# Question on high speed astrophysics — when an object goes near of the speed of light

## 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).

## Main Question or Discussion Point

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. 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 ?

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

I have another possible explanation but I will wait first your answers.

Best regards

John SpaceY

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DaveC426913
Gold Member
Welcome John.

... proportional to the 2 masses and inversely proportional to the square of the distance between the 2 masses.
I fixed the above statement.

When the planet moves towards the « black-hole » this attraction force increases. And the planet speed will increase : when the speed will be near the speed of light,
It is not necessary for an object to get anywhere close to the speed of light before falling into a black hole.

That fact should dramatically change how you re-ask this question. (i.e.: do you want to know about falling into a black hole OR do you want to know about relativistic velocities and Lorentz transforms?)

the planet mass will become infinite and the attraction force will also become infinite.
No and no.

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 ?
Just because the planet's velocity continues to increase does not mean it reaches the speed of light - it simply gets arbitrarily close to the speed of light.

At some time, its velocity is .9c, then after some more time, its velocity is .99c, and some time later its velocity is .999c. Its velocity is always increasing, but it never reaches c.

Could you confirm that this is the right explanation to my question ?
No.

You have enough misconceptions about black holes and relativistic velocity that it would be better for you to read up on the subject a bit, and then come back with specific questions if you still don't understand.

Let's see if we can point you at some good reading material...

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Hello
You are right but what I want to show is that the mass of a "black hole" is very high and so the attraction force on the planet will be very high. And so the planet speed will increase very quickly.
When you arrive to a speed close to the light speed the planet mass will increase and the force will also increase and in the same time the distance is decreasing : as you mentioned the attraction force is inversely proportional to the square of the distance between the 2 masses and so the force will be very very high.
I have assumed that as the speed continues to increase, the speed will tend towards the light speed and here comes my question : what will happen if the speed will want to continu to increase but cannot because the speed is limited to the light speed ?

DaveC426913
Gold Member
I have assumed that as the speed continues to increase, the speed will tend towards the light speed
Yes. "tends towards"

and here comes my question : what will happen if the speed will want to continu to increase but cannot because the speed is limited to the light speed ?
The speed will continue to increase - it will get closer and closer to c.
For example:
t0: .9c
t1: .99c
t2: .999c
t3: .9999c

In the relativistic realm, speeds don't add simply the way they in the everyday realm.
You need to use the relativistic velocity formula.

What you will find using this formula is that no two velocities, when added together, will ever result in a velocity greater than c.

Say your planet takes one month to accelerate to .9c.
After one more month, its new velocity will not be 1.8c,
it will be (if you put it in the formula) (.9c+.9c=) .9945c.

and after another month it will be (.9945c+.9c=) .9997c.

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Yes yes it is clear : the speed continue to increase and goes closer and closer to c (never higher than c) : but in the same time the planet kinetic energy tends towards infinity (because the planet mass will tend towards infinity) and in this case normally we should see an explosion : and we don't see it
So my question is what is reducing the planet kinetic energy in the condition where its speed is continue to increase because the attraction force will continu to increase?

DaveC426913
Gold Member
...the planet kinetic energy tends towards infinity (because the planet mass will tend towards infinity)
Again, matter falling into black holes does not tend to be moving at a velocity "infinitely" close to c, so the above tends not to occur.

... normally we should see an explosion : and we don't see it...
Where do you expect to see this explosion? And what makes you think we don't see it?

The explosion, for me, should come, because the kinetic planet energy will become infinite and in nature when we are in the presence of a big quantity of energy, it often finish by an explosion...
You are right : it is difficult to see the explosion if it is very far in space.
I can take another example for this point : there is a particle accelerator in the CERN in Geneva and they accelerate particles near the speed of light : in 2011 there was the OPERA experiment where they say they reach a speed higher than c but in 2013 they explained that this was a mistake in the measure. But they succeeded to reach a speed very close to the light speed : the particle was a Neutrinos with a mass (very low but not zero) : and so the particle kinetic energy should be very high. And they don't see any explosion in this experiment.
And so I have the same question here : where goes this high energy ? maybe transformed into new particles ? this is where I want to have some answers... it is not easy to explain (sorry for this).

DaveC426913
Gold Member
The explosion, for me, should come, because the kinetic planet energy will become infinite and in nature when
Not infinite.
Large, yes.

Black holes are generally surrounded by mass that emits a lot of energy. But no, not infinite.

we are in the presence of a big quantity of energy, it often finish by an explosion...
Not an explosion - radiation. Black holes tend to shine in X-ray. That's how we spot them tens of thousands of light years away.

PeroK
Homework Helper
Gold Member
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. 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 ?
You are assuming that "relativistic" mass equates to gravitational mass. This is not the case. We have a FAQ on this:

In this scenario, nothing special happens. The planet reaches the event horizon of the black hole in a finite proper time. The speed of the planet relative to the black hole does not come close to the speed of light.

The planet may be pulled apart by tidal gravity before it reaches the event horizon, depending on the size of the black hole. In any case, it falls into the hole and - according to GR - is destroyed.

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Thank you PeroK for these information.
What about also my question in my post #7 (the Neutrinos at high speed : what happens because we see no explosion here ?)

PeroK
Homework Helper
Gold Member
Thank you PeroK for these information.
What about also my question in my post #7 (the Neutrinos at high speed : what happens because we see no explosion here ?)
Kinetic energy is frame dependent. A neutrino moving at near the speed of light relative to you is just an ordinary neutrino in its own rest frame. It has no reason to explode.

Relative to the particles at CERN, the Earth is moving at near the speed of light. But, the Earth is not going to explode either.

The first postulate of special relativity is that all (inertial) motion is relative. There is in fact no such thing as (absolutely) moving at the speed of light. There is only motion relative to other objects.

jbriggs444
Homework Helper
2019 Award
The speed of the planet relative to the black hole does not come close to the speed of light.
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?

PeroK
Homework Helper
Gold Member
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?
You're right. It's better not to talk about the speed of the planet relative to the black hole at all.

DaveC426913
Gold Member
Thank you PeroK for these information.
What about also my question in my post #7 (the Neutrinos at high speed : what happens because we see no explosion here ?)
John, there is no explosion.

A black hole does not have a surface that anything - including neutrinos - can impact.

Particles fall (free fall) through the event horizon - right to the singularity at the centre. And - once they cross the event horizon - they won't be emitting any radiation outside the black hole.

mfb
Mentor
But they succeeded to reach a speed very close to the light speed : the particle was a Neutrinos with a mass (very low but not zero) : and so the particle kinetic energy should be very high.
Very high compared to their rest energy. Very small in macroscopic terms. Each neutrino had a typical energy of just a few nanojoule. You would need hundreds of millions of them to have enough energy to lift an apple by 1 meter (if you could use them in that way). The few neutrinos that interacted with matter in OPERA produced showers of secondary particles in the detector - that's how the detector could find them.

Thank you all for the information
I still have a question : there is some particle accelerators in the world and their objective is to increase the speed of particles and create collision at high energy with other particles. I understand that speed is relative but in these particle accelerators the particles speed is very high (the Chinese are making a very powerful particle accelerator to reach to light speed, as I have understood).
So if we take the hypothesis that we succeed to have non zero mass-articles that have a very high speed (near the light speed), these particles should have a very high energy. And here is my question : what happen here if we want to continue to increase the particle speed ? the energy will continu to increase and there is no explosion : so where is going the energy ? I suppose that this energy is transformed into new particles but is there an experiment that has proven this ? if this is true I can understand what is happening : the new non zero mass particle created and moving to a very high speed (less than c) will have a high energy and will reduce the huge energy of the accelerated particles and so this will reduce their speed and their energy : is this hypothesis right ?
How the accelerated particles could reach a very high speed is not my question : I just take 2 examples (the black hole and the CERN OPERA experiment to try to have examples of high speed particles) to have very high speed particles and my question arrive after : when we have these high speed particles, what will happen (see before) if we continu to accelerate them?
Is the creation of new particles the right explanation to decrease the speed because it is limited to c or is there another explanation ? is another theory possible to imagine in order to decrease the initial particle speed if we want to continue to increase its speed ?

PeroK
Homework Helper
Gold Member
Thank you all for the information
I still have a question : there is some particle accelerators in the world and their objective is to increase the speed of particles and create collision at high energy with other particles. I understand that speed is relative but in these particle accelerators the particles speed is very high (the Chinese are making a very powerful particle accelerator to reach to light speed, as I have understood).
So if we take the hypothesis that we succeed to have non zero mass-articles that have a very high speed (near the light speed), these particles should have a very high energy. And here is my question : what happen here if we want to continue to increase the particle speed ? the energy will continu to increase and there is no explosion : so where is going the energy ? I suppose that this energy is transformed into new particles but is there an experiment that has proven this ? if this is true I can understand what is happening : the new non zero mass particle created and moving to a very high speed (less than c) will have a high energy and will reduce the huge energy of the accelerated particles and so this will reduce their speed and their energy : is this hypothesis right ?
How the accelerated particles could reach a very high speed is not my question : I just take 2 examples (the black hole and the CERN OPERA experiment to try to have examples of high speed particles) to have very high speed particles and my question arrive after : when we have these high speed particles, what will happen (see before) if we continu to accelerate them?
Is the creation of new particles the right explanation to decrease the speed because it is limited to c or is there another explanation ? is another theory possible to imagine in order to decrease the initial particle speed if we want to continue to increase its speed ?
The energy of a particle is given by: $$E = \gamma mc^2$$ where $$\gamma = \frac{1}{\sqrt{1- v^2/c^2}}$$

You can see from this equation that the energy of a particle can increase indefinitely without its speed exceeding $c$. As $v \rightarrow c$, $E \rightarrow \infty$.

This is a fundamental difference between relativity and classical physics. In classical physics, the energy of a particle was proportional to $v^2$ ($E = \frac 1 2 m v^2$). If you keep putting energy into a particle its speed would increase without limit. But, under the laws of special relativity, if you keep putting energy into a particle its speed never exceeds $c$. All the energy is still there. It doesn't have to go anywhere. It's all wrapped up in $E = \gamma m c^2$.

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Thank you PeroK,
I agree that the speed never exceeds c if I keep putting energy into a particle.
All the energy is still there : OK for this but this energy will be very high if the speed tends to c.
In your equation m will tend to infinity (because mass increase when the speed increase in the relativistic area) and the coefficient also will tend to infinity when v tends to c.
And so I don't understand the end of your last sentence "it doesn't have to go anywhere"
is it possible to have a particle with an infinite energy without any huge explosion or things last this ?
Is there nothing that will tend to decrease this energy when we would like to increase it ? like the creation of new particles or things like this ?

In your equation m will tend to infinity (because mass increase when the speed increase in the relativistic area)
As already been said in post #9 this is not true. Mass is constant.

is it possible to have a particle with an infinite energy
And that also was said already - there is no infinite energy anywhere. We have large energy, not infinite.

PeroK
Homework Helper
Gold Member
Thank you PeroK,
I agree that the speed never exceeds c if I keep putting energy into a particle.
All the energy is still there : OK for this but this energy will be very high if the speed tends to c.
In your equation m will tend to infinity (because mass increase when the speed increase in the relativistic area) and the coefficient also will tend to infinity when v tends to c.
And so I don't understand the end of your last sentence "it doesn't have to go anywhere"
is it possible to have a particle with an infinite energy without any huge explosion or things last this ?
Is there nothing that will tend to decrease this energy when we would like to increase it ? like the creation of new particles or things like this ?
There is no "infinite" energy here. There is only finite energy. Any particle only has a finite energy at any point in time. In theory, that energy can be as large as you like, but it's always finite. In any case, any practical means of accelerating a particle reaches its limit. There will be a maximum energy for any particular particle accelerator. So, it makes no sense to take about "inifinite" energy. CERN only has a finite amount of energy at its disposal. Where would CERN get "infinite" energy from?

The point you continue to miss is that energy is frame dependent. None of these particles at CERN is fundamentally changed by speed. In a sense, acceleration achieves nothing. Certainly not any physical change to a particle.

If two particles collide at high relative speed, that is something.

I get the feeling you may not believe this because you've read a popular science book by Professor X, who emphasises that mass increases with speed. And, this leads to the idea that the particle undergoes some physical change, knows its moving fast and starts to feel the need to dispose of some of its excess energy: like someone going on a diet after the Christmas binge!

This is all popular science myth.

The only question I cannot answer is why popular science writers insist on talking about mass increasing with speed.

In any case, it leads you astray and when you ask for an answer on a "academic" science forum, we have to unpick this myth to explain SR to you in any reliable scientific terms.

I'll link to the page I did before in case you missed it the first time:

In short: a particle at CERN, travelling at $0.999c$ is physically no different from a particle at rest. You better believe it!

If there is large energy you could have an explosion : not necessary to have an infinite energy
If there is something that tends to increase the speed v and as this speed cannot exceed c where goes this high energy ? because if the mass is supposed constant, if the speed c increase in the equation the coefficient increase and so the energy increase (and if the speed v tends to c the coefficient tends to infinity and so the energy could tend to infinity)

There is no "infinite" energy here. There is only finite energy. Any particle only has a finite energy at any point in time. In theory, that energy can be as large as you like, but it's always finite. In any case, any practical means of accelerating a particle reaches its limit. There will be a maximum energy for any particular particle accelerator. So, it makes no sense to take about "inifinite" energy. CERN only has a finite amount of energy at its disposal. Where would CERN get "infinite" energy from?

The point you continue to miss is that energy is frame dependent. None of these particles at CERN is fundamentally changed by speed. In a sense, acceleration achieves nothing. Certainly not any physical change to a particle.

If two particles collide at high relative speed, that is something.

I get the feeling you may not believe this because you've read a popular science book by Professor X, who emphasises that mass increases with speed. And, this leads to the idea that the particle undergoes some physical change, knows its moving fast and starts to feel the need to dispose of some of its excess energy: like someone going on a diet after the Christmas binge!

This is all popular science myth.

The only question I cannot answer is why popular science writers insist on talking about mass increasing with speed.

In any case, it leads you astray and when you ask for an answer on a "academic" science forum, we have to unpick this myth to explain SR to you in any reliable scientific terms.

I'll link to the page I did before in case you missed it the first time:

In short: a particle at CERN, travelling at $0.999c$ is physically no different from a particle at rest. You better believe it!

If there is large energy you could have an explosion : not necessary to have an infinite energy
And where are you getting this from?

PeroK
Here's my guess. We have $E = \frac 1 2 m v^2$. If mass is constant and $v < c$, then the maximum energy is $\frac 1 2 mc^2$ and any extra energy must be dissipated in an explosion of addition particles.