The difference is that light travels through space, but not time (similar to how a vertical line does not travel the x axis, only the y axis). The ball travels through both space and time.
The faster you go, the less you travel through time. Thus, if the ball were travelling at the speed of light, it would not travel through time either and would follow the same path as light.
> The difference is that light travels through space, but not time
This is a common pop science statement, but it's not correct. A correct statement is that the concept of "speed through spacetime", which is what has to be split into "speed through space" and "speed through time" in the pop science statement, does not apply to a light ray.
In more technical language, the tangent vector to the light ray's worldline is not a unit vector, it's a null vector, and the concept of "speed through spacetime" only makes sense for a worldline whose tangent vector is a unit vector.
> From the point of view of a photon, no time elapses between its the origin and destination endpoints.
No, this is not correct. The correct statement is that the concept of "elapsed time" does not apply to a photon; it only applies to timelike worldlines, not null worldlines.
To put it another way, if your statement were true, it would mean that the origin and destination events were the same point in spacetime. But they're not; they're distinct points in spacetime. Which means that, since the spacetime interval along the worldline is zero, you can't use the interval to distinguish points on the photon's worldline. And the concept of "elapsed time" requires that you be able to do that. So the concept of "elapsed time" can't be used for a photon.
It's impossible for an object with mass to go the speed of light. But you can observe what happens as you approach it:
Let's say I put you in a spaceship and accelerate you to 50% the speed of light toward the sun. From an inertial viewer's perspective you are travelling toward the sun at half the speed of light and it takes you ~16 minutes to crash into the sun. But from your perspective it only took ~14 minutes to crash into the sun[0].
Repeat the experiment except I accelerate you to .99c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took ~1 minute to crash into the sun.
Repeat the experiment except I accelerate you to .999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 20 seconds to crash into the sun.
Repeat the experiment except I accelerate you to .9999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 6 seconds to crash into the sun.
Repeat the experiment except I accelerate you to .99999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 2 seconds to crash into the sun.
See what's happening? As you approach the speed of light, the amount of time that elapses until you reach your destination approaches zero. So from an inertial observer's point of view, time has completely frozen for travelers approaching light speed.
Yes, but you cannot extrapolate from this to say that the time lapse for a photon would be zero. A photon is not the limit of objects with mass going closer and closer to the speed of light, because "closer and closer to the speed of light" is frame-dependent, but a photon's speed being c is not. I can find an inertial frame in which each of your objects is at rest, and in that frame, you are the one who is "close to c" (in the opposite direction). But that doesn't mean your elapsed time approaches zero. By contrast, it is impossible to find any frame in which a photon is at rest. The two types of objects are fundamentally different.
In more technical language, the action of Lorentz transformations on photons is fundamentally different from their action on timelike objects. So it is simply not valid to view photons as some sort of limit "as speed approaches c" of timelike objects.
>> In more technical language, the action of Lorentz transformations on photons is fundamentally different from their action on timelike objects.
I don't believe that, and have never heard it before. There are many ways in which light actually behaves just like particles with mass traveling at speed c. It has to or conservation of momentum is violated.
But is there any physical way to distinguish these fundamentally different situations? If not, then perhaps the fundamentalness of it is just an artifact of the formulation.
I'm thinking of solar neutrinos which, for a while, we weren't sure if they were massless or not. We had to observe them experiencing a duration of time to conclude they were massive. If we didn't find that, maybe it was just an even shorter duration, not the absence of one and we would never be able to tell the difference.
> is there any physical way to distinguish these fundamentally different situations?
Are you asking if there is a way to distinguish a timelike object from a lightlike object? Of course there is. The fact that, for something that has a very, very small invariant mass, it might be practically difficult does not change the fundamental principle.
Also note that the reason it was difficult, for example, to tell whether neutrinos have mass or not is that we can't just do the obvious and straightforward thing and find an inertial frame in which they are at rest (by, for example, taking a rocket and accelerating it in the direction of a neutrino to see if we can bring it to rest relative to the rocket). So we have to resort to indirect methods. But, again, that's a practical limitation that doesn't change the fundamental principle.
It still doesn't sound physically distinct any more than distinguishing any continuous quantity as being zero or nonzero. If we measure something that looks like 0, we can't be sure if it's just below the sensitivity of our instruments.
For neutrinos, even if we accelerated an rocket and somehow checked if a neutrino was at rest relative to it, we might find that it's not. That means we won't know if we need more speed or if it's impossible. I suppose it's a bit easier than that because we only have to accelerate the rocket fast enough that the neutrino's speed becomes measurably less than c, rather than 0. But still, what if we can't even get it to go fast enough for that? No way to prove that it's travelling at c, it seems.
I'd like to add that even photons have a nonzero upper bound to their possible rest mass. At least they used to. Is there any way, in principle, to show that it's exactly zero, and thus falls into this distinct category?
If you try what I described with a light ray, it will be moving away from you at c no matter how much you accelerate in its direction.
If you try it with a massive object, even a neutrino with a very, very tiny invariant mass, that will not be the case; its speed relative to you will decrease as you accelerate after it, eventually to zero.
There is no continuum between those two possibilities; they are distinct and discrete. The only continuum is in the latter case, where the final speed of the object relative to you will depend continuously on how long you accelerate.
> even if we accelerated an rocket and somehow checked if a neutrino was at rest relative to it, we might find that it's not. That means we won't know if we need more speed or if it's impossible
Yes, you will know, because you will know if the neutrino's speed relative to you has decreased or not. If it has, it's possible to bring it to rest relative to you. If it hasn't, it's not. See above.
> I suppose it's a bit easier than that because we only have to accelerate the rocket fast enough that the neutrino's speed becomes measurably less than c, rather than 0.
Exactly.
> But still, what if we can't even get it to go fast enough for that?
That's basically the position we are in now: we have no way of building a rocket or other device that can accelerate after a neutrino long enough to tell whether its speed relative to the rocket is measurably decreasing. So we have to resort to indirect measurements. But as I said before, that doesn't change the principle.
> even photons have a nonzero upper bound to their possible rest mass
Yes, because, as I said, practically speaking we can't run the obvious and straightforward experiment I described, to confirm that a photon moves away from you at c no matter how much you accelerate after it. So we have to resort to indirect measurements, like trying to measure its invariant mass by other means. But that doesn't change the principle.
> Yes, you will know, because you will know if the neutrino's speed relative to you has decreased or not. If it has, it's possible to bring it to rest relative to you. If it hasn't, it's not. See above.
I don't think this quite works because of relativistic addition of velocities. Naively, it seems to. For example, if the object was travelling at 0.999999c relative to you (appears to be 1.0c according to your limited instruments), then you accelerate to 0.50c in its direction, you'd see its speed reduce to 0.50c (same 2s.f. instrument), which would clearly prove it's not massless. But velocities don't add like that relativistically and I think you'd still see it as travelling at 1.0c because it only decreased a tiny amount, below what you instrument can detect. If you use a more precise instrument or a faster rocket, you might measure it as 1.00000c but then you still won't know if it's exactly c or a smidgen less.
Maybe I've got my relativistic velocity addition wrong? But it still looks like the same measurement problem as trying to prove a classical object has a speed of exactly 0, which can't be done no matter how accurate our instruments are.
So if your accuracy is, say, 1 part in 100,000, you wouldn't be able to see the difference. But with an accuracy of 1 part in 500,000, you would, even though you wouldn't have been able to see the difference before the acceleration.
Also, suppose you accelerated for a second increment equal to the first; you would get
As you can see, the differences in velocity grow fairly quickly for each equal increment of acceleration; the growth is not at all linear. And, as I said in my other post just now, for any given measurement accuracy, it would be simple to calculate how much acceleration you would need to be able to distinguish moving at exactly c from moving at 0.999999c (or any other speed less than c that you choose) to that accuracy.
> velocities don't add like that relativistically and I think you'd still see it as travelling at 1.0c
Not indefinitely. Sure, if you accelerated for a short enough time in the direction of the neutrino, you might still be within your measurement error and so not have learned anything. But that just means you need to accelerate for a longer time. For any given measurement accuracy, you will be able to calculate how long you need to accelerate, by your clock, to definitely distinguish the two cases. Relativistic velocity addition does not change that fact. All it changes is the details of that calculation; yes, for a given measurement accuracy, you need to accelerate for a longer time, by your clock, to definitely distinguish the cases than you would if velocity addition were linear. But that doesn't mean relativistic velocity addition makes it impossible to distinguish the cases at all, ever. It doesn't.
With neutrinos we might find that it's not but it'd be impossible to catch a photon as it would always have the same speed of c in our reference frame.
> I'd like to add that even photons have a nonzero upper bound to their possible rest mass. At least they used to.
Not sure what you're talking about, their momentum?
No object with mass can reach the speed of light and we know they're travelling at that exact speed.
How do we know they're travelling at exactly c? That's my concern. Last I heard, a couple of decades ago, physicists would occasionally measure a new maximum possible rest-mass for photons. It would be very tiny, of course, but they couldn't say it's exactly zero.
> How do we know they're travelling at exactly c? That's my concern.
We don't, strictly speaking. The measurements you refer to aren't even measuring the speed of photons. They're measuring their rest mass.
> physicists would occasionally measure a new maximum possible rest-mass for photons. It would be very tiny, of course, but they couldn't say it's exactly zero.
Based on just those measurements, no. The most they can say is that the photon rest mass is zero to within some error bar, and the size of the error bar keeps getting smaller. (The current error bar, IIRC, is 10^-52 grams, or about 24 orders of magnitude smaller than the electron mass.)
However, we have a ton of indirect evidence that photons are massless; the most extensive body of such evidence is all the evidence for the gauge invariance of electromagnetism. If photons had a nonzero rest mass, that would break electromagnetic gauge invariance. So photons having a nonzero rest mass would be a huge issue for our current theories, in the way that neutrinos having a nonzero rest mass would not; there is no important symmetry coresponding to electromagnetic gauge invariance that is broken by neutrinos having a nonzero rest mass.
Show me an actual textbook or peer-reviewed paper Tyson has written where he makes this claim. Pop science videos don't count. (Tyson is by no means the only one; Brian Greene is notorious for the same thing.)
You won't be able to because there aren't any. No scientist who talks about a photon "experiencing zero time" in informal contexts will try it in a textbook or paper. That's because they know that if they did, other scientists would call them out on it, so they confine such claims to contexts where there are no other experts so there's nobody to call bullshit.
Another point is that if this concept were actually scientifically useful, somebody would be using it in a textbook or peer-reviewed paper. The fact that nobody is is a huge clue that the concept is not scientifically useful. It's only useful for selling pop science books or getting views of pop science videos, where, again, there are no other experts around.
Dude, this is basic theory at the high school level. Here's how it works: spacetime is 4-dimensional, and a vector in spacetime is always c units long. You can restrict your travel solely to X, Y, Z, or time if you like. If you do that, the other three components are going to be zero.
Photons put it all into the X, Y, and Z components, leaving nothing for the t component. They experience a change of position in space, but not in time. What's so hard to grasp about this?
Another point is that if this concept were actually scientifically useful, somebody would be using it in a textbook or peer-reviewed paper.
Seems that a fellow named Maxwell got a lot of mileage out of the concept, even if he didn't know what was really going on.
> Dude, this is basic theory at the high school level.
No, Tyson's claim is not "basic theory at the high school level". It is a particular interpretation of a theory (Special Relativity) that does not work, for the reasons I gave.
> Photons put it all into the X, Y, and Z components, leaving nothing for the t component.
Wrong. The spacetime vector that describes a photon's trajectory does have a t component.
> Seems that a fellow named Maxwell got a lot of mileage out of the concept
Dude, if you think the concept Tyson described is the same as the concept that Maxwell got a lot of mileage out of, then you are the one who needs to learn more about "how it works".
Again, take it up with Tyson and others with doctoral-level credentials who've made a career out of explaining these subjects to the unwashed laity. I'm not one of those people. Nobody posting on Hacker News is, as far as can be discerned.
If you and others in the thread feel that these popular authorities are spreading misinformation or using inappropriate analogies, doesn't it behoove you to raise an objection with them directly? Or perhaps with the appropriate faculty committees at their institutions?
> If you and others in the thread feel that these popular authorities are spreading misinformation or using inappropriate analogies, doesn't it behoove you to raise an objection with them directly?
If they want to make money by getting "the unwashed laity" to buy their books, why should I stop them? I simply don't buy them myself. If other people want to get told comforting nonsense, that's their problem. Caveat lector.
> Or perhaps with the appropriate faculty committees at their institutions?
Which would be pointless and absurd, since, as I have already said, the claims in question are not being made in textbooks and peer-reviewed papers.
The faster you go, the less you travel through time. Thus, if the ball were travelling at the speed of light, it would not travel through time either and would follow the same path as light.