stupid physics questions

[zip accident]

More comment on the LHC from Ars:

http://arstechnica.co.uk/science/2015/1 ... gravitons/

[gravy]

Here's a stupid physics question

[pogo]

No. Various arguments for it, but the easiest is one invoking just special relativity. Consider observer B. C is moving towards them at great speed (in SR there is no absolute frame so you can consider B or C to be at rest). C has a rest mass, an intrinsic mass, which large enough it is “nearly a black hole”. It also has mass due to its motion, it’s relativistic mass. But this does not add to its rest mass; it exists only for observer B. It is e.g. a measure of how much extra energy is needed to accelerate or decelerate C. It is why masses cannot go at the speed of light as the mass and so energy needed converges to infinity as the speed approaches that of light.

But C does not experience this mass increase. In C‘s frame of reference there is no mass increase. C is still almost but not quite a black hole.

This is the only way that makes sense. Every body in the universe is moving with different speeds relative to other things. It clearly cannot have different properties for each of these “observers”. E.g. a planet cannot have different rates of gravity, different geosynchronous orbit heights. A star cannot have a different propensity to explode or collapse into a black hole. These are intrinsic properties, depending only on the rest mass and other properties of the body itself.

[gravy]

You're re-describing the relativistic mass and then saying the duality I descrive can't happen because it doesn't make sense.

Well I know that, it's what I'm saying I'm pointing out a paradox based on my sketchy understanding of relativistic mass. You're just saying it's silly. I know that. I want to know what I've got wrong here in my interpretation

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.

[zip accident]

Here's a stupid physics question

Also to the point, when does B achieve c relative to A? If C is very massive, then B is being accelerated by gravity, which requires no fuel, so B can achieve c, and if it's nearly at c already, presumably does. So what does A see?

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.

That's relatively easy. Small black holes evaporate very fast, a one kg hole evaporates in 10^-6 seconds, which is about the time it takes for a critical mass of fissile material to detonate, so a tiny one photon one evaporates so fast it doesn't really exist. It probably becomes one of those Feynman diagram junctions.

[Dio]

Also to the point, when does B achieve c relative to A? If C is very massive, then B is being accelerated by gravity, which requires no fuel, so B can achieve c, and if it's nearly at c already, presumably does. So what does A see?

I think it can only achieve c if it touches an event horizon. Until that point, ever smaller increases in velocity mean ever larger increases in mass and then that it takes so much more energy to accelerate it a bit more that it never gets there - whatever its initial velocity and mass. (Since the Lorentz transfrom is asymptotic at c). Maybe not even then.

Effectively, you can add (infinity-1) energy to a particle and it still never achieves c.

[zip accident]

Also to the point, when does B achieve c relative to A? If C is very massive, then B is being accelerated by gravity, which requires no fuel, so B can achieve c, and if it's nearly at c already, presumably does. So what does A see?

I think it can only achieve c if it touches an event horizon. Until that point, ever smaller increases in velocity mean ever larger increases in mass and then that it takes so much more energy to accelerate it a bit more that it never gets there - whatever its initial velocity and mass. (Since the Lorentz transfrom is asymptotic at c). Maybe not even then.

Effectively, you can add (infinity-1) energy to a particle and it still never achieves c.

The thing that bothers me is, that another way of defining an event horizon is that it's the point at which an object that was initially at at rest at infinity from a given black hole would achive c when it fell into the hole. Which implies to me, that if you found the path such an object would fall along, and put an object on that path but faster than the object infalling from rest (which should be easy, since the acceleration should be exponential, so it would be quite slow until it got close), then that faster object should achieve c before the event horizon.

[gumboot]

The thing that bothers me is, that another way of defining an event horizon is that it's the point at which an object that was initially at at rest at infinity from a given black hole would achive c when it fell into the hole. Which implies to me, that if you found the path such an object would fall along, and put an object on that path but faster than the object infalling from rest (which should be easy, since the acceleration should be exponential, so it would be quite slow until it got close), then that faster object should achieve c before the event horizon.

I think fast-moving and slow-moving objects see the same event horizon because it's an asymptote. Starting out moving faster just pushes you deeper into an infinitely small difference.

[gumboot]

Here's a stupid physics question

Also to the point, when does B achieve c relative to A? If C is very massive, then B is being accelerated by gravity, which requires no fuel, so B can achieve c, and if it's nearly at c already, presumably does. So what does A see?

By what I understand of approaching a black hole's event horizon, and extrapolating to masses slightly less than that, time dilation would play a big factor in the perceived approach of B towards C. Presumably limiting, if not actually slowing as with a black hole, B's approach to C to being less than light speed.

Could this same time dilation asymptotically limit B's perception of C's r+r mass?


Alternatively; dilate perception of density. Perhaps by observing C at different stages of collapse.

[pogo]

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. Plank’s constant is 6.6 x 10E-34. The ratio of mass to energy is the square of the speed of light, about 10E-17. Combine those and you get 10E-51 or thereabouts. So the frequency you need to get a photon of just 1kg of mass is about 10E51 Hz. Simply implausible. Nothing we know of generates such photons.

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.

[Dio]

The thing that bothers me is, that another way of defining an event horizon is that it's the point at which an object that was initially at at rest at infinity from a given black hole would achive c when it fell into the hole. Which implies to me, that if you found the path such an object would fall along, and put an object on that path but faster than the object infalling from rest (which should be easy, since the acceleration should be exponential, so it would be quite slow until it got close), then that faster object should achieve c before the event horizon.

I think that doesn't work because it implies (infinity + finite number) != (infinity), and that's not the case. I think. Given that, any initial speed you still end up meeting the infinity at the same point...?

[toxibunny]

sorry to butt in, but if there is no universal reference frame and it's impossible to accelerate to faster than the speed of light, then why don't physics textbooks say that the speed limit of anything approaching another thing is 2x the speed of light?

[zip accident]

sorry to butt in, but if there is no universal reference frame and it's impossible to accelerate to faster than the speed of light, then why don't physics textbooks say that the speed limit of anything approaching another thing is 2x the speed of light?

Because it's not? I don't exactly believe this, but from they way people have answered me in the past I think they are going to say something like:

The frame of reference of either is itself. and compared to that the fastest something else can go is the speed of light, the highest possible approach speed is something a bit less than the speed of light.

[pogo]

sorry to butt in, but if there is no universal reference frame and it's impossible to accelerate to faster than the speed of light, then why don't physics textbooks say that the speed limit of anything approaching another thing is 2x the speed of light?

As speeds don't add like that in relativistic physics, I.e. in our universe. Here is the formula you should use:

From here: https://en.wikipedia.org/wiki/Velocity-addition_formula

[pogo]

I can expand a little on the last answer. When you write “there is no universal reference frame” that is correct and fundamental. The name Special Relativity arises from this: everything is relative to some observer, in some frame of reference. And the physics arises when considering these different frames, relative to each other.

So when you write “[why not] anything approaching another thing is 2x the speed of light?”, I think that is wrong due to a subtle misunderstanding. Yes, you could stand in a room, with lights at either end, and the light is approaching you at the speed of light from each direction. But there is no “2x the speed of light”. You can only measure the speed of one thing, such as one photon, and that is the speed of light.

To work out the relative speed you need to work in the frame of reference of one thing, such as one of the photons, and use a formula like the one above. In some ways that does not make much sense as nothing with mass can travel at the speed of light, so you cannot have a physical detector to measure the speed. But it might arise if the photons interacted in some way. Certainly you can get things moving very close to the speed of light.

This happens routinely now in particle accelerators, where beams of particles are accelerated then smashed into each other, in the hope two will hit head on and combine to form new particles. One way to think of this is by just summing the energy of the particles colliding. Or you could consider it in the frame of reference of one of the particles, summing the velocities again using the above formula, so it’s as if all the velocity and energy comes from one of the two particles. The answer is the same either way.
One way to think o