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

[jbriggs444]

For me in relativistic theory M = Gamma * m (sorry for my mistake, I have written Beta but I was thinking to your term Gamma). So it is strange to me to see that M = m in relativistic theory ?
I don't understand where I make the mistake ? when a mass is moving at high speed, Einstein second equation explain that the mass increase, because Gamma is increasing : but what mass is it ?

Did you read the link provided by @PeroK in response #9 above?

https://www.physicsforums.com/threa...-and-why-it-is-not-used-much-comments.826906/

 

[John SpaceY]

No sorry
Probably I will find the answer to my mistake in this link
I will read it and I will come back later
Thank you very much for your help

 

[weirdoguy]

I don't understand where I make the mistake ?

Your mistake is not reading other responses and repeating false statements as if they were not debunked here at least twice...

 

[pervect]

Summary:: I have a question linked to high speed in space, when an object goes to a speed near of the speed of light (I am new in this forum).

I take the following example to explain my question : when a « black-hole » is attracting a planet there is a Force which is proportional to the 2 masses and inversely proportional to the distance between the 2 masses. When the planet moves towards the « black-hole » this attraction force increases.

I haven't read the rest of the responses to this thread, but the notion of gravity you describe is Newtonian gravity, not the GR notion of gravity.

As such, you should not expect the notion of gravity you describe (Newtonian gravity) to work in the cases of black holes, which require GR and not Newtonian theory.

And the planet speed will increase : when the speed will be near the speed of light, the planet mass will become infinite and the attraction force will also become infinite. On the one hand the planet speed will continue to increase and on the other hand the speed is limited to the light speed. So what will happen ?

One possibility could be that the planet will create a lot of new particles : these particles will have a non-zero mass and will move to a speed less than the speed of light, in order to decrease the planet energy and decrease also the planet speed. And so the planet speed will be always less than the speed of light.

Could you confirm that this is the right explanation to my question ?

No. I'm pretty sure it's wrong.

Or is there other explanations ? what it could be in this case ?

An explanation in the spirit of GR is that the planet essentially follows a geodesic. To be precise, we are actually saying the planet is a test particle.

We do not need any "forces" to use this explanation. There are only geodesics. The relative velocity of the planet following this geoodesic relative to any stationary, hovering observer that actually exists is always less than "c" as the planet falls into the hole.

Hovering observers do not exist at or inside the event horizon of the black hole, however. Anything that is capable of "observing" at or inside the black hole simply cannot be stationary. It must fall into the black hole.

Note that we must compare the velocity of the infalling planet to an observer located where the planet is. THe reasons for this are rather technical. I'll quote from an article by Baez:

http://math.ucr.edu/home/baez/einstein/node2.html

In special relativity, we cannot talk about absolute velocities, but only relative velocities. For example, we cannot sensibly ask if a particle is at rest, only whether it is at rest relative to another. The reason is that in this theory, velocities are described as vectors in 4-dimensional spacetime. Switching to a different inertial coordinate system can change which way these vectors point relative to our coordinate axes, but not whether two of them point the same way.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.

 

[PeterDonis]

If CERN should explode it is the risk that I fear

CERN is not going to explode. Energy is frame dependent, as others have already commented, so you can't just use "energy" without qualification as a criterion for when something will explode, since exploding is not frame-dependent; it either happens or it doesn't, and you can't change whether it happens by changing frames. So a correct analysis should just pick the most convenient frame and do the analysis there. Then you can translate that analysis into other frames to see how the result ("explode" or "not explode") stays the same.

To see whether CERN might explode, it's most convenient to analyze things in CERN's rest frame. In that frame, the energies involved are miniscule compared to the energy it would take to make CERN explode. So CERN won't explode.

In the rest frame of a particle moving at very high speed inside the CERN accelerator, CERN has a very high energy, but if CERN's detector hits the particle it keeps on moving at almost exactly the same speed, because it's so much bigger than the particle that it just picks up the particle and keeps on going. So CERN won't explode; it will just keep moving at very, very high speed in this frame. (The particle changes speed drastically in this frame--it goes from rest to a very, very high speed. But the energy involved in the particle changing speed that much is miniscule--it's the same as the energy involved in stopping the particle in the CERN rest frame, which, as above, is miniscule.)

 

[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.

 

[Herman Trivilino]

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!

 

[Herman Trivilino]

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?

 

[Herman Trivilino]

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

 

[Herman Trivilino]

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.