a finite number. But nevertheless the physics does mean that this does have a lot of the characteristics that we would expect of a infinite speed.

Can anyone here who has more knowledge of the subject please shed some light on just what the hell he's talking about, or is my initial suspicion correct and he's completely full of crap?

Thanks in advance!

Cheers - MM

 

[Vorpal]

At least some of his comments make almost-sense if you assume that he's just confusing proper speed aka celerity, dx/dτ, with, uh, actual speed, dx/dt.

 

[Pulvinar]

Howdy all,

I am engaged in a discussion on another message board over at the Christian and Atheist forums (you have to sign up to see the thread, sorry), and I'm wrangling with a chap who seems to be pushing some kind of nonsense to me about relativity. This fellow, Mitch McKain, seems to push himself as some kind of physics expert there (he says he "teaches online", whatever that means) and he does seem to understand some relativity, but he seems to be explaining things in a really weird way that doesn't make sense.

So, I wanted to come check with some of you to see if anyone here can translate just what the hell he's talking about, because from what I know of relativity (though I'm no expert) this just seems like word salad to me...

In the OP he states the following:



That first line is what is troubling me. So I challenged him on it, and he responded thusly...



Can anyone here who has more knowledge of the subject please shed some light on just what the hell he's talking about, or is my initial suspicion correct and he's completely full of crap?

Thanks in advance!

Cheers - MM

He's correct in that from the point of view of light, light travels at an infinite speed. A way to see this is to put yourself on the "crest" of a lightwave. You leave on the crest and arrive at your destination still on the same crest. In order for that to happen, in your frame of reference no time at all must have passed-- the light wave didn't have a chance to "wave". Covering a distance in no time requires infinite speed. Not useful of course since traveling along with light is impossible.

 

[MattusMaximus]

At least some of his comments make almost-sense if you assume that he's just confusing proper speed aka celerity, dx/dτ, with, uh, actual speed, dx/dt.

And by proper speed you mean the speed as measured from the frame of reference at rest wrt the observer, yes? And celerity is the speed as measured from another reference frame? Just trying to really pin things down here. Thanks, btw!

 

[Twiler]

Wouldn't an infinite speed imply movement in no time, i.e. instant movement?

So, the speed of light can't be infinite in that sense, or 'light-year' would be meaningless.

 

[MattusMaximus]

He's correct in that from the point of view of light, light travels at an infinite speed. A way to see this is to put yourself on the "crest" of a lightwave. You leave on the crest and arrive at your destination still on the same crest. In order for that to happen, in your frame of reference no time at all must have passed-- the light wave didn't have a chance to "wave". Covering a distance in no time requires infinite speed. Not useful of course since traveling along with light is impossible.

Yes, this is what I was wondering. I suspected that he was getting at this, but he never bothered to mention it in the discussion (or, at least, he didn't clarify it very well).

He also said something else which confused me. He has stated on numerous occasions that within a particular frame of reference that the speed of light doesn't act like a barrier and that there is no limit on how fast one can travel in a particular frame (at least, he made it sound that way). Again, I'm wondering if he really knows what he's talking about and he's explaining it poorly, or if he's just making stuff up.

 

[MattusMaximus]

Wouldn't an infinite speed imply movement in no time, i.e. instant movement?

So, the speed of light can't be infinite in that sense, or 'light-year' would be meaningless.

Yes, but as was pointed out above, this only makes sense in the context of things viewed from a photon's frame of reference.

 

[MattusMaximus]

Incidentally, one other thing he said which tweaked me was that he felt no need to introduce people to the concept of a frame of reference when talking about relativity because they wouldn't necessarily have the mathematics background to understand it all. It seems to me that is a very stupid way to approach the subject, since frames of reference underlie the entire subject, and I know how to teach the concept in a very non-mathematical manner.

This would also make sense (that is, his avoidance of frames of reference) given his apparent refusal to clarify that he seems to be talking about things from the reference frame of photons. Really damn sloppy, if you ask me, especially because he claims to be teaching relativity online.

 

[sol invictus]

This part "the speed of light in our universe is like an infinite speed. No it is not an infinite velocity" is particularly alarming. Speed is defined to be the magnitude of velocity. So how can the speed be infinite, but not the velocity?

Anyway, the speed of light is obviously not infinite, it's c - it takes finite time for light to go from point A to point B.

 

[sol invictus]

He's correct in that from the point of view of light, light travels at an infinite speed. A way to see this is to put yourself on the "crest" of a lightwave. You leave on the crest and arrive at your destination still on the same crest. In order for that to happen, in your frame of reference no time at all must have passed-- the light wave didn't have a chance to "wave". Covering a distance in no time requires infinite speed. Not useful of course since traveling along with light is impossible.

It's true that no time passes - but in the reference frame of the light that's because the distance is Lorentz contracted to zero, not because the speed is infinite.

 

[Vorpal]

And by proper speed you mean the speed as measured from the frame of reference at rest wrt the observer, yes? And celerity is the speed as measured from another reference frame?

It's analogous to proper acceleration, d²x/dτ², which is the acceleration a particle would measure with an accelerometer, but as a speed, it's kind of a bastard offspring, being observer-distance per traveler-time. Physically, it would be momentum per unit mass, dx/dτ = (dt/dτ)(dx/dt) = γv, which does go to infinity as v→c.

Mind, part of his argument is rather incomprehensible to me, so I'm not sure if that's what he's doing or not. Parts of it are sort of right: you can cover any distance in arbitrarily small amount of your time by accelerating sufficiently near c because you'll be time-dilated ("at that speed you could go anywhere in no time at all"), which is suggestive of celerity. Considering it "infinite" is as well. Going above lightspeed/infinite celerity does make you go backwards in time in some inertial frame, too.

But despite rattling off a bunch of statements that make some sense individually, there doesn't seem to be a coherent argument. "The problem is that it is space-time" doesn't actually imply anything (why not Galilean spacetime?). So at best it's a very strange repackaging of relativity rather than a derivation: you can't go faster than lightspeed because it is "'infinite'" but it is "'infinite'" because of relativity.

 

[Pulvinar]

Yes, this is what I was wondering. I suspected that he was getting at this, but he never bothered to mention it in the discussion (or, at least, he didn't clarify it very well).

He also said something else which confused me. He has stated on numerous occasions that within a particular frame of reference that the speed of light doesn't act like a barrier and that there is no limit on how fast one can travel in a particular frame (at least, he made it sound that way). Again, I'm wondering if he really knows what he's talking about and he's explaining it poorly, or if he's just making stuff up.

Well it is true if you're always measuring your own speed. No matter how much you accelerate you never reach a barrier (other than running out of means to accelerate more). Nothing like crossing the sound barrier in air. From other frames you appear to make less and less progress as you approach the speed of light.

 

[mike3]

This part "the speed of light in our universe is like an infinite speed. No it is not an infinite velocity" is particularly alarming. Speed is defined to be the magnitude of velocity. So how can the speed be infinite, but not the velocity?

Anyway, the speed of light is obviously not infinite, it's c - it takes finite time for light to go from point A to point B.

But he said it is "LIKE" an infinite speed, not that it "IS" an infinite speed.

 

[sol invictus]

But he said it is "LIKE" an infinite speed, not that it "IS" an infinite speed.

It's "like" an infinite speed only in that you arrive at a seemingly distant destination in zero time. But as I said, that's not because the speed is large - it's because the distance is small (it gets Lorentz contracted in your rest frame).

The two explanations aren't the same. For instance, objects will get distorted because they are Lorentz contracted in one direction but not in the other two - and that wouldn't happen if it were just a matter of going very fast.

So it's really not at all like infinite speed.

 

[MattusMaximus]

But he said it is "LIKE" an infinite speed, not that it "IS" an infinite speed.

Actually, in the beginning he said it WAS an infinite speed, and he only changed it to "like" an infinite speed after I pinned him down on it. Then he dismissed the difference as being irrelevant.

 

[MattusMaximus]

At least some of his comments make almost-sense if you assume that he's just confusing proper speed aka celerity, dx/dτ, with, uh, actual speed, dx/dt.

Vorpal, here is Mitch's response to what you said...

I am not confused about the difference here in the slightest. I was simply speaking to a different audience who would not know the difference between these things. The question I wonder about is whether maximus knows the difference between these two things since he didn't respond to my questions about proper time which is what that funny looking t or greek letter tau stands for.

When I am talking about the speed of light being like an infinite speed I am certainly talking a speed with respect to proper time and it is interesting to hear that there is a relevant term, "celerity" (no matter how rarely used) defined as gamma times velocity, which rapidly approaches gamma in light units (such as light years per year). This is a quantity that does indeed go to infinity as the velocity approaches the speed of light, and it is in same units as a velocity. In these terms my point would be that celerity would be much more like what many people would think of as a speed because that is the quantity that is relevant to how quickly you can get to a destination as YOU measure time.

Btw folks, Mitch has agreed to come over to this Forum to join in. I'm looking forward to the ensuing discussion

 

[Roboramma]

Actually, in the beginning he said it WAS an infinite speed, and he only changed it to "like" an infinite speed after I pinned him down on it. Then he dismissed the difference as being irrelevant.

It's interesting that he points out the importance of mathematics in understanding relativity. Given that, if the speed were infinite he should be able to derive that mathematically.

He seems to be saying something like this:

I am on the earth and I look off at a distant galaxy, millions of light years away. Given that it's millions of light years away, it should take at least millions of years to get there. But I get in my spaceship, accelerate to extremely close to the speed of light, and somehow, in an arbitrarily short period of time, I've arrived at my destination. Maybe it took me a year or a month or a day, but that's only dependent upon how close to the speed of light I got. Thus, since I can cover any distance in an arbitrarily short period of time by approaching the speed of light, that speed must be infinite.

This completely ignores what actually accounts for that fact: that it's not the speed that is potentially infinite, but the distance that is potentially infinitesimal. And if he were willing to look at the lorentz contraction he would see that.

In other words, when doing his analysis of what's going on he take the distance in one frame (the rest frame before I set out) and the time in another (the frame after I've accelerated) and uses them to compute the velocity (infinite! Or at least, arbitrarily large!). This is completely contrary to relativity: you can use any reference frame, but you can't just switch between them. If you could, you could literally get any value for anything. I could show that the speed is zero.*

*Start out in a reference frame near the speed of light toward the destination and then decelerate to a frame at rest with respect to the journey's origin. The distance begins at zero (or arbitrarily close to it). Use that distance. Now, how long does the journey take? Let's look in my rest frame with respect to the origin: millions of years! Thus, the time it takes to go 0 meters is millions of years. That's 0m/millions of years = 0 m/s.
The moral of the story is that if you switch reference frames midway through your examination, you can end up with any result you choose.

 

[MattusMaximus]

To be fair to Mitch, I think he is taking into account Lorentz contraction, but he seems to keep wanting to cling to this notion of infinite speed. My primary criticism of him all along hinges on his use of terminology, which seems quite confusing.

 

[Vorpal]

But you can formalize it mathematically quite easily. All he seems to be doing is taking the spatial part of the four-velocity and mistakenly calling it "velocity" and its magnitude "speed" (which is really specific momentum). Other than a conflation of vocabulary, the entirety of special relativity for massive particles can obviously be put in those terms, since normalization of four-velocity means this "velocity" uniquely determines the four-velocity.

The point of this and the rest of the argument is still impenetrable to me, though.

 

[MattusMaximus]

Well it is true if you're always measuring your own speed. No matter how much you accelerate you never reach a barrier (other than running out of means to accelerate more). Nothing like crossing the sound barrier in air. From other frames you appear to make less and less progress as you approach the speed of light.

But this seems to imply that within a given frame you can measure your own speed as greater than c, since there is no limit on your speed. I thought that went completely against special relativity. Am I missing something?