What Happens When a Planet Nears the Speed of Light Near a Black Hole?

[Nugatory]

You're right. It's better not to talk about the speed of the planet relative to the black hole at all.

It is OK, however, to talk about the coordinate velocity of the planet using Schwarzschild coordinates, or to talk about the instantaneous speed of the planet relative to a colocated object that is hovering at constant $r$ as the infalling object passes it.

 

[phinds]

... when a mass is moving at high speed, Einstein second equation explain that the mass increase ...

@John SpaceY what you don't seem to realize is that YOU, right now as you read this, are traveling almost at the speed of light (relative to a particle in the CERN accelerator). Do you feel any heavier? Are you getting ready to explode?

 

[PAllen]

This statement does not seem sensible to me. In what sense can a planet approaching a black hole meaningfully be said to have a hole-relative speed at all?

Surely, its speed at the time of horizon-crossing is relative to a coordinate system. One cannot use a coordinate system (e.g. Scharzchild coordinates) with a singularity at the event horizon. Nor can one use a speed relative to the horizon (an outgoing null surface). A speed relative to the central singularity is right out -- that's not even part of the manifold.

Or am I missing the point badly?

You can say that the speed of the horizon relative to anybody crossing it is exactly c for the simple reason that it is light like. However, nothing has a velocity relative to the horizon because it cannot have local frame - because it is light like.

 

[Mister T]

And I think my error comes from this equation if the mass I am considering when moving is not m.

There is no sense in getting mixed up over the mass. The mass is $m$ and the total energy is $\gamma mc^2$ (where $\gamma=\frac{1}{\sqrt{1-(v/c)^2}}$).

You'll not get more energy out than you put in.

 

[John SpaceY]

Thank you all for your information.
To summarize what I have understood :
When you want to accelerate a particle of mass m at the CERN for example with a particle accelerator, the mass m will not change considering the particle frame.
The particle could be a Neutrinos like in the OPERA expriment in the CERN, where they reach to have a speed very near to the light speed c. As the neutrinos mass m is very low the energy of the Neutrinos is very low : as the energy is frame dependent, in the neutrinos particle frame this energy will be E = mc2 (energy at rest in this frame) and will be low.
And there will be no explosion of the neutrinos, because the energy is very low.

Now considering the CERN frame, the particle energy is E = gamma m c2
as v tends to c gamma will be very high and will tend to infinity when v tends to c : and so the energy seen by the CERN will tend towards infinity (but this energy will never be infinite because v will never reach c).
There will be no explosion of the CERN because this huge energy is not in the CERN frame but it is just seen by the CERN frame.
I am still asking me if there is nothing on the neutrinos particle level that will tend to reduce this huge energy seen by the CERN ? like creation of new particles on the neutrinos level or radiations emitted by the neutrinos (like X rays or ? ...) ? do you know if there is an experiment that has already shown this ?
Could we imagine another theory that will tend to reduce this huge energy seen by the CERN ?

Thank you again for your answers

 

[jbriggs444]

There will be no explosion of the CERN because this huge energy is not in the CERN frame but it is just seen by the CERN frame.

This energy is not "huge" in the first place. It is just the energy that was put into the particle by acceleration. Or by being produced by a collision with accelerated particles. Either way, the resulting energy is equal to the energy that went in.

 

[PeterDonis]

There will be no explosion of the CERN because this huge energy is not in the CERN frame

No, there will be no explosion of CERN because the energy is not huge in the CERN frame.

but it is just seen by the CERN frame

I have no idea what you mean by this. Energy is a well-defined quantity in any frame, there's no vague "seen by" involved.

 

[Ibix]

Now considering the CERN frame, the particle energy is E = gamma m c2
as v tends to c gamma will be very high and will tend to infinity when v tends to c : and so the energy seen by the CERN will tend towards infinity (but this energy will never be infinite because v will never reach c).
There will be no explosion of the CERN because this huge energy is not in the CERN frame but it is just seen by the CERN frame.

The energy of the neutrinos as measured in the CERN frame is many times larger than the energy measured in the neutrino rest frame, yes. But many times larger than almost nothing is only a little bit more than almost nothing.

 

[PeroK]

I am still asking me if there is nothing on the neutrinos particle level that will tend to reduce this huge energy seen by the CERN ? like creation of new particles on the neutrinos level or radiations emitted by the neutrinos (like X rays or ? ...) ? do you know if there is an experiment that has already shown this ?
Could we imagine another theory that will tend to reduce this huge energy seen by the CERN ?

The highest energy particle at CERN was $6.5 TeV$, which is equal to about $10^{-6} J$.

By contrast, the energy of the tennis ball in a high-speed serve is about $100 J$ - that's 100 million times more energy than a particle at CERN. I'd keep away from tennis matches if I were you!

 

[Mister T]

To summarize what I have understood :

The most basic fact that happens to be also a simple to understand concept, is that you can't get more energy out of an explosion than you put into it. Moreover, just because something has a certain amount of energy, there is no reason to assume that it will explode. Earth has a mass of about $10^{24}$ kg. It moves around the sun at a speed of about $10^4$ m/s. It therefore has a kinetic energy of about $10^{32}$ joules.

Is there any reason to expect an explosion?!

Or, if you prefer, Earth has a rest energy $mc^2$ of about $10^{41}$ joules. Again, no reason to expect it to explode!

By the way, CERN is now called the Large Hadron Collider (LHC). When it's used to smash protons into each other we do expect an explosion. But the energy is small compared to the above, and again, you will never get more energy out of the collision than you put into it.

 

[John SpaceY]

In the neutrinos frame the energy is m c2
For me the energy seen by the CERN, will be M c2, where M will be the relativistic value of the mass m, seen by the CERN frame. And this mass is not m but Gamma x m
And so the energy seen by the CERN frame will be multiplacted by Gamma and this coefficient Gamma will tend towards infinity when the neutrinos particle tends to c, and so the energy seen by the CERN frame will tend also towards infinity when v tends to c.
this is the way I understand things...

 

[jbriggs444]

In the neutrinos frame the energy is m c2
For me the energy seen by the CERN, will be M c2, where M will be the relativistic value of the mass m, seen by the CERN frame. And this mass is not m but Gamma x m
And so the energy seen by the CERN frame will be multiplacted by Gamma and this coefficient Gamma will tend towards infinity when the neutrinos particle tends to c, and so the energy seen by the CERN frame will tend also towards infinity when v tends to c.
this is the way I understand things...

But, since the energy we inject at CERN is only $10^{-6}$J, v will only get close enough to c to yield a relativistic mass equavalent to $10^{-6}$J. The infinite limiting value is irrelevant if v does not actually approach c infinitely closely.

 

[Vanadium 50]

@John SpaceY , are you asking us a question? You seem to be repeating statements and not asking questions.

 

[mfb]

By the way, CERN is now called the Large Hadron Collider (LHC).

No. CERN is a research institute. The LHC is one of many particle accelerators at CERN. The largest one, but not the only one.

And so the energy seen by the CERN frame will be multiplacted by Gamma and this coefficient Gamma will tend towards infinity when the neutrinos particle tends to c, and so the energy seen by the CERN frame will tend also towards infinity when v tends to c.

But the speed doesn't go to c. The speed stops to increase at some finite value, given by the maximum energy the accelerators can achieve. This energy is tiny in macroscopic terms, as discussed before.

 

[weirdoguy]

this is the way I understand things...

Did you even read what other people said to you? This thread is going nowhere...

 

[John SpaceY]

I understand that the neutrinos energy, accelerated by the CERN is very low because the neutrinos mass is very low. It will be maximum: m c2. And the neutrinos speed is very near of the light speed in the OPERA experiment (they say higher but it was finally a measurement error). And they succeed to achieve this neutrinos high speed with only 10-6J transferred to the neutrinos by the CERn particle accelerator.
What I don't understand is the the CERN energy limitation to 10-6J
I though that the maximum energy the CERN accelerator can achieve was much higher than the max energy of the neutrinos at rest (m c2). If this was the case the energy transmitted by the CERN to the neutrinos, which would have a consequence to accelerate the particle, should try to continue to increase the neutrinos speed.
On one hand this energy transferred to the neutrinos should increase v (and more than c because only 10-6J has succeeded to achieve a speed very near of c) and on the other hand max speed is c.
And here is my question : what is limiting the transfer of energy between the CERN accelerator and the Neutrinos which is limiting the neutrinos speed ?
The question I ask myself is only to understand where goes the energy transferred to the neutrinos because its speed cannot increase ? is there a creation of new particles on the neutrinos level ? is there creation of radiation on the neutrinos particle level ? is there experiments that shows something on this point, that decrease the neutrinos energy when the particle accelerator try to increase it ? or is there another theory that could explain why the CERN accelerator cannot inject more energy into the neutrinos and increase its speed ?
It seems that the CERN accelerator can transfer more energy than 10-6J but this energy is not used to increase more an more the neutrinos speed : the CERN has the objective to accelerate the neutrinos particle but something is limiting the energy transformed into speed : and this is what I try to understand.
As the neutrinos speed will be limited to c, where goes the energy that the CERN is transferring to the neutrinos ?

 

[jbriggs444]

I understand that the neutrinos energy, accelerated by the CERN is very low because the neutrinos mass is very low. It will be maximum: m c2.

The mass of the neutrino is unchanged by its acceleration. This has been pointed out many times. What you mean to refer to is its "relativistic mass" which is given by $m \gamma c^2$. This "relativistic mass" does increase with the neutrino's kinetic energy.

And the neutrinos speed is very near of the light speed in the OPERA experiment (they say higher but it was finally a measurement error). And they succeed to achieve this neutrinos high speed with only 10-6J transferred to the neutrinos by the CERn particle accelerator.

"Very near" is not a quantitative measure of anything. Without further information, it is meaningless.

What I don't understand is the the CERN energy limitation to 10−610−6J. I though that the maximum energy the CERN accelerator can achieve was much higher than the max energy of the neutrinos at rest (m c2).

"Much higher" is not a quantitative measure of anything. The rest mass of a neutrino (which flavor?) is extremely tiny and difficult to measure. However, the LHC succeeds in creating neutrinos with kinetic energies about a trillion times as great as the best guess at their rest energy, so "much higher" would seem appropriate.

It is hard to accelerate particles to high energies. You have to use charged particles because it give you a "handle" that you can use to accelerate them.

You can try to use high electrical fields to accelerate them in a long linear accelerator. But you are limited in the field strength you can produce and in the length of a tube you can build with the funds at hand.

You can try to use a ring and accelerate the particle (particle burst actually) over a very large distance as it circles through the ring. But charged particles that are deflected to follow the circular path emit so-called "synchrotron radiation" due to the centripetal acceleration. That drains energy and limits what you can achieve. Bigger rings help, but funding limits that. The LHC main ring is big and expensive.

You can try to accelerate heavier charged particles since they pack more energy per unit charge than light charged particles. That is why one normally uses protons rather than electrons. I seem to recall some attempts to accelerate charged nuclei rather than protons, but I am not an accelerator guy. The LHC does protons, per my understanding.

You can run counter-rotating beams so that you are slamming particles into one another rather than into a stationary target. That buys you a factor of two, but poses other challenges. The LHC is a collider, hence the name.

The bottom line is that, as in all things, the practicalities of engineering and cost intrude on the ideals that the equations might suggest are achievable.

 

[A.T.]

...the CERN has the objective to accelerate the neutrinos...

Does it?

 

[Mister T]

I understand that the neutrinos energy, accelerated by the CERN is very low because the neutrinos mass is very low.

Nope, as has been pointed out repeatedly, the reason is because a very low amount of energy is transferred to the particle from the accelerator.

 

[phinds]

I understand that the neutrinos energy, accelerated by the CERN is very low because the neutrinos mass is very low.

as has been pointed out repeatedly, most recently by Mister T, no, it's because the accelerator only puts in a relatively low amount of energy.

On one hand this energy transferred to the neutrinos should increase v

and that is exactly what happens

(and more than c because only 10-6J has succeeded to achieve a speed very near of c) and on the other hand max speed is c.

Ok, first you say "more than c" which is nonsense, then you correctly say "max speed is c". Make up your mind. Hint; nothing goes "more than c".

And here is my question : what is limiting the transfer of energy between the CERN accelerator and the Neutrinos which is limiting the neutrinos speed ?

There is none. They just keep going faster and faster. You are getting confused because the faster they are going, the smaller the amount of additional speed per unit of input energy.

The question I ask myself is only to understand where goes the energy transferred to the neutrinos because its speed cannot increase ?

As I have pointed out, there is no limit to the energy that can be input, and they can keep increasing speed forever (just by smaller and smaller amounts), they just keep getting closer and closer to c.

 

[jbriggs444]

As I have pointed out, there is no limit to the energy that can be input, and they can keep increasing speed forever (just by smaller and smaller amounts), they just keep getting closer and closer to c.

Just to avoid any possible confusion, there is no theoretical limit. However, real world practical constraints apply.

 

[phinds]

Just to avoid any possible confusion, there is no theoretical limit. However, real world practical constraints apply.

Yes, that's a good point.

 

[PeroK]

Just to avoid any possible confusion, there is no theoretical limit. However, real world practical constraints apply.

It's actually quite amusing to think how little energy the LHC is capable of inputting to a particle. It's so easy to boil a litre of water in a kettle in less than 5 minutes, which takes about $300,000J$.

They spend billions of Euros at CERN to get particles up to $10^{-6}J$. And my kettle cost £19.99 or thereabouts.

 

[Ibix]

They spend billions of Euros at CERN to get particles up to $10^{-6}J$. And my kettle cost £19.99 or thereabouts.

As the old joke goes:
Delivering $10^{-6}\text J$: £19.99
Delivering it to one subatomic particle: £4,999,999,980.01

 

[Mister T]

And here is my question : what is limiting the transfer of energy between the CERN accelerator and the Neutrinos which is limiting the neutrinos speed ?

The design of the accelerator.

As the neutrinos speed will be limited to c, where goes the energy that the CERN is transferring to the neutrinos

The energy goes into increasing the speed. Theoretically, the more energy you transfer the faster the speed. It's just that the increases in speed will never get you up to a speed of $c$. But the laws of physics allow you to get arbitrarily close, so no matter how close you get, you can always get closer.

Let's consider a particle moving at a speed of 0.99900 $c$. Double its energy and its speed increases to 0.99975 $c$. You can (theoretically) continue to increase the energy, and each increase is accompanied by an increase in speed.

I'm really confused about what it is you're trying to understand. On the one hand, if you're trying to understand the lack of the danger of an explosion, you need only understand that the amount of energy associated with such an explosion is less than what you'd get from exploding a fire cracker because that's how much energy was put into the explosion.

On the other hand, if you're trying to understand the relativistic dynamics involved you need to build that understanding by working through a good textbook on the subject. When you get stuck or otherwise have questions ask here in the forum. But you cannot reasonably expect to understand it from information gleaned from these forum posts.

 

[mfb]

CERN's SPS accelerator can accelerate protons to an energy of at most 7*10^-8 J. From there the protons are transferred into the LHC, used to produce neutrinos, or used in one of the other experiments around SPS.

• It can transfer these protons to the LHC, where they are accelerated to an energy of at most 1.0*10^-6 J.
• It can shoot these protons onto a fixed target, the collisions create some pions with an energy of at most 7*10^-8 J. Energy is conserved - the pions can't have more energy than the protons used to make them. The pions then decay, among the decay products are neutrinos with an energy of at most 7*10^-8 J - again, this limit is given by conservation of energy. "At most" because some energy will go into other particles produced in both processes.

The energy in the SPS is limited because the SPS must be able to keep the protons on their circular track using strong magnets. If you would try to increase the energy then the protons wouldn't stay in the beam pipe and more and crash into the outer wall, getting lost in the process.

The LHC can reach a higher energy than the SPS because it is larger and has stronger magnets. It could be used to create neutrinos at higher energy - but similar to the SPS, the neutrino energy could not exceed the proton energy, so you get at most 1.0*10^-6 J (and usually much less). Stronger magnets might double that in the future, but it will stay a tiny energy in macroscopic terms.

Note that I didn't use speed values anywhere: You can find the corresponding speed for each energy, but in practice this doesn't matter. The energy is a more useful quantity, then you don't have to count digits in things like "0.999999995 times the speed of light".

 

[John SpaceY]

Yes I have understood that the CERN energy transfer to the neutrinos is low : but it is enough to increase the neutrinos speed in the relativistic area. As explained before by jbriggs444 (point #52), the kinetic energy of the neutrinos, seen by the CERN is 1 trillion more than the neutrinos rest energy. So the coeffcient Gamma is equal to 1 trillion (around) and so I have calculated that the neutrinos speed (seen by the CERN frame) should be : v = 0, 99999…9995 c with 24 numbers 9 !
So it is very near to c
And I understand also that the neutrinos speed limitation comes only by the reduction of energy transfer from the CERN particle accelerator. Reasons are technical and cost, as explained by jbriggs444 (point #52).

If we take the hypothesis that we arrive to increase the accelearor particle power (like the Chinese are doing now) or find a technical way to increase the energy transfer to the neutrinos speed, the effect will be to increase more the neutrinos speed : there will be more 9 in the value of v, but the speed v will always be less than c. The only consequences of increasing the energy transfer between the particle accelerator and the neutrinos particles will be to increase their speed : there is nothing know today that will try to reduce the neutrinos speed, even if the energy seen by the CERN will increase a lot : no creation of new particles on the neutrinos level, or creation of radiation on the neutrinos level or other effects (or new theory not known) ?

I am still very surprised that if we find a way to increase the transfer of energy between a particle accelerator and a particle with no limit the only effect will be to only to increase its speed ? but is what today the science explains
If there is no limit for the transfer of energy from a particle accelerator to a particle, the energy of this particle seen by the CERN (for example) would be very very high : and nothing will happen on the particle level or on the CERN side : no explosion I understand this now but nothing will try to reduce this huge energy ? this is what is difficult for me to understand, even if it is well explained by all your remarks : thank you again for this !
The CERN will see a huge energy and that's it !

 

[PeroK]

Anyone for tennis?

 

[Ibix]

I am still very surprised that if we find a way to increase the transfer of energy between a particle accelerator and a particle with no limit the only effect will be to only to increase its speed ?

Why would anything else happen? As far as the neutrino is concerned, it is at rest. Adding a bit more energy to a particle we've accelerated can no more have a weird effect than adding the first bit of energy.

 

[PeterDonis]

have understood that the CERN energy transfer to the neutrinos is low

The CERN will see a huge energy and that's it !

You are contradicting yourself. You need to take a step back and think about what you are saying.

If there is no limit for the transfer of energy from a particle accelerator to a particle

There is a limit; any accelerator can only transfer a limited amount of energy to any particle. In the case of CERN, that limit is $10^{-6}$ J.