Can an imminent laser strike ever be observable?

[davidjoe]

Some of your difficulty with relativity may come from not fully appreciating how this description is incorrect (or more precisely, includes a hidden assumption that is incorrect). It makes no sense to talk about the speed of the ship being more or less than the speed of the missile - all we can talk about is the speed of the ship relative to the missile and its negative, which will be the speed of the missile relative to the ship.

The missile is introduced only to illustrate a certain contrast.

Neither your ship nor the missile can attain light speed but are not prevented from traveling just under it.

The purpose of the missile is simply to relate that an object ever-so-close to the speed C, can be in your view eternally, basically.

However, add that tiniest additional speed, the delta between the missile and light, which brings to bear the laser, and now that thinnest of differences in velocity results in seeing a velocity difference of, the speed of light.

In the first thread I posted, if I remember correctly, many pages over many days, it was stated by a member that we no longer use infinite mass in relativity to represent what happens to matter at light speed. But I believe in AE’s time, infinite quantity may have been a nonnegotiable.

To my mind’s thinking, if infinite mass is problem, and I for one think so, (and have since school) such a distinct line between two particular speeds that are virtually identical, may also be.

 

[davidjoe]

Well yes, that is a claim, but so is the claim that there is only one natural number $N$ such that $2+2=N$. That claim is backed up by a mathematical proof starting from the axioms of number theory, but of course you don't need a lot of advanced mathematics to satisfy yourself that $2+2=4$ and never anything else.

Likewise it has been mathematically proven that either there is no invariant speed, or if there is, then there is exactly one. And likewise, you don't need the math to satisfy yourself of this - just assume that there are two, play around with various objects moving at various speeds relative to one another and greater or less than one or both of your hypothetical invariant speeds, and you will quickly arrive at a contradiction.

So the question has always been whether there is no invariant speed, in which case we have Galilean relativity and velocities add as $w=u+v$; or there is one invariant speed, in which case we have Einstein's relativity and velocities add according to $w=(u+v)/(1+uv)$. (And note that the "very specific speed" doesn't show up in this formula at all because I've sensibly chosen units in which the invariant speed is unity).

It's actually something of an accident of history that we call the invariant speed "the speed of light" and represent it with the same symbol $c$ that we used for the measured speed of light. A more modern view would be that there is an invariant speed and the interesting question about light speed is whether light moves at that speed, or at some speed so close to it that our most sensitive measurements have been unable to find any difference.

To your last paragraph, the only logical answer is that the particular “speed” is what is invariant, not what speed light goes, in my opinion. Particularly, again my opinion, it’s that speed which represents 100% of that which is attainable, and it happens to be that electromagnetic radiation fills that position, alone.

 

[PeterDonis]

@davidjoe in 91 posts you have not shown a single line of math. Without math you are just waving your hands, and nobody else can have any precise understanding of what you are talking about. Physics is not done in vague ordinary language. It's done in math.

Here's what the math you need to do should include: pick an inertial frame (the easiest would be the one in which the laser's target is at rest, but if you prefer to use one in which the target is moving at 0.99999c, be my guest, the laws of physics are invariant); write down the equation of the worldline of the laser pulse and the equation of the worldline of the target; find where they intersect; and then search for any path from anywhere on the laser pulse worldline that (a) is not spacelike, and (b) intersects the target worldline before the laser pulse worldline does. After you have failed at enough attempts to find such a path, perhaps you will see why it is impossible. But you will not see it by continuing to concoct more and more complicated assemblages of vague ordinary language.

 

[PeterDonis]

the only logical answer is that the particular “speed” is what is invariant, not what speed light goes, in my opinion.

This is quite correct--and entirely irrelevant to the question you are struggling with in this thread.

 

[Nugatory]

However, add that tiniest additional speed, the delta between the missile and light, which brings to bear the laser, and now that thinnest of differences in velocity results in seeing a velocity difference of, the speed of light.

Are you confusing the closing speed between two things with the velocities of the two things?

I consider myself to be at rest. A ship passes me moving at speed .99999c.

That ship emits a flash of light in the direction of its travel. I will measure (the question of how I perform these measurements is irrelevant here, but also not trivial) that the flash of light is moving at speed c relative to me. I will measure that the flash of light is gaining on the ship at speed .00001c, calculated by subtracting the forward speed of the ship from the forward speed of the light.

The ship also launches a missile in the direction of travel. Say that this missile moves at speed .5c (relative to its launcher, of course). I will measure its speed to be .9999967c. So how fast is the light gaining on the missile? It's .0000033c, the forward speed of the light minus the forwards speed of the missile. How fast is the missile gaining on the ship? It's the forward speed of the missile minus the forward speed of the ship.

So we aren't treating the speed of light differently here - it adds and subtracts just like the subluminal speeds of the ship and the missile. Relativistic corrections only come in when we add speeds measured in different frame (here the .5c of the missile using a frame in which the ship is at rest and the .99999c speed of the ship using a frame in which I am rest); then we must use the relativistic velocity addition formula which also does not treat the speed of a flash of light differently than the speed of anything else.

 

[davidjoe]

I’ll come back. Client stuff.

 

[sophiecentaur]

The final step up could be an inch a year, or infinitely smaller than that.

The missile is introduced only to illustrate a certain contrast.

To your last paragraph, the only logical answer is that the particular “speed” is what is invariant, not what speed light goes, in my opinion. Particularly, again my opinion, it’s that speed which represents 100% of that which is attainable, and it happens to be that electromagnetic radiation fills that position, alone.

You really are desperate not to be wrong. But you are. No amount of analogies and arm waving will make Einstein's Special Relativity fit your daft idea. Learn some maths and then read Einstein's own Book on Special Relativity. It is not hard to follow what he says (if you are not convinced he's wrong.

 

[Nugatory]

To your last paragraph, the only logical answer is that the particular “speed” is what is invariant, not what speed light goes, in my opinion. Particularly, again my opinion, it’s that speed which represents 100% of that which is attainable, and it happens to be that electromagnetic radiation fills that position, alone.

If by "that speed" you mean the invariant velocity, then yes, of course, everyone has understood that for many decades.
It's a distinction without a difference though, if light also moves at that invariant speed and there are many good reasons to think that it does.
One hand-waving but fairly convincing argument is that we can calculate the speed of light directly from the laws of electricity and magnetism; these laws are the same in all frames so yield the same speed in all frames. So we expect that the speed of light will be invariant, and we've established by other means that there can be only one invariant speed, so we conclude that either something is wrong with our understanding of E&M or the speed of light and the invariant speed are necessarily the same.

Note 1: The invariant velocity shows up in contexts other than electromagnetic waves. Gravitational waves propagate at that speed, and it is a key element of relativistic quantum field theories, even though these have nothing that we would recognize as a "speed".

Note 2: Were it to turn out that light does not move at the invariant velocity, the metrologists would have to look long and hard at the definition of the meter. We wouldn't have taken this chance if there was any realistic possibility of this happening.

 

[davidjoe]

We will be talking.

 

[Nugatory]

Learn some maths and then read Einstein's own Book on Special Relativity. It is not hard to follow what he says (if you are not convinced he's wrong.

@davidjoe, you should also try a more modern textbook. This is an “as well as” not an “instead of” recommendation (although if you’re only going to do one, it should be the modern one), and Taylor and Wheeler’s “Spacetime Physics” which is available free from https://www.eftaylor.com/spacetimephysics/ is my first choice.

Einstein developed special relativity 120 years ago starting with the perspective of a turn-of-the-last-century physicist, as opposed to that of a motivated 21st century student. Since then generations of physicists have built on that work, corrected some wrong turns, and starting with Hermann Minkowski enormously strengthened and simplified the presentation of the underlying principles.

 

[ohwilleke]

While it is a military consideration rather than a physics consideration, often prior to firing a laser that would blast you out of the universe, there would be light other than the killing laser itself that would be emitted as the laser device warms up to fire, that would be visible briefly before the laser that is fired itself arrives.

 

[davidjoe]

While it is a military consideration rather than a physics consideration, often prior to firing a laser that would blast you out of the universe, there would be light other than the killing laser itself that would be emitted as the laser device warms up to fire, that would be visible briefly before the laser that is fired itself arrives.

Actually, I can feel the infrared glow of incoming fire love missives even before the “post reply” button gets hit. AE was a really likable, humble man. I’m that far in.

 

[berkeman]

Nonsense thread is closed for Moderation...

Update -- thread is not working in either the SciFi forum or the technical forums, so it will remain closed.