stupid physics questions

[Dio]

You can have closing velocities up to 2c measured by an independent oberver. But stand on either particle and A. you can't tell how fast you are moving and B. the other approaches at less than c. (Because of the distortion of time, if you like; you are moving so fast that the other thing is coming towards you more slowly because time is passing quicker).

[pogo]

You can have closing velocities up to 2c measured by an independent oberver. But stand on either particle and A. you can't tell how fast you are moving and B. the other approaches at less than c. (Because of the distortion of time, if you like; you are moving so fast that the other thing is coming towards you more slowly because time is passing quicker).

You can say that, but it is meaningless: there is no velocity of or approaching 2c in our universe. You only get that from naïvely adding the velocities as in Galilean physics, but you just can’t do that as Galilean physics gets less and less applicable the closer you get to the speed of light.

This is not just of theoretical interest. If the particles were electrons moving at near light-speed (in a particle accelerator say) and collide head-on then the collision velocity is larger than if only one were moving, and the collision releases more energy. But their relative velocity, i.e. the velocity of one relative to the other, the closing velocity of one on the other, is still less than c.

[Dio]

This is not just of theoretical interest. If the particles were electrons moving at near light-speed (in a particle accelerator say) and collide head-on then the collision velocity is larger than if only one were moving, and the collision releases more energy. But their relative velocity, i.e. the velocity of one relative to the other, the closing velocity of one on the other, is still less than c.

Yes. The velocity of one relative to the other is < c and that's what matters in determining the energy of the impact.

But a stationary observer watching the collision observes the particles closing upon each other at 2c. Indeed, that's the case in the LHC. You know the collision is going to happen at a given time, and that time relies on both beams approaching the target point from opposite directions at c. So the closing velocity is nearly 2c.

(Or you could note that "velocity is a vector quantity").

[toxibunny]

Righto, I get it now. You're never going to 'see' anything coming towards you at anything appreciably over the speed of light because: a) You can't 'see' anything under that condition, and b) even if you somehow could, you'd have to be travelling at an appreciable fraction of the speed of light, which would mess with time and kindof factor things down so you'd never observe anything moving faster than the speed of light anyway.

[pogo]

I’d still say its meaningless. Yes, you can calculate “closing velocity” by adding two speeds which are in opposite directions, to get one speed. But it only works in the classical sense. Only there can you add two speeds to get a larger speed, by ignoring relativistic effects, to get a result is only accurate at low speeds, well below the speed of light. It gets less and less accurate as you approach the speed of light, and breaks down completely at the speed of light.

The name is I think a clue. If you are calculating a “closing velocity”, so treating it as a velocity, you need to be summing velocities. Just adding speeds in opposite directions won’t work, they will cancel out. So you only get a meaningful answer if you work in the frame of reference of one of the bodies, or particles. And there, in that frame of reference, everything is limited to light speed or below.

Every time you add velocities you should use the formula I posted above:

When velocities are non-reletavistic you can just add them as the vu / c^2 term is negligible. But with speeds close to c the term comes into play, limiting the result to the speed of light.

[KlaxonCow]

The way I think of it is that the speed of light is the universal reference. That's the bit that never changes and is always the same in all reference frames.

Everything else is subservient to that, so spacetime will slow down and distort, in order that the speed of light remains constant.

That's why there's no such thing as a universal reference frame and it's all relative.

What's it relative to? The speed of light!

That's the bit that's universal and never changes and is always the same in every reference frame. It's everything else - time and space - that slows down and distorts, so as to make this true.

(Well, phrasing it as "so as to make this true" is perhaps misleading, as the logic is backwards there. It's not time and space actively making this true, it's just true - a universal truth - and the nature of time and space conforms to that truth. Because, well, true things are true. Anyway, you get the gist. Don't think about spacetime as the solid thing with light flowing through it. Light actually is the universal thing here and it's spacetime that's the thing flowing and distorting around it.)

[zip accident]

A bit of history, this popped from reading about photon's energy being dependent on wavelength which if high enough means the it'd collapse into a black hole. But the wavelength / energy isn't absolute, it's dependent on difference of inertial frames.

Photon energy depends on frequency; the ratio of the two is Plank’s constant. And of course energy and mass are related by Einstein’s famous formula.

Could you therefore have a photon with high enough frequency that it gains a mass to form a black hole? In theory, until you realise that the numbers involved are so ridiculous that no plausible photon could come close.

I think this is mistaken, I mentioned small black holes evaporating in Hawking radiation, and I believe it's the case that as the mass of a black hole approaches zero, the black body temperature approaches infinity. Therefore, coming out of an exploding black hole, there ought to be photons with the energy to decay to black holes and in turn explode into multiple less energetic photons.

The way I think of it is that the speed of light is the universal reference. That's the bit that never changes and is always the same in all reference frames.

Everything else is subservient to that, so spacetime will slow down and distort, in order that the speed of light remains constant.

That's why there's no such thing as a universal reference frame and it's all relative.

What's it relative to? The speed of light!

That's the bit that's universal and never changes and is always the same in every reference frame. It's everything else - time and space - that slows down and distorts, so as to make this true.

(Well, phrasing it as "so as to make this true" is perhaps misleading, as the logic is backwards there. It's not time and space actively making this true, it's just true - a universal truth - and the nature of time and space conforms to that truth. Because, well, true things are true. Anyway, you get the gist. Don't think about spacetime as the solid thing with light flowing through it. Light actually is the universal thing here and it's spacetime that's the thing flowing and distorting around it.)

However, the speed of light being constant is also a frame of reference. You could have space-time being constant, and a variable speed of light, that's just another way of looking at it. A constant speed of light makes for easier maths, but it's not itself anything other than a way of looking at things.

[KlaxonCow]

However, the speed of light being constant is also a frame of reference. You could have space-time being constant, and a variable speed of light, that's just another way of looking at it. A constant speed of light makes for easier maths, but it's not itself anything other than a way of looking at things.

Indeed. Relativity and all that jazz.

I did open that post with "The way I think of it is..." to make clear that I'm just giving one possible way of looking at things that I feel makes it easier to understand, whilst implicitly signposting that, well, the way I think of it isn't necessarily the way other people think of it.

I was just giving folks a way of looking at things. My way of looking at things. There are other ways also, of course, and "your mileage may vary".

[gravy]

A bit of history, this popped from reading about photon's energy being dependent on wavelength which if high enough means the it'd collapse into a black hole. But the wavelength / energy isn't absolute, it's dependent on difference of inertial frames.

Photon energy depends on frequency; the ratio of the two is Plank’s constant. And of course energy and mass are related by Einstein’s famous formula.

Could you therefore have a photon with high enough frequency that it gains a mass to form a black hole? In theory, until you realise that the numbers involved are so ridiculous that no plausible photon could come close.

I think this is mistaken, I mentioned small black holes evaporating in Hawking radiation, and I believe it's the case that as the mass of a black hole approaches zero, the black body temperature approaches infinity. Therefore, coming out of an exploding black hole, there ought to be photons with the energy to decay to black holes and in turn explode into multiple less energetic photons.

Hawking radiation is theoretical, its never been detected.

Evaporating black holes are interesting when seen by different observers. A black hole's event horizon size depends on its mass, its observed mass has a dependency on differences between the black hole and observer's inertial frames and the amount of hawking radiation particles emitted depends on the event horizon size.

Which would imply different amounts of hawking depending on whether you were moving to towards or aware from a black hole.

Particles would only exist for one observer and not another. Which is cobblers.

I'm obviously not understanding something right

Here's an interesting relativistic mass paradox I found googling around to get a better understanding:

https://en.wikipedia.org/wiki/Supplee%27s_paradox

[pogo]

I think this is mistaken, I mentioned small black holes evaporating in Hawking radiation, and I believe it's the case that as the mass of a black hole approaches zero, the black body temperature approaches infinity. Therefore, coming out of an exploding black hole, there ought to be photons with the energy to decay to black holes and in turn explode into multiple less energetic photons.

Approaches infinity. But you cannot get infinite energy out of a finite but large mass. As it gives off more and more energy it loses mass more and more quickly, until it has no more to lose and vanishes. Or at least that makes much more sense, given that have never observed or measured Hawking radiation, it is still just a theory.

However, the speed of light being constant is also a frame of reference. You could have space-time being constant, and a variable speed of light, that's just another way of looking at it. A constant speed of light makes for easier maths, but it's not itself anything other than a way of looking at things.

Relativity based on a constant speed of light is the only accepted theory. That’s simply as it is so successful. Not only does it coincide with our repeated measurement of the speed of light, which under other systems should not be constant (e.g. where is the contribution from the Earth rotating and moving through space?) but it has been tested in many other ways and shown to not only be correct but make many testable predictions. In 100+ years it has proven very solid and not in need of modification.

[gravy]

A bit of history, this popped from reading about photon's energy being dependent on wavelength which if high enough means the it'd collapse into a black hole. But the wavelength / energy isn't absolute, it's dependent on difference of inertial frames.

In theory you can boost the frequency of photons by going faster towards them, or their source. The problem with that is it takes energy. Lots of it. Nothing that we know of in the universe goes fast enough. Even going at a significant fraction of the speed of light you achieve a noticeable blueshift but not the many orders of magnitude of frequency shift needed.

Yeah I know. It's why I went for something more tractable, an object on the verge of gravitational collapse so the effect relatavistic mass would have is scaled up. Which brings us back to where I came in.

[KlaxonCow]

In 100+ years it has proven very solid and not in need of modification.

Hey, Newton lasted over 200 years, proving very solid and not in need of modification...

...before Einstein showed up and modified it all, because it wasn't actually quite as solid as first thought.

[zip accident]

Hawking radiation is theoretical, its never been detected.

It's strange stuff. It probably can't be detected from most black holes because there's so little of it, because the holes are big. At just the right/wrong mass they go bang! very fast, they are one of the candidates for the sources of gamma ray bursts, and we don't want to be near one of those.

There had better be Hawking radiation, otherwise when an atomic mass black hole is created in a collider it will not decay in a shower of particles and will fall to the centre of the planet and eat it away.

I've just noticed I remembered the lifetime of a kilogram black hole wrong, it'a not 10^-6 seconds, it's 10^-19 seconds.

[pogo]

In 100+ years it has proven very solid and not in need of modification.

Hey, Newton lasted over 200 years, proving very solid and not in need of modification...

...before Einstein showed up and modified it all, because it wasn't actually quite as solid as first thought.

People knew Newtonian physics was incomplete long before Einstein came along, both for theoretical reasons and due to measurements not agreeing with predictions. That’s why his discoveries were so important, they essentially provided answers to all the questions physicists had been asking for decades. So it’s not just the last 100 years.

Even more importantly the rate of scientific advance in the last century has been phenomenal. Partly driven by Einstein’s discoveries, but more just driven by technology. We can measure things to an unprecedented degree of accuracy to confirm relativity. It’s hardly fair to compare it to the previous 200 years, or however long, when they just did not have the tools to make significant discoveries.

[gumboot]

Evaporating black holes are interesting when seen by different observers. A black hole's event horizon size depends on its mass, its observed mass has a dependency on differences between the black hole and observer's inertial frames and the amount of hawking radiation particles emitted depends on the event horizon size.

Which would imply different amounts of hawking depending on whether you were moving to towards or aware from a black hole.

This doesn't seem to consider time and space distortions, though. You might alter an objects mass by moving it, but its density and event horizon are functions of the shape of the space they occupy and the rate of radiation is a function of time.

I'm not saying these implicitly bring everything to parity, but it's where I'd start looking.