Here is something that I placed once upon a time on another board for people to ponder:

If two objects of equal mass were both traveling at just under light speed, and they have a head on collision, What happens?
(Note: This would be the equivalent of a +Lightspeed collision with a stationary object.)

Or if they travel both Faster than light speed and collide head on what happens?

If you can answer it, good :D
If you can't, then answer what you think would happen.

If two objects of equal mass were both traveling at just under light speed, and they have a head on collision, what happens?

In this type of problem you need to be very careful with reference frames. When you say "travelling at just under light speed" I assume you mean "A stationary observer sees each object moving at a little less than light speed." Alternatively you could mean "Each object sees the other as moving at a little less than light speed."

In fact, due to relativistic velocity addition, both these situations are similar here, so the answer is more or less the same for both.

In the collision, energy will be converted from kinetic energy (energy of motion) to other forms. The objects might deform and/or vapourise. Some of the energy may be released as light or heat. In some cases, some of the energy may be converted to matter and go to creating new particles out of the vacuum. Or, it may be that the particles just bounce off each other and fly away at close to their original speeds. It really depends on the details of the collision.

A collision between two particles at a faster than light relative speed is impossible since the speed of light is the fastest possible relative speed for any two objects.

Okay I should rephrase,

You the observer spot two objects of equal mass collide, both objects were travelling at just under light speed (meaning the collision total is faster than light).

I also mention the other also refering to the same, but fast, of course you'll mention that impossible, I would say it's improbable, and that to travel at faster speeds you would suffer a paradoxal problem which can only be speculated through some of Schrodingers Thoughts.

Hi Stryderunknown,


You the observer spot two objects of equal mass collide, both objects were travelling at just under light speed (meaning the collision total is faster than light).

You're mixing up two things here. You're using a statement from special relativity (lightspeed) and a classical Newtonian addition of speeds (V_total = V₁ + V₂), which is not allowed.

The correct reasoning would be:
1) From a classical Newtonian mechanics stand:
The two particles collide, one with V₁, the other with V₂, so the total collision speed is V₁ + V₂. The particles emerge with their respective velocities. In classical Newtonian mechanics, no particles can be destroyed or created. The collision is determined by the conservation of momentum.

2) From the point of view of special relativity
The two particles collide, with a total velocity V = c²*(V₁ + V₂)/(c² + V₁* V₂). This formula can be deduced from the postulates Einstein formulated to write his theory of SR. In the case of SR, the creation and annihilation of particles is allowed, so here (depending on the exact velocities) you'd probably end up with loads of kinetic energy being converted into streams of particles.

Bye!

Crisp

Stryder, I remember when you made this same post at thepark. I wish I could have answered it with the details crisp did but it seems that he answered in escence the same as I did way back when :)

The velocity of the two objects do not add up to faster than light speed just because they are travelling towards each other.

The power of the impact of the objects will be dependent on the velocity combined..

Reign,
It was actually the Prophet that brought the topic up at the park, but I couldn't resist reposting it here as it was a kind of fun topic. It wen't along with his whole "If Itravelled faster than light for a year..." kind of post.

I did have some fun with Crisp's calculation though it would see everything is virtually 1 with it. :D

(I tried it with equal velocities.)

All I know is that if a ship traveling at one-tenth the speed of light hit one gram of matter, the resulting transfere of energy would be equivlent to many nuclear bombs detonating.

Suppose, for example, one observes relatively to him a solid mass moving with the velocity of almost the speed of light in the direction x enters a gas moving with that speed in the direction -x. Would that mean that they would go back in time because as a particle approaches the speed of light, time ceases to exist and they would be going at a speed more than that of light relative to each other?

With this in mind, further suppose a container with a circular hole of area πx² in its front, filled with a gas and containing a solid sphere of volume (πx^3)/6 inside of it (to avoid friction between the object and the hole), is moving through space (no-gravity vacuum) at almost light-speed. Further suppose the solid is accelerated to a large speed before it exits the gas through the hole in the front of the container (for example, like a bullet is accelerated through a gun; more sophisticated acceleration techniques, such as matter-antimatter reaction, are possible). Upon exiting the gas, would the sphere go back in time, because it would be going at a speed greater than that of light (for the same reason as above)?

Now then, I realize that the formula above in this thread tells the resulting speed of the sphere. However, I would think that mass would have to do with it too: because shooting off two objects of mass x each should produce the same effect as shooting off of one object of mass 2x. So what is the formula with the mass included?

They do this in particle accelerators. Particles traveling in opposite directions at relativistic speeds are caused to collide.

it is difficult to do it with larger objects.

Objects collide and result is a lot of energy including light in the Electromagnetic Spectrum. Otherwise, we would be witnessing a lot of light travelling faster than their brothers....those particles do carry high energy until the energy is released in the vacuum of space but the speed limit is the same.

I think!

So have they not collided, say, an electron with a proton, and figured out the formula with the mass included thence?

This is pretty much exactly what happens millions of times a day at FermiLab.


Would that mean that they would go back in time because as a particle approaches the speed of light, time ceases to exist and they would be going at a speed more than that of light relative to each other?

No.

the same thing would happen as happens when you turn 2 flashlights on eachother.
seeing as light has mass, i dont see a dilemma here.

Light does not have mass, The Devil Inside.

The photon is massless.

Light doesn't have mass, but it does have momentum.

Actually if you shine two very bright beams of light at each other, there is a chance of a photon/photon collision which would result in the creation of an electron/positron pair;
http://en.wikipedia.org/wiki/Matter_creation

seeing as light has mass, i dont see a dilemma here.

seriously?


Actually if you shine two very bright beams of light at each other, there is a chance of a photon/photon collision which would result in the creation of an electron/positron pair;

Yes, as long as the photons both has 511 keV of kinetic energy.

...Yes, as long as the photons both has 511 keV of kinetic energy.You should note that he is wrong to call those gamma ray photons "light" and more gererally, I think they need only total slightly more than 1022Kev in your frame. -The total energy in your frame being the rest mass of two electons plus their "post-creation" kinetic energy. I.e. in some other frame, where the produced electron & positron are at rest, one gamma is downshifted and the other blue shifted to be equal in energy (511KeV each).

I am not sure but think it is possible that other slightly higher still total energy in you frame may be possible if the gammas do not collide "head on."

I think I got that right, but will defer to your corrections, if needed.

511 KeV annihilation radiation is routinely produced, on a daily basis, in medicine in hundreds of locations around the globe. Positron emitters are produced in quantity (Curies) in medical cyclotrons worldwide, and shipped to hospitals/clinics for injection into patients, who are placed under PET or PET/CT equipment, which detect with scintillators the two 511 KeV photons produced when the positron emitted collides with an electron, allowing for an ability to locate where the positron emitter was located in the body, visualzing various biochemical activities. You can learn more about that at www.snm.org

The reverse process is not as common, but has been done in laboratory settings, in which high-E photons are forced into producing electron/positron pairs.

And yes, BillyT is correct, the photons need not be head-on collisions, though it would require a higher energy (to conserve momentum). The annihilation photons are at 180 degrees in their rest frame, conserving momentum.

I think I got that right, but will defer to your corrections, if needed.

No I think you are exactly correct. I have not studied the process in any great detail---I'm more interested in much higher energies:)

I believe I have a similar quistion like stryder. Let's say that a single atmos travel at 99,9999999%of c but this time it is aproaching a black hole. Let's say that their is no spin because it's going afther 1 of the poles in a straight line head on collision.
Now at the same time there is artificial wormhole with a enormous event horizon that is going to move our black hole to a save location.

The particle enters the event horizon of the black hole but the black holes singularity is transported before the particle could collide.

Will that particle move fasther then light or would it have been destroyed the second it (or before) enetered the black hole events horizon

I;m confused---does the particle fall in the black hole or not?

Anyway, the answer is easy: no.

If it falls in the event horizon, it just keeps accelerating towards the singularity, but at an ever slowing rate.

If it doesn't, then it just becomes a free particle.

I tought that ones it entered the even horizon it is being accelerated beyond c, because the downwards gravitational pull is larger then c. However the event horizon isn't the sigularity so it hasn't crashed into anything yet.
So it falls inside the black holes event horizon the point where light can not escape but it doesn't reach the singularity inside the black hole.

PS the wormhole only takes the singularity the speeding atom never meets the wormhole

... If it falls in the event horizon, it just keeps accelerating towards the singularity, but at an ever slowing rate.... I understand and believe that time in that intense gravitational field, AS WE who are FAR AWAY experience it slows down. (Before you became active here, I made a short story about a medical old-folks home in orbit about a black hole, just outside the EH (with local gradient neutralizer of course)* - The rich patients admitted were typically only a few days from death, but expecting that surely during the 10,000 years that were passing back on Earth every minute as they aged, someone would find a cure for their disease, Not all went well, as some of the sick, but religious, Klingans wanted extra insurance and used one of the Earthlings in a sacrificial ritual etc.)
-----------------------
*I did not give all the details of how it worked but it was based on fact the chosen black hole was very** big so its gradient was small and the local masses of the neutralizer were much closer, exploiting the inverse cube fall off the gradient to locally cancel the gradient of the black hole. It was perfect, but only at a set of spots and the imbalance elsewhere did require the use of hand rails ("claw rails" for the klingons) when going between these low gradient regions.

**omit this word if you hold the standard belief. I think most black holes are only a few solar masses (many think none are) so I need to say "very" but much smaller than a glactic center one. I.e. a gradient neutralizer was required, but none would be for a BH as big as a glactic center BH. (The sick did not have time to travel that far - had to use a more local one.)

But to return to my thread point/question:

If you take the POV you seem to be (our clocks & our measure of the EH radius) then the speed of light is steadily approaching zero when starlight falls inside the black hole’s EH (we believe, but do not see). I guess that is OK with SRT etc, if gravity and accelerating frames are in fact one and the same identically, but some how I am not very comfortable with near zero speed light, are you? I.e. my INERTIAL FRAME measurements have c approaching zero - Is Mr. Einstein happy with that? You know more about this than I do - any comments?

A collision between two particles at a faster than light relative speed is impossible since the speed of light is the fastest possible relative speed for any two objects.
So how about if two objects are each traveling at .99C relative to a object, say, an asteroid. If the two objects each hit the asteroid, would the energy released be more than if they collided with each other? Or if they each hit different asteroids that were next to each other?

So how about if two objects are each traveling at .99C relative to a object, say, an asteroid. If the two objects each hit the asteroid, would the energy released be more than if they collided with each other? Or if they each hit different asteroids that were next to each other? Assuming they are of equal mass, at 99% of C they would become a plasma and make some new particles, I think, in all cases. Which new particles probably does change when they impact the asteroid instead of each other. Certainly, the volume of plasma would be greater if an asteroid is hit. Also in the asteroid case, some of their mass would probably "plate out" on the asteroid surface, instead of just expand into space. - That is about it, I think, but probably not what you were hoping for. :D

PS space is quite empty - If planning a trip to another star's planet, not necessary to worry about space traffic control.;) The internal "cosmic ray" showers if you pass thru a cosmic gas cloud is more of a concern - only hitting one or two hydrogen atoms at that speed may make a small shower inside your ship, (I am guessing - too lazy to put any numbers in.)

So have they not been able to find a way to put the mass into Einstein's equation of relative velocity of two particles?

what equations sasha?

V = (V1 + V2)/(1 + V1* V2/c²).

Oh right. This tells you how velocities add relativistically. There are similar equations for mass, length and time.

If you take the POV you seem to be (our clocks & our measure of the EH radius) then the speed of light is steadily approaching zero when starlight falls inside the black hole’s EH (we believe, but do not see). I guess that is OK with SRT etc, if gravity and accelerating frames are in fact one and the same identically, but some how I am not very comfortable with near zero speed light, are you? I.e. my INERTIAL FRAME measurements have c approaching zero - Is Mr. Einstein happy with that? You know more about this than I do - any comments?

When I said "accelerates at an ever decreasing rate", the speed is approaching c at a slowing rate---it takes infinitely long to get to that speed. The speed of light is constant in every reference frame---this is the first postulate of special relativity.

When I said "accelerates at an ever decreasing rate", the speed is approaching c at a slowing rate---it takes infinitely long to get to that speed. The speed of light is constant in every reference frame---this is the first postulate of special relativity.I understood that you were speaking of a mass falling in. I switched to a photon falling in towards the black hole singularity, not mater. Sorry if that was not clear. I have the impression from what you said that even the photon will fall "forever." (For example, during one of my years at some point on its journey it advances only one light second, not a light year.) Is this correct?

If it is, I think the reason I would see (if I could see things inside the EH) that speed of light in that strange part of space, but still part of my inertial frame, is still the unchanged C, even for this photon, is that not only is time slowing down, but lengths are shrinking also. Is this correct?

I.e. no matter how long the photon has been falling, there is still and infinite distance to go to the singularity. I am not sure of this, somewhat confused, and would appreciate your comments on a photon falling from the EH directly towards the singularity, the constancy of the speed of light (in my distant inertial frame, which includes this region of space) etc.

Thanks.

I think it is quite simple. Maybe too simple. Maybe that is the problem, we would like it to be more complicated.

They go "BOOM" and they do it with vilence. Perhaps you get something new out of it, but they just collide and do what the universe always does with something like this. They put on a light show.

So how about if two objects are each traveling at .99C relative to a object, say, an asteroid. If the two objects each hit the asteroid, would the energy released be more than if they collided with each other? Or if they each hit different asteroids that were next to each other?

The energy released would be the same in either case, provided it is measured by the same observer.

The result would be the same as if object A had collided with an immovable object. Their impact speed would not increase at the P.O.I. but rather dissapate (however minute) through the release of alternate energies.

Hi Stryderunknown,



You're mixing up two things here. You're using a statement from special relativity (lightspeed) and a classical Newtonian addition of speeds (V_total = V₁ + V₂), which is not allowed.

The correct reasoning would be:
1) From a classical Newtonian mechanics stand:
The two particles collide, one with V₁, the other with V₂, so the total collision speed is V₁ + V₂. The particles emerge with their respective velocities. In classical Newtonian mechanics, no particles can be destroyed or created. The collision is determined by the conservation of momentum.

2) From the point of view of special relativity
The two particles collide, with a total velocity V = c²*(V₁ + V₂)/(c² + V₁* V₂). This formula can be deduced from the postulates Einstein formulated to write his theory of SR. In the case of SR, the creation and annihilation of particles is allowed, so here (depending on the exact velocities) you'd probably end up with loads of kinetic energy being converted into streams of particles.

Bye!

Crisp

i tried the formula for calculating the speed of the colission and it works fine if i use small speeds (for instance 2 objects moving at 60km/h) and when i use Vt=c x (99%c + 99%c)/(c + 99%c x 99%c) then i olso get a good number, but when i decide to imput the actual speeds in m/sec or km/h i get this wierd result

2.02019514 m/sec (for 99%c)
2.0202011 km/h (also for 99%c)

but as i said when i imput the formula with the percentages i get 0.9999%c

is this some sort of wierd mathamatical fenomena or am i doing it wrong?

"edit never mind, i forgot to put C to the second power hihi"

Incidentally Although this is very old, the LHC thats due to collide proton's (www.cern.ch) will be colliding proton's running in two different directions at around 0.99c each and obviously it's going to generate small instances of what occurred a few seconds after the Big Bang.

hense my intrest in the subject :)

Since the proton has a mass of 1.67262 x 10-27 kg, would not anihilation of two protons produce a lot of energy in perhaps every spectrum and may be a few elementary particles?

Is that what happened in the LHC? Anyone monitoring it?

. . . . The particle enters the event horizon of the black hole but the black hole's singularity is transported before the particle could collide. Will that particle move fasther than light or would it have been destroyed the second it (or before) enetered the black hole's event horizon?We need to make one thing very clear in this discussion: No particle EVER moves faster than the speed of light. Not from ANY frame of reference. That is what the theory of relativity is all about.

Duh?

In fact, only massless particles like photons can even achieve the SOL. Particles with mass (what we humans refer to as matter) are limited to sublight speeds.

Someone made an example in another forum: if we would travel at the speed of light to and from the nearest star, the person travelling wouldn't notice the the trip and would as it were step out of the "spaceship" thinking he hasn’t been gone but on earth he would have been gone for 8.84 years (nearest star is 4.42 light-years)

So would it be right to consider that the traveller has just made a one-way trip forward into time? Hence making time travel possible? Be it a one-way trip!

What it would also mean is that if we travel at just below the speed of light then even the most distant places would be accessible! For example
The Orion nebula is 1270LY away
Considering the length contraction and travelling at 99.99995% C then the distance becomes 1.26999LY meaning that we could traverse that distance in 1.27 years (approximately)

Of course this all depends upon if we could ever achieve that speed!

To Lord Stylus:

Welcome to sf. Your post 40 (or copy from another forum) is Ok, but better known as the "twin paradox." (but you are considering only the twin who traveled.)

Yes indeed i'm only considering the twin that traveld... but he did "jump" into the future did he not?

But not only the twin paradox also the fact that we could reach distant places in the lifetime of a traveller...

Yes indeed i'm only considering the twin that traveld... but he did "jump" into the future did he not?

But not only the twin paradox also the fact that we could reach distant places in the lifetime of a traveller...Yes, he jumped into the future in some sense, but so do all who go to bed and sleep in my POV, but these jumps are smaller and much less costly.

As you are relatively new here, you do not know that I hold what most would consider a crackpot POV about what "I" am (AND OTHERS ARE TOO). It includes my not existing while in dreamless sleep. (Only my body does then.) My brain makes "me" (in the parietal cortex) as part of a Real Time Simulation, RTS, which when body is awake is tightly constrained to model the sensed world around me (Not things like the radio wave which my neural transducers do not sense).

The RTS compensate for the neural delays that accumulate as neurotransmitters diffuse across synaptic clefs to let me, for example, play fast ping pong game - perceive the ball where it is "now" and not where it was more than 10 synaptic delays earlier.* "I" am created as part of the RTS but when the body is dreaming the RTS is running but more freely as less tied to the neural inputs.

The link below was about how the RTS might enable free will to be possible (not just an illusion) without violation of natural laws that control nerve discharges, which control your every thought and action. The RTS POV explains many mysteries of science, such as phantom limbs, why visional perceptions are clear over large solid angle despite only one degree of high resolution input from the fovea. For details, and evidence supporting this non-standard POV, see:

http://www.sciforums.com/showpost.php?p=1294496&postcount=52
Be warned, it is a long read, about 8 pages if printed.

The price of genuine free will is high: You are only non-material information in a simulation, not a physical body which is under the control of the natural laws.

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*Humans evolved the RTS before the Neanderthals did so were better at ducking thrown rocks etc. and killed them off despite their bigger brains and stronger bodies.

What it would also mean is that if we travel at just below the speed of light then even the most distant places would be accessible! For example: The Orion nebula is 1270LY away. Considering the length contraction and travelling at 99.99995% C then the distance becomes 1.26999LY meaning that we could traverse that distance in 1.27 years (approximately). Of course this all depends upon if we could ever achieve that speed!The energy required to attain that speed is, well, astronomical. The familiar equation from Newtonian physics, f=ma, is greatly perturbed at relativistic speeds. It's as if your mass increases at a non-linear rate, so each increase in speed requires a disproportionate increase in acceleration force.

This in fact is the way the arcane theory of relativity would manifest itself in a practical scenario. Without "warp drive," the actual dialog on the bridge of the Enterprise would go something like this: "Ensign Crusher, you've been accelerating at full throttle for two years. Why has there only been a barely measurable increase in the ship's velocity in all that time?"

Interstellar travel at relativistic speed is therefore not practical because of the fuel requirements. Who would fund such a voyage? How much of the ship's fuel would be expended on simply pushing the enormous fuel tanks? But if it were possible, people could indeed travel to distant stars or even other galaxies within a single lifetime. Of course that would have very little impact on civilization. Their transit time would be so long to the people who stayed home, that the concepts of "communication" and "trade," much less "community," would not apply.

Generation starships will undoubtedly be the only means of interstellar travel, which means that a voyage even partway across a single galaxy and back would take tens of thousands of years.

Have you calculated how long it would take, at a comfortable acceleration of one gee, to reach a speed of seven hundred million miles per hour? :)

....
Have you calculated how long it would take, at a comfortable acceleration of one gee, to reach a speed of seven hundred million miles per hour? :)

Considering i usually use the metric system i took 700.000.000,00miles/hour and divided it by 2.25 to make m/s and noticed that you gave speed greater that light speed, 311.111.111,11m/s.
Then to continue with the calculation, I divided that (impossible speed) by 9.81m/s² giving me the time in seconds to reach that speed in seconds, 31.713.670,86 sec.
This number i divided by 86400 to give the day's, it would take 367,06 day's, just over a year!

This is of course using Newtonian mechanics, What is the proper solution for this question using Relativistic calculations, propelling a mass of lets say 5.000.000,00kg (2 space shuttles) and a "possible" speed of lets say 250.000.000,00 m/s?

i know that the force needed to achieve sub light speed is impossible to manufacture, that’s why it was hypothetical :)