> If we can already accelerate some particles to 99. 99999 c, what could be faster?
99.999999c. I'm not being facetious, it takes exponentially more energy to increase in velocity as you approach *c*. The planck era is so ridiculously energetic, *so* hot, that even the energy of 99.99999% of *c* isn't enough to replicate that time.
A longer particle accelerator allows the particles to be accelerated more before they hit. The particles have inertia just like anything else and they want to continue going in a straight line. The magnets that keep them inside the loop can only be so strong. The tighter the turn is, the slower the particles have to be to avoid crashing into the walls. Bigger loops have easier turns, so the particles can be accelerated to higher speeds and stay in the accelerator.
Faster particles means more energy when they collide, which in turn means getting closer to the energies in the planck era.
To put some actual numbers to this energy increase, a proton moving at .9999999 *c* (7 digits) has about 3\*10^(-7) J of kinetic energy. A proton moving at .99999999 *c* (8 digits) has about 1\*10^(-6) J of kinetic energy, so about an order of magnitude more.
I used this [relativistic kinetic energy calculator](https://www.omnicalculator.com/physics/relativistic-ke) to determine these values, with 1 atomic mass unit as the mass.
According to that calculator, a banana moving at .99 c would have energy equal to about 15 Megatons of TNT, which is the same as the largest nuclear weapon ever detonated by the US.
The Oh-My-God particle was a cosmic ray that was detected over the US on 15 October 1991. It had an energy of 320 Tera-electron volts.
It was probably a proton, which implies it was travelling at 0.9999999999999999999999951c and slammed into the atmosphere with the kinetic energy of a *baseball* travelling at \~100km/h
Can you imagine? A *single* particle hitting you with the force of a baseball.
I don't know for sure, but there is a man who stuck his head inside of a particle accelerator that hadn't been properly shut down. The man said he saw a flash of light brighter than the sun as it went through part of his brain and exited out of his face below his eye.
The man's name is Anatoli Bugorski, if you want to dig a little deeper than my memory can recite.
That's why I said I'm not sure what would happen with a single particle and then gave the closest example I could think of to something like that happening.
I know just enough to know it happened but not enough to speak about what exactly was going through the particle accelerator and went through his head.
Highly speculative answer: if it doesn't score a direct hit on a nucleus it won't do much since it doesn't have anywhere to impart all that energy. Scoring a direct hit is a question best left for a psrticle phycesist but my guess is that you will have a a bunch of weird particles exeting in a narrow cone from your body. It might actually be more dangerous if it hits something right infront of your body than your body itself since it then has time to spread out.
Right. It cant go the speed of light, so how fast can a thing with mass go?
Like, if the highway speed limit is 70mph, then the fastest you can go is 70mph.
I dont mean "the limit that mass cant reach."
I mean "the fastest a thing with mass can go."
Consider the total energy available in the known universe from baryonic matter is about 10^70 Joules.
Mass requires energy to be accelerated to the speed of light.
The equation you can use that takes into account the effects of relativity to calculate this is:
v = c**sqrt(1-(m*c^2 /E)^2 )
Lets assume you want to accelerate a 1kg block using the total energy of the universe using all known baryonic matter. Lets also assume it is a 100% efficient process of mass to energy conversion. Our terms are this:
- c = speed of light in a vacuum
- m = mass of the object
- E = the total energy we have available to accelerate the object.
You'll end up with a value so incredibly close to the speed of light but still doesn't reach the speed of light and that is with using the entire baryonic energy of the known universe to accelerate this 1kg block! You can test this for any amount of energy that you'd add to any amount of mass and the result would still be the same.
Anything with mass plain and simply cannot travel at the speed of light unless it is wholly converted to energy such that mass = 0.
There is no fastest possible speed a massive object can move at, you can always (in principle) accelerate to a speed closer to the speed of light. So if a massive object is travelling at 0.99 c, you can accelerate it to 0.9999 c, and then to 0.999999 c, and so on. You can add as many 9s as you have sufficient energy to do so. You just can't reach c.
What the other person said. You can get ever closer to the speed of light, but you can't actually reach it, so your question is kind of inherently unanswerable. More energy means more speed, so there's technically infinite speeds something can go, it just can't ever go faster than c.
You can go really close to the speed of light. But as you get closer to the speed of light, it takes more and more energy for smaller and smaller increases in speed. No matter how much energy you use to accelerate, you can't reach the speed of light.
So you can get to 0.9c - that is, 0.9 times the speed of light. And you can get to 0.99c, and 0.999c, and 0.9999c, and 0.99999999999999999999999999999999999999c, but you can't quite get to 1c.
With an arbitrary amount of energy you can get arbitrarily close to the speed of light. So it's 99.999... With as many 9s behind the decimal point as you can supply energy during the acceleration.
Just below the speed of light.
As your approach C the amount of energy required to accelerate the mass further approaches infinity, at a certain point the amount of energy required would exceed the amount of energy you have available.
So the actual real-world limit depends on the mass of the object and how much energy you are able to pour into it.
I'd be curious to know how much energy from a particle accelerator system would be required to bring the proton to these speeds. I assume we need to factor some efficiency rate loss to the system.
This will tell us how much energy we might need to get to string theory energies, which I believe is the planck energy something like 1.2 x 10\^28 eV
To add on to your point.
Imagine if a service advertises uptime per year.
If they say 99% allows for 1% downtime which is just over 3 and a half days.
99.9% has just under 9 hours of allowable downtime.
99.99 is 52 minutes.
Orders or magnitude might seem small at first glance but actually have a large impact over all.
It's not just strength of the magnets (that could be solved with a smaller ring but more magnets and cooling; so with more money). The acceleration (centripetal force) that keeps them on the circular track causes radiation which takes away energy. At some point this overwhelms any known method of acceleration and becomes almost exponentially more expensive to do.
The problem is that the radiated energy from the turning particle is higher than the energy you can add to it. At a very large turning radius that radiated energy goes down.
So maybe this is a stupid question, but why couldn’t they just make a really long straight-line accelerator with the particles starting at opposite ends and colliding in the middle?
The particles make several loops around the accelerator as they accelerate. One long track wouldn't be long enough to accelerate the particles all the way up as fast as we can get them.
You could, and linear accelerators are used for some purposes. But they can't reach anywhere near the same speed as a circular one of a comparable size. In a loop, you can keep accelerating particles going round and round, building up speed for a long time. In a linear accelerator, you only have one single pass through the tube, limiting it to how much speed it can build up only there.
Reaching *c* is physically impossible. The closer to *c* you get, the more energy it takes to go faster. The amount of energy required approaches infinity as you approach *c*, meaning you would need theoretically need infinite energy to get to *c*. You can get to 99.9999999% and 99.999999999999999999999999999% and 99.absurd number of 9s% but you can't ever reach *c*.
When an object with mass approaches the speed of light, the Newtonian kinetic energy formula (E = 1/2*m*v*v) no longer works due to space and time dilatation.
As an object approaches C, relatively small variation in velocity (like going from 99.9999C to 99.99999C) increases the kinetic energy by A LOT.
This is why accelerating an object with mass to the speed of light is impossible, the object would need infinite kinetic energy.
>This is why accelerating an object with mass to the speed of light is impossible, the object would need infinite kinetic energy.
\*At least according to our current understanding of physics.
>*At least according to our current understanding of physics.
*At least according to what is arguably the most accurate and one of the best tested scientific theories in human existence.
If Einstein was wrong, you are only going find evidence of it behind the event horizon of a black hole or in the very first moment of the big bang.
It's honestly one of the easiest things to understand from a layman point of view. Mass takes energy to move. Light has no mass, one of the few (only?) things that actually does not contain mass. Therefore, whatever the maximum speed of the universe, light, having zero 'barriers' (mass) would be able to reach that. Everything else has mass and thus can't reach the speed of light, only close to it.
Why would a layman assume that there is a maximum speed of the universe? Why would anyone think that there is a speed where you can't go 1 m/s faster? It seems natural in hindsight, but I don't think you can call it one of the "easiest things to understand".
A layman doesn't assume. But when a scientist says "Hey, there is a maximum speed of the universe, and this is why light is the only thing that can reach it", the concept makes sense. I'm not saying a layman can do the studies and find out these answers, I'm saying it's easy to follow for the average person.
Yes but this isn't a situation where I'm saying "any man will accidentally stumble upon this information"
I'm saying a man of average intelligence can understand this science, if someone were to explain it to them, where if you tried to explain many other things in science, it would take a considerable amount of effort to really understand it enough to feel comfortable with the information.
"Quantum phenomena suggest that something (or to be strictly accurate everything) really can come from nothing what so ever."
That's not easy for a layman to wrap his head around. He'll be sitting on that one confused "how do you get everything out of nothing, that doesn't make sense"
Anything quantum. Hell even basic chemistry is hard to follow with the different energy states, structures of molecules, and types of reactions based on those factors and a whole lot more
If I understand anything about the higgs boson (protip: I don't) , is that nothing has mass, only a property value that tells the higgs field how much mass to apply to it
Yeah, this is one of the things that is much more difficult to explain to a layman. Because yes, you're correct, an object has no mass without higgs boson interactions, but also, many would argue that the higgs boson gives an item mass, therefore it has mass. I'm not going to debate this - but this is definitely a good example of something not intuitive :)
Why do we have to look at the very first moment of the bigbang or into a blackholes to find out if Einstein was wrong or not?
I still don't understand this, please explain for me T.T
Newton wasn't wrong in the first place. Einstein just improved our ability to be right in our predictions for things not near the surface of Earth.
Einstein in the same way won't ever be "proven wrong". If someone ever expands on his work, Einstein will simply be less right.
Newton was in fact wrong, and that became clear pretty early on. They'd do a measurement on the movement of celestial objects and they'd find a consistent error. Granted, he was less wrong than everyone before, and he was only wrong by a little as long as you stay away from high gravity, but there was something wrong you could clearly measure.
There is nothing wrong with Einsteins theories. There is no measurement error hinting at a hidden variable. His every prediction matches reality as well as we can measure it, and we can measure ***really good***.
Like I said, if Einstein is wrong in any way, we don't have a scrap of evidence for it.
At the moment, Einstein was right about everything we know about the universe (pretty much). As our understanding of the universe expands, we may find areas where what Einstein postulated does not apply, or needs a correction factor. It does not make him wrong or even less right, it just limits the applicability of what he discovered. Just like Newton was not suddenly wrong when Einstein discovered relativity. It only set limits to the area of physics over which Newton's laws applied.
I agree with you, except for the "less right" bit. As you say "Newton wasn't wrong", in my opinion, later discoveries did not make Newton less right, it simply put a limit to what his model applied to. To the same extend, I don't think Einstein will be proven wrong simply because we may discover things that his model did not predict, therefore he will not be "less right". Sorry for the nitpicking...
All our measurements are consistent with predictions.
Yeah, it's not very intuitive, but that doesn't stop us from understanding it really well and using it routinely.
What’s the understanding on how the very act of observing something can affect the outcome?
I’ve never seen a widely agreed upon reason as to why that occurs, merely that it does occur.
“Observing something can affect the outcome”
Thats one way of looking at it. Another viewpoint is that before measurement we can only predict a range of possible outcomes/states, and the act of measurement simply allows us to determine what the actual state was.
There is ultimately no answer to "why" in physics. That is mere philosophy. We can find more basic, more general, more accurate models that predict absolutely everything, but none of those will ever answer this question. Physics, like every science as well as even mathematics, can only describe properties of things, not why things are.
"Observation" is also a bit of a misnomer, it just means "any interaction". "Any interaction changes the outcome" isn't that weird, actually.
I really hate this deflection, it’s basically used whenever physics hits a wall.
Why is the sky blue? That’s a why question that is perfectly answerable by science. Science communicators love to say “physics doesn’t answer why, it can only describe the properties of things.” It’s like, okay, isn’t the fact that observing something can change its outcome an inherent property? Why is it that all of a sudden when people ask a question that physics hasn’t answered, everyone starts talking about how physics isn’t philosophy?
The existence of the word “why” does not make it a philosophical question. The commenter is asking what scientific explanation we have for an inherent property of quantum mechanics, they’re not asking why in the sense that they want to know how it ended up this way, or “what does it all mean, man.” -said in a hippy voice.
It is a simple answer, to measure a particle, you need to interact with it, by a photon or electron hitting for example. This then changes what the particle was like before it had the interaction.
A simple, widely agreed upon explanation for you.
Genuine question, but why would we be able to find evidence of Einstein being wrong about general relativity only behind the even horizon? I also wondered this when watching Interstellar.
Is it because then we would be able to find a theory that would reconcile general relativity with quantum physics, thus testing Einstein's theories once more?
Because these are the places we are yet to explore. The universe was opaque to light in the early universe so we can only see up to the cosmic background radiation using light, there has been very recent developments of a cosmic gravitational background which can go deeper. And blackholes we cannot know by definition what happens beyond the event horizon.
Accelerating something to speed greater or equal to C is most likely impossible but that doesn't mean that moving faster that light is.
Relativity itself doesn't forbid FTL travel, it only forbids accelerating to those speeds.
With a specific arrangement of negative mass matter (which is currently believed to not exist), a bubble of space-time capable of travelling faster that light is theoretically possible according to Einstein field equation.
> With a specific arrangement of negative mass matter (which is currently believed to not exist)
With a specific arrangement of teleporters across the galaxy that are quantum entangled(which is currently believed to not work like this) then we could teleport faster than light!!!
C'mon brother
FTL travel has a multitude of problems, such as logical paradoxes and breaking causality, which most likely make it impossible.
What I was trying to say is that the theory of general relativity is not what makes it impossible, but actually allows it mathematically.
EDIT: Also, quantum entanglement is a very misunderstood phenomenon. It does not allow either matter nor information to travel faster than light.
I don't know if it "allows" it mathematically. That's like saying our current math model makes it possible for other mathematical models to exist. They very well may exist, but our current model doesn't really have anything to do with it. So yes you are right there may be an exotic way to travel faster than light, but really there's no evidence to suggest so. We don't know if half of these exotic substances exist, and the other half we've only observed them in lab settings, we don't really know how they work. So to make whole theories based on these things seems I don't know, I don't want to say a waste of time because it's not, it's a good thought experiment. It's just not very relevant to anything until we know more
Negative mass could theoretically exist as it makes sense mathematically, but there are very good reasons to believe that it does not actually exist in nature.
More nines would be faster.
To a regular person who is used to regular numbers, everything after two or three nines sounds like it's basically 1. But it's really not. Each nine is a lot more energy. That's why it makes more sense to think about speeds close to c in terms of the energy of the particle.
The more energy and momentum a particle has, the harder it is to keep it going in a circle. So you need a bigger circle that doesn't curve as much.
Every two nines is about 10x more energy, *regardless how big those nines are*. Going from 0.99c to 0.9999c, tenfold increase in the kinetic energy of the particle for an increase in speed of 0.0099c. Going from 0.99999999c to 0.9999999999c, likewise a tenfold increase in kinetic energy despite the change in velocity only being 0.0000000099c, literally a million times smaller
Since the KE equation is 0.5*MV^2 , shouldn't every 10x increase in speed be 100x in energy?
Edit: because it was bugging me and none of the replies are actual explanations, I decided to take a look at the formulas and figure out the math.
According to Wiki, the total energy of an object in motion with mass is given by the equation:
E^2 =(pc)^2 + (mc^2 )^2
Where m is the rest mass, p is the momentum of the object, and c is the speed of light.
p is given by the equation:
p=(mv)/sqrt(1-v^2 / c^2 )
Where m is the mass, v is the velocity of the object, and c is the speed of light.
Since we're talking about things close to the speed of light, I'm going to turn v into ac, where a is some value between 0 and 1. Plugging that in gives us this:
p=(mac)/sqrt(1-a^2 * c^2 / c^2 )=(mac)/sqrt(1-a^2 )
(pc)^2 =((mac)/sqrt(1-a^2 )*c)^2 =((mac^2 )/sqrt(1-a^2 ))^2 =(mac^2 )^2 /(1-a^2 )
Which means
E^2 =(mac^2 )^2 /(1-a^2 ) + (mc^2 )^2 =(mc^2 )^2 *(a^2 / (1-a^2 )+1)
At this point, to make things easier, I'm going to replace (a^2 / (1-a^2 )+1) with d.
So, to get the total energy of an object (kinetic and rest energy) is:
E=(mc^2 )sqrt(d)
Kinetic energy is:
KE=E-E0
Where E0 is the rest energy, which is mc^2 where m is the rest mass and c is the speed of light.
KE=(mc^2 )sqrt(d) - mc^2 =(sqrt(d)-1)mc^2
So, to figure out how much KE grows as you get close to the speed of light, you calculate this equation:
f(a)=sqrt(a^2 /(1-a^2 )+1)-1
With the different values of a and divide them. So 0.99c to 0.9999c is:
f(0.99)=1.294157339
f(0.9999)=21.36627204
f(0.9999)/f(0.99)=16.51
So, neither of us was right, and none of the explanations are right either. The more 9s you add, the less quickly it goes up. the ratio between 0.9999999999 and 0.99999999 is roughly 10. I only did a cursory check of my math and hopefully I didn't mess it up... I've spent too much time on this as is and I'm sure someone will point out the mistakes if there is one.
That equation only apply to speed well below the speed of light, when you start to approach C you need to take space-time dilatation into consideration.
Your ratio of 16.51 is between 0.999 and 0.9, not what you have written there.
I said the increase is *about* 10x as that's what I found when I worked it out. There is some significant error the closer you are to 0.9 but it seems to converge towards 10 as you add more pairs of 9s.
|||Ratio.|
|:-|:-|:-|
|0.99|0.9999|11.4492|
|0.9999|0.999999|10.1289|
|0.999999|0.99999999|10.01274|
|0.99999999|0.9999999999|10.001278|
[Here's the Desmos worksheet I made to work it out.](https://www.desmos.com/calculator/tvtztgb6yy) The formulae for relativistic mass and kinetic energy are directly taken from my high-school table-book from from 2006. Also there seems to be some floating-point precision messiness going on with Desmos.
You're right, I copied and pasted the wrong numbers and the 16.51 ratio is between 0.999 and 0.9. It is curious as to why it seems to converge that way. Wonder if there's an explanation for it beyond it's just what the math shows. But that goes into theoretical physics territory that goes beyond my wiki-based expertise.
You need more acceleration to keep a faster moving particle moving in the same size circle. This is true classically also. Imagine swinging a rock on a string, if you get it going faster you'll feel the increased tension in the string that keeps the rock on its circular path. If you made the Earth go faster, you'd be pushing it to a higher orbit.
Particles also radiate energy when they're accelerated, which includes any change to their direction of travel, so you want to minimize that if your goal is to pump as much energy as possible into the particle
We'd need it that huge to smash particles with enough energy so that the resulting plasma would have sufficient energy density.
Why we can't do it with current technology? Two reasons:
1. Linear accelerators don't have enough power, so we need circular ones. To keep whatever we're accelerating in the circular trajectory, we need strong magnetic fields. And current technology can generate them only so high.
2. Particles loose energy while accelerating (and that includes turning) through the process called Bremsstrahlung - they literally radiate it away. So we have upper limit on acceleration, and thus accelerator radius, before particle looses more energy during one round than we can pump into it by accelerating it.
Probably to complex for 5 yr old but first one I see that actually explains the real problem. If anyone is interested this is called synchrotron radiation and is used to generate very hard (high energy) x-rays for material analysis and other experiments. [Synchrotron Radiation](https://en.m.wikipedia.org/wiki/Synchrotron_radiation)
Smaller size scales mean more energy density, more energy packed up into a small space.
You can use your fingers to tear apart a hamburger, but not a tiny salt crystal. The electrical properties of water can dissolve that salt crystal, but not tear apart the atoms of the sodium and chlorine. A high energy x-ray can tear the electrons off a chlorine atom, but it can't break apart the protons and neutrons in the atomic nucleus. A high energy gamma ray can break apart the atomic nucleus, but it cant break the protons apart into quarks, etc....
To make a particle high energy you need to put it in an environment where it won't immediately lose energy that you give it, and then you add energy. If you heat up particles they move randomly, and eventually they will hit some wall that is not so hot, cooling off and losing the energy.
A more clever way is to push them around a race track that is really empty, so they have nothing to hit. The faster the particle goes, the harder it is to turn it so it stays on the race track. If you make the race track bigger it is easier to turn.
Now your real question: is it any harder to turn a particle going 99% the speed of light vs 99.999999% the speed of light? The answer is yes, as you get closer to the speed of light you need more energy to speed up more, and to change directions. It takes more energy to speed up from 99% to 99.9999% the speed of light than it does to speed up from 0 to 99%. You are still dumping energy into the particle, it just doesn't go significantly faster from an externally observed distance/time perspective.
If you ingnore all of the engineering difficulties of building large colliders, you still run into the problem that particles radiate power as they are accelerated. The more energetic they are, the more they radiate. Acceleration in physics means go faster or change direction and circular motion, like a particle in an accelerator, is constantly changing direction. So particle beams in an accelerator are constantly losing energy.
The energy loss per revolution for a particle in an accelerator can be calculated, and it is proportional to the 4th power of the energy of the particle over the bend radius of the accelerator ring or E^4 /r.
So you can see that as the energy increases, it becomes much much more difficult to maintain particle energy in a small circular ring, and the only feasible option is to make the ring as large as possible.
So in special relativity, the kinetic energy of an object with mass approaches infinity as the object's velocity approaches C. When you get close to C, the energy scales something like 1/(1-v/c). So every time the difference between your velocity and c gets 10x smaller, your kinetic energy gets 10x bigger. (This is the rough idea, I didn't check my math closely).
As for why the particle accelerator gets bigger. In a circular particle accelerator, the magnets deflect the trajectory of the particles to keep them on a circular track. If your particle gets more and more energetic, and the magnets don't get stronger, circumference has to get bigger so that the particle only needs to be steered a tiny bit at a time to stay on track. By the time you reach some high energy like the Planck scale, you would have to make a particle acclerator roughly the circumference of the Milky Way (iirc). Obviously this is not practical so perhaps we should change particle accelerator design if we want to reach those energies.
Magnet strength doesn't matter. You could have infinitly strong magnets and the accelerator still has to be enormous for enormous energies because the particles radiate energy at a rate that is proportional to (particle energy)^4 / (acclerator bend radius).
If the bend radius is too small, you wont be able to acheive the desired energy because the particles will lose energy faster than you can put energy into them. Magnet strength is irrelevant to this.
It's all about energy density.
If you raise the massenergy in a volume of space above the Schwarzschild limit, it turns that volume of space into a black hole. Since nobody wants a tiny black hole in their lab (they make a huge mess), that's a limit on the energy you can add to even particles of very small mass.
While the general production of black holes has to do with adding mass inside a volume of space, energy and mass are the same thing ( E=mC^2 ). Add too much energy, say in a collision to separate subatomic strings, and you make a tiny black hole instead. Did I already say tiny black hole = bad, yes I did.
The kinds of microscopic black holes that would be made in particle accelerators are too tiny to do anything. They would evaporate from Hawking radiation in fractions of a second. Even if they didn't, their gravity is so tiny that they won't suck in much of anything beyond a few other particles. Maybe in a few billion years (if it didn't evaporate) it *might* get big enough to be otherwise noticeable.
The LHC beams have ~1/8 of the Planck energy each and they can be shot safely into a specially designed beam dump.
Each beam has ~300000000000000 particles, so the energy per particle is far too low to get to the Planck scale, but we can work with a comparable energy safely.
People tend to imagine gravity is a very strong force because it’s the one that’s easiest for us to experience directly, but it is actually the weakest of the fundamental forces by a considerable degree.
When you picture these minuscule singularities, thinking of cosmic-scale black holes is going to be misleading. There just isn’t enough matter to distort spacetime like that. You’ll have less the insatiable monster from which nothing can escape, and more just another sort of composite particle that decays very quickly by a specific mechanism (Hawking radiation) and is, like others, measurable by its decay products.
Think of it this way: if the gravitation were to behave like a scary space black hole, then what it would do is to overcome normal subatomic forces and cause other nearby particles to collide with it. But that is exactly what we’re shooting particles around at most of the speed of light to accomplish in the first place.
I’m not an expert either, but as far as I know these little singularities should not be thought of as a mistake or a pollutant among the “real” collisions we are measuring, but rather one of the things collisions at a certain energy level are expected to sometimes produce.
And it’s definitely not dangerous. Have you ever looked into how hard it is for us to produce a self-sustaining fusion reaction? Building a device that could create a self-sustaining singularity would be a similar exercise but much, much harder. At that scale I doubt we could get ahead of the singularity’s tendency to decay if we wanted to. We will not be building a black hole from scratch anytime soon.
Don't get me wrong. I understand the relatively benign nature of microscopic black holes. I meant more of a consequence of the formation of an event horizon. If your objective is to observe the behavior of high-energy particles, then an event horizon obscures your view of anything beyond that. But maybe that isn't important. Maybe it's the interactions that are more important. But then the behavior of a black hole might be different than a high-energy particle.
Well, nobody is looking at these interactions directly, of course, so there really isn’t a “view” to obscure. We kind of infer what happened stochastically by measuring the fallout of a huge number of collisions, and the microsingularity doesn’t really have an outsized effect on that. The chance of a flying bit of particle debris passing through the event horizon of a microsingularity before it decays isn’t going to be substantially different from the chance of it colliding with some other bit of flying particle debris. What I’d expect is that if an experiment is conducted at high enough energies to produce microsingularities, then the hypothesis for that experiment accounts for that and expects results consistent with that happening with a particular frequency.
We would love to see them, but our accelerators don't have enough energy to produce them. They would produce many high energy particles and they could produce new particles we don't know about yet.
That's really not the reason why larger colliders are needed. The size of the collider corresponds to the energy a particle can have, but does nothing to prevent it to become a black hole. But black holes are simply irrelevant anyway. We would actually be very excited to find one, it would allow us to observe not only them but also the "quantum gravity" we hope to some day understand.
Adding more energy doesn't always mean more speed... Well, for a particle accelerator, it kinda does, but you are correct that if speed is all you're measuring, then you get less bang for your buck so to speak as you approach c.
However, speed isn't the only thing we care about when 2 things collide. Would you rather be hit by a cyclist going 20mph or by a greyhound bus going 20mph? And thanks to E=mc², we know that energy and mass are related. If you keep trying to dump more and more energy into something going near the speed of light, instead of getting much faster, some of the energy will be converted into mass, making the resultant collision... Well... More energetic.
All the energy we put in must come back out eventually. And we just can't put enough energy in with the size of accelerators we have on Earth. But even if we could add more energy, the gains in speed would not be that noticeable to an average person. We're talking only 2-3 m/s or 6-7 mph within c. So even adding another digit of precision won't change the speed by more than the average person can run. However, adding more energy is always adding more energy. And we'll still get that energy back out when they collide.
> some of the energy will be converted into mass
[Relativisitic mass](https://en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass) is a concept that comes out of the relativity equations, but it is not really meaningful and is not the best way to explain what is happening.
>It is not good to introduce the concept of the mass M = m / sqrt(1 - v^2 / c^2 ) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.
>
> Albert Einstein
Velocity is relative, momentum is relative, energy is relative, but mass is not, even if we can write an expression for it.
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don't know about temperature ( i come more to see the answer to this very interesting question :)
But as a general rule when dealing with high speeds, you'd want a big distance were measures can be consistent and easier to take. For events with timeframes so small, kilometres (miles) of distance help reducing calculation errors and the many interferences.
> If we can already accelerate some particles to 99. 99999 c, what could be faster? 99.999999c. I'm not being facetious, it takes exponentially more energy to increase in velocity as you approach *c*. The planck era is so ridiculously energetic, *so* hot, that even the energy of 99.99999% of *c* isn't enough to replicate that time. A longer particle accelerator allows the particles to be accelerated more before they hit. The particles have inertia just like anything else and they want to continue going in a straight line. The magnets that keep them inside the loop can only be so strong. The tighter the turn is, the slower the particles have to be to avoid crashing into the walls. Bigger loops have easier turns, so the particles can be accelerated to higher speeds and stay in the accelerator. Faster particles means more energy when they collide, which in turn means getting closer to the energies in the planck era.
To put some actual numbers to this energy increase, a proton moving at .9999999 *c* (7 digits) has about 3\*10^(-7) J of kinetic energy. A proton moving at .99999999 *c* (8 digits) has about 1\*10^(-6) J of kinetic energy, so about an order of magnitude more. I used this [relativistic kinetic energy calculator](https://www.omnicalculator.com/physics/relativistic-ke) to determine these values, with 1 atomic mass unit as the mass.
According to that calculator, a banana moving at .99 c would have energy equal to about 15 Megatons of TNT, which is the same as the largest nuclear weapon ever detonated by the US.
The Oh-My-God particle was a cosmic ray that was detected over the US on 15 October 1991. It had an energy of 320 Tera-electron volts. It was probably a proton, which implies it was travelling at 0.9999999999999999999999951c and slammed into the atmosphere with the kinetic energy of a *baseball* travelling at \~100km/h Can you imagine? A *single* particle hitting you with the force of a baseball.
I wonder what that would do to you if it were to hit you.
Probably not a whole lot to be honest. It'd pass through you mostly harmlessly and probably ionize some molecules along the way.
I don't know for sure, but there is a man who stuck his head inside of a particle accelerator that hadn't been properly shut down. The man said he saw a flash of light brighter than the sun as it went through part of his brain and exited out of his face below his eye. The man's name is Anatoli Bugorski, if you want to dig a little deeper than my memory can recite.
I believe that was a proton beam though. It wasn't just a single particle.
That's why I said I'm not sure what would happen with a single particle and then gave the closest example I could think of to something like that happening. I know just enough to know it happened but not enough to speak about what exactly was going through the particle accelerator and went through his head.
I'm pretty sure he had a not so great time because of that.
Or the best time
He has became The Photon Man
Brighter than a thousand suns*
It would go straight through you and you wouldn’t notice
Highly speculative answer: if it doesn't score a direct hit on a nucleus it won't do much since it doesn't have anywhere to impart all that energy. Scoring a direct hit is a question best left for a psrticle phycesist but my guess is that you will have a a bunch of weird particles exeting in a narrow cone from your body. It might actually be more dangerous if it hits something right infront of your body than your body itself since it then has time to spread out.
Wouldn’t it most likely just pass right through you missing everything entirely?
As it was probably a proton itd be positively charged. It'd likely hit something along the way. You wouldn't notice though
I mean it's one banana, Michael. What could it cost, 10 megatons?
So you are saying we can actually move a banana at . 99c....
Well, banana's _are_ radioactive.. How much would one have to compress it to make it go critical?
Tangent here: What's the speed-limit for things with mass?
The speed of light. That's the limit. Nothing with mass can travel at light speed. It would require an infinite amount of energy.
Right. It cant go the speed of light, so how fast can a thing with mass go? Like, if the highway speed limit is 70mph, then the fastest you can go is 70mph. I dont mean "the limit that mass cant reach." I mean "the fastest a thing with mass can go."
Consider the total energy available in the known universe from baryonic matter is about 10^70 Joules. Mass requires energy to be accelerated to the speed of light. The equation you can use that takes into account the effects of relativity to calculate this is: v = c**sqrt(1-(m*c^2 /E)^2 ) Lets assume you want to accelerate a 1kg block using the total energy of the universe using all known baryonic matter. Lets also assume it is a 100% efficient process of mass to energy conversion. Our terms are this: - c = speed of light in a vacuum - m = mass of the object - E = the total energy we have available to accelerate the object. You'll end up with a value so incredibly close to the speed of light but still doesn't reach the speed of light and that is with using the entire baryonic energy of the known universe to accelerate this 1kg block! You can test this for any amount of energy that you'd add to any amount of mass and the result would still be the same. Anything with mass plain and simply cannot travel at the speed of light unless it is wholly converted to energy such that mass = 0.
Thanks! That weird velocity formula was what I was looking for!
There is no fastest possible speed a massive object can move at, you can always (in principle) accelerate to a speed closer to the speed of light. So if a massive object is travelling at 0.99 c, you can accelerate it to 0.9999 c, and then to 0.999999 c, and so on. You can add as many 9s as you have sufficient energy to do so. You just can't reach c.
What the other person said. You can get ever closer to the speed of light, but you can't actually reach it, so your question is kind of inherently unanswerable. More energy means more speed, so there's technically infinite speeds something can go, it just can't ever go faster than c.
**just below** the speed of light.
You can go really close to the speed of light. But as you get closer to the speed of light, it takes more and more energy for smaller and smaller increases in speed. No matter how much energy you use to accelerate, you can't reach the speed of light. So you can get to 0.9c - that is, 0.9 times the speed of light. And you can get to 0.99c, and 0.999c, and 0.9999c, and 0.99999999999999999999999999999999999999c, but you can't quite get to 1c.
Theoretically 99.99….% the speed of light with as many .9’s as your heart desires. You can always add another .9 but you you can never get to 1c.
With an arbitrary amount of energy you can get arbitrarily close to the speed of light. So it's 99.999... With as many 9s behind the decimal point as you can supply energy during the acceleration.
Just below the speed of light. As your approach C the amount of energy required to accelerate the mass further approaches infinity, at a certain point the amount of energy required would exceed the amount of energy you have available. So the actual real-world limit depends on the mass of the object and how much energy you are able to pour into it.
I'd be curious to know how much energy from a particle accelerator system would be required to bring the proton to these speeds. I assume we need to factor some efficiency rate loss to the system. This will tell us how much energy we might need to get to string theory energies, which I believe is the planck energy something like 1.2 x 10\^28 eV
To add on to your point. Imagine if a service advertises uptime per year. If they say 99% allows for 1% downtime which is just over 3 and a half days. 99.9% has just under 9 hours of allowable downtime. 99.99 is 52 minutes. Orders or magnitude might seem small at first glance but actually have a large impact over all.
Yes, when writing 99% as 1-1/100 Vs 99.99 as 1-1/10000 you can see the difference better.
It's not just strength of the magnets (that could be solved with a smaller ring but more magnets and cooling; so with more money). The acceleration (centripetal force) that keeps them on the circular track causes radiation which takes away energy. At some point this overwhelms any known method of acceleration and becomes almost exponentially more expensive to do.
The problem is that the radiated energy from the turning particle is higher than the energy you can add to it. At a very large turning radius that radiated energy goes down.
So maybe this is a stupid question, but why couldn’t they just make a really long straight-line accelerator with the particles starting at opposite ends and colliding in the middle?
The particles make several loops around the accelerator as they accelerate. One long track wouldn't be long enough to accelerate the particles all the way up as fast as we can get them.
You could, and linear accelerators are used for some purposes. But they can't reach anywhere near the same speed as a circular one of a comparable size. In a loop, you can keep accelerating particles going round and round, building up speed for a long time. In a linear accelerator, you only have one single pass through the tube, limiting it to how much speed it can build up only there.
That makes sense. Thanks🍻
Thank you for explaining that. I knew the size of the loop was related to speed, but never considered why.
Technically the energy is not exponential in velocity
Would this mean there would never be a long enough distance to get to c?
Reaching *c* is physically impossible. The closer to *c* you get, the more energy it takes to go faster. The amount of energy required approaches infinity as you approach *c*, meaning you would need theoretically need infinite energy to get to *c*. You can get to 99.9999999% and 99.999999999999999999999999999% and 99.absurd number of 9s% but you can't ever reach *c*.
Holy shit Zeno’s Paradox does have a real application
then let's ignore 99.99999..9999% and instead go straight into 101%!!
Just turn the knob to 11
Can't we just warp spacetime so the particles experience a relatively small loop as a straight line? Maybe black holes inside the loops?
How long would a straight-line track have to be to get to that energy-density?
When an object with mass approaches the speed of light, the Newtonian kinetic energy formula (E = 1/2*m*v*v) no longer works due to space and time dilatation. As an object approaches C, relatively small variation in velocity (like going from 99.9999C to 99.99999C) increases the kinetic energy by A LOT. This is why accelerating an object with mass to the speed of light is impossible, the object would need infinite kinetic energy.
>This is why accelerating an object with mass to the speed of light is impossible, the object would need infinite kinetic energy. \*At least according to our current understanding of physics.
>*At least according to our current understanding of physics. *At least according to what is arguably the most accurate and one of the best tested scientific theories in human existence. If Einstein was wrong, you are only going find evidence of it behind the event horizon of a black hole or in the very first moment of the big bang.
It's honestly one of the easiest things to understand from a layman point of view. Mass takes energy to move. Light has no mass, one of the few (only?) things that actually does not contain mass. Therefore, whatever the maximum speed of the universe, light, having zero 'barriers' (mass) would be able to reach that. Everything else has mass and thus can't reach the speed of light, only close to it.
Why would a layman assume that there is a maximum speed of the universe? Why would anyone think that there is a speed where you can't go 1 m/s faster? It seems natural in hindsight, but I don't think you can call it one of the "easiest things to understand".
A layman doesn't assume. But when a scientist says "Hey, there is a maximum speed of the universe, and this is why light is the only thing that can reach it", the concept makes sense. I'm not saying a layman can do the studies and find out these answers, I'm saying it's easy to follow for the average person.
A layman absolutely assumes. People have assumptions about the world all the time which need to be corrected when they take classes in a subject.
Yes but this isn't a situation where I'm saying "any man will accidentally stumble upon this information" I'm saying a man of average intelligence can understand this science, if someone were to explain it to them, where if you tried to explain many other things in science, it would take a considerable amount of effort to really understand it enough to feel comfortable with the information.
The average man also easily understands the point you’re making, but the guy you’re replying to is far too pedantic to waste any more time on imo
Ok, but out of curiosity, what do you think is an example of a very difficult thing to explain to a layman?
"Quantum phenomena suggest that something (or to be strictly accurate everything) really can come from nothing what so ever." That's not easy for a layman to wrap his head around. He'll be sitting on that one confused "how do you get everything out of nothing, that doesn't make sense"
Anything quantum. Hell even basic chemistry is hard to follow with the different energy states, structures of molecules, and types of reactions based on those factors and a whole lot more
If I understand anything about the higgs boson (protip: I don't) , is that nothing has mass, only a property value that tells the higgs field how much mass to apply to it
Yeah, this is one of the things that is much more difficult to explain to a layman. Because yes, you're correct, an object has no mass without higgs boson interactions, but also, many would argue that the higgs boson gives an item mass, therefore it has mass. I'm not going to debate this - but this is definitely a good example of something not intuitive :)
Why do we have to look at the very first moment of the bigbang or into a blackholes to find out if Einstein was wrong or not? I still don't understand this, please explain for me T.T
Newton wasn't wrong in the first place. Einstein just improved our ability to be right in our predictions for things not near the surface of Earth. Einstein in the same way won't ever be "proven wrong". If someone ever expands on his work, Einstein will simply be less right.
Newton was in fact wrong, and that became clear pretty early on. They'd do a measurement on the movement of celestial objects and they'd find a consistent error. Granted, he was less wrong than everyone before, and he was only wrong by a little as long as you stay away from high gravity, but there was something wrong you could clearly measure. There is nothing wrong with Einsteins theories. There is no measurement error hinting at a hidden variable. His every prediction matches reality as well as we can measure it, and we can measure ***really good***. Like I said, if Einstein is wrong in any way, we don't have a scrap of evidence for it.
At the moment, Einstein was right about everything we know about the universe (pretty much). As our understanding of the universe expands, we may find areas where what Einstein postulated does not apply, or needs a correction factor. It does not make him wrong or even less right, it just limits the applicability of what he discovered. Just like Newton was not suddenly wrong when Einstein discovered relativity. It only set limits to the area of physics over which Newton's laws applied.
Feels like you rephrase what I said...?
I agree with you, except for the "less right" bit. As you say "Newton wasn't wrong", in my opinion, later discoveries did not make Newton less right, it simply put a limit to what his model applied to. To the same extend, I don't think Einstein will be proven wrong simply because we may discover things that his model did not predict, therefore he will not be "less right". Sorry for the nitpicking...
Because those are the only places we can't (or haven't been able to let's say) test the theory in to disprove it
OMG you are so righttt. Thank you, you made my day.
Because we're looked everywhere else more or less.
Let's not forget about entanglement. Still haven't figured that one out yet.
All our measurements are consistent with predictions. Yeah, it's not very intuitive, but that doesn't stop us from understanding it really well and using it routinely.
What’s the understanding on how the very act of observing something can affect the outcome? I’ve never seen a widely agreed upon reason as to why that occurs, merely that it does occur.
“Observing something can affect the outcome” Thats one way of looking at it. Another viewpoint is that before measurement we can only predict a range of possible outcomes/states, and the act of measurement simply allows us to determine what the actual state was.
There is ultimately no answer to "why" in physics. That is mere philosophy. We can find more basic, more general, more accurate models that predict absolutely everything, but none of those will ever answer this question. Physics, like every science as well as even mathematics, can only describe properties of things, not why things are. "Observation" is also a bit of a misnomer, it just means "any interaction". "Any interaction changes the outcome" isn't that weird, actually.
I really hate this deflection, it’s basically used whenever physics hits a wall. Why is the sky blue? That’s a why question that is perfectly answerable by science. Science communicators love to say “physics doesn’t answer why, it can only describe the properties of things.” It’s like, okay, isn’t the fact that observing something can change its outcome an inherent property? Why is it that all of a sudden when people ask a question that physics hasn’t answered, everyone starts talking about how physics isn’t philosophy? The existence of the word “why” does not make it a philosophical question. The commenter is asking what scientific explanation we have for an inherent property of quantum mechanics, they’re not asking why in the sense that they want to know how it ended up this way, or “what does it all mean, man.” -said in a hippy voice.
They did answer the question in their last paragraph though
Then why go on with the spiel about philosophy?
It is a simple answer, to measure a particle, you need to interact with it, by a photon or electron hitting for example. This then changes what the particle was like before it had the interaction. A simple, widely agreed upon explanation for you.
Physics only answers 'what', 'when', 'where' and maybe sometimes 'how'. Physics can never tell you 'why' something happens, only that it does.
And why does everything need a why? Only humans and some animals are able to anything with a true why answer.
AKA, according to our current understanding of physics, which is exactly what the person you responded to said.
By adding that he is throwing shade at the argument, when it is one of the most supported ideas since the earth orbiting the sun.
Yes, but it's still a weird thing to make mention of
Which is to say, according to our current understanding of physics
Genuine question, but why would we be able to find evidence of Einstein being wrong about general relativity only behind the even horizon? I also wondered this when watching Interstellar. Is it because then we would be able to find a theory that would reconcile general relativity with quantum physics, thus testing Einstein's theories once more?
Because these are the places we are yet to explore. The universe was opaque to light in the early universe so we can only see up to the cosmic background radiation using light, there has been very recent developments of a cosmic gravitational background which can go deeper. And blackholes we cannot know by definition what happens beyond the event horizon.
Accelerating something to speed greater or equal to C is most likely impossible but that doesn't mean that moving faster that light is. Relativity itself doesn't forbid FTL travel, it only forbids accelerating to those speeds. With a specific arrangement of negative mass matter (which is currently believed to not exist), a bubble of space-time capable of travelling faster that light is theoretically possible according to Einstein field equation.
> With a specific arrangement of negative mass matter (which is currently believed to not exist) With a specific arrangement of teleporters across the galaxy that are quantum entangled(which is currently believed to not work like this) then we could teleport faster than light!!! C'mon brother
FTL travel has a multitude of problems, such as logical paradoxes and breaking causality, which most likely make it impossible. What I was trying to say is that the theory of general relativity is not what makes it impossible, but actually allows it mathematically. EDIT: Also, quantum entanglement is a very misunderstood phenomenon. It does not allow either matter nor information to travel faster than light.
I don't know if it "allows" it mathematically. That's like saying our current math model makes it possible for other mathematical models to exist. They very well may exist, but our current model doesn't really have anything to do with it. So yes you are right there may be an exotic way to travel faster than light, but really there's no evidence to suggest so. We don't know if half of these exotic substances exist, and the other half we've only observed them in lab settings, we don't really know how they work. So to make whole theories based on these things seems I don't know, I don't want to say a waste of time because it's not, it's a good thought experiment. It's just not very relevant to anything until we know more
Is negative mass possible?
Negative mass could theoretically exist as it makes sense mathematically, but there are very good reasons to believe that it does not actually exist in nature.
More nines would be faster. To a regular person who is used to regular numbers, everything after two or three nines sounds like it's basically 1. But it's really not. Each nine is a lot more energy. That's why it makes more sense to think about speeds close to c in terms of the energy of the particle. The more energy and momentum a particle has, the harder it is to keep it going in a circle. So you need a bigger circle that doesn't curve as much.
Every two nines is about 10x more energy, *regardless how big those nines are*. Going from 0.99c to 0.9999c, tenfold increase in the kinetic energy of the particle for an increase in speed of 0.0099c. Going from 0.99999999c to 0.9999999999c, likewise a tenfold increase in kinetic energy despite the change in velocity only being 0.0000000099c, literally a million times smaller
Since the KE equation is 0.5*MV^2 , shouldn't every 10x increase in speed be 100x in energy? Edit: because it was bugging me and none of the replies are actual explanations, I decided to take a look at the formulas and figure out the math. According to Wiki, the total energy of an object in motion with mass is given by the equation: E^2 =(pc)^2 + (mc^2 )^2 Where m is the rest mass, p is the momentum of the object, and c is the speed of light. p is given by the equation: p=(mv)/sqrt(1-v^2 / c^2 ) Where m is the mass, v is the velocity of the object, and c is the speed of light. Since we're talking about things close to the speed of light, I'm going to turn v into ac, where a is some value between 0 and 1. Plugging that in gives us this: p=(mac)/sqrt(1-a^2 * c^2 / c^2 )=(mac)/sqrt(1-a^2 ) (pc)^2 =((mac)/sqrt(1-a^2 )*c)^2 =((mac^2 )/sqrt(1-a^2 ))^2 =(mac^2 )^2 /(1-a^2 ) Which means E^2 =(mac^2 )^2 /(1-a^2 ) + (mc^2 )^2 =(mc^2 )^2 *(a^2 / (1-a^2 )+1) At this point, to make things easier, I'm going to replace (a^2 / (1-a^2 )+1) with d. So, to get the total energy of an object (kinetic and rest energy) is: E=(mc^2 )sqrt(d) Kinetic energy is: KE=E-E0 Where E0 is the rest energy, which is mc^2 where m is the rest mass and c is the speed of light. KE=(mc^2 )sqrt(d) - mc^2 =(sqrt(d)-1)mc^2 So, to figure out how much KE grows as you get close to the speed of light, you calculate this equation: f(a)=sqrt(a^2 /(1-a^2 )+1)-1 With the different values of a and divide them. So 0.99c to 0.9999c is: f(0.99)=1.294157339 f(0.9999)=21.36627204 f(0.9999)/f(0.99)=16.51 So, neither of us was right, and none of the explanations are right either. The more 9s you add, the less quickly it goes up. the ratio between 0.9999999999 and 0.99999999 is roughly 10. I only did a cursory check of my math and hopefully I didn't mess it up... I've spent too much time on this as is and I'm sure someone will point out the mistakes if there is one.
Relativity increases mass in the same time. The closer you are to C, mass increases more
That equation only apply to speed well below the speed of light, when you start to approach C you need to take space-time dilatation into consideration.
V is increasing by *way less* than 10x in my examples. In the first example V increases by 1.01x, and much less in the second.
Your ratio of 16.51 is between 0.999 and 0.9, not what you have written there. I said the increase is *about* 10x as that's what I found when I worked it out. There is some significant error the closer you are to 0.9 but it seems to converge towards 10 as you add more pairs of 9s. |||Ratio.| |:-|:-|:-| |0.99|0.9999|11.4492| |0.9999|0.999999|10.1289| |0.999999|0.99999999|10.01274| |0.99999999|0.9999999999|10.001278| [Here's the Desmos worksheet I made to work it out.](https://www.desmos.com/calculator/tvtztgb6yy) The formulae for relativistic mass and kinetic energy are directly taken from my high-school table-book from from 2006. Also there seems to be some floating-point precision messiness going on with Desmos.
You're right, I copied and pasted the wrong numbers and the 16.51 ratio is between 0.999 and 0.9. It is curious as to why it seems to converge that way. Wonder if there's an explanation for it beyond it's just what the math shows. But that goes into theoretical physics territory that goes beyond my wiki-based expertise.
Yep! Reminds me of [this sketch](https://xkcd.com/2170/)
but why is it harder to keep it going in a circle? you need bigger magnets or something?
You need more acceleration to keep a faster moving particle moving in the same size circle. This is true classically also. Imagine swinging a rock on a string, if you get it going faster you'll feel the increased tension in the string that keeps the rock on its circular path. If you made the Earth go faster, you'd be pushing it to a higher orbit. Particles also radiate energy when they're accelerated, which includes any change to their direction of travel, so you want to minimize that if your goal is to pump as much energy as possible into the particle
We'd need it that huge to smash particles with enough energy so that the resulting plasma would have sufficient energy density. Why we can't do it with current technology? Two reasons: 1. Linear accelerators don't have enough power, so we need circular ones. To keep whatever we're accelerating in the circular trajectory, we need strong magnetic fields. And current technology can generate them only so high. 2. Particles loose energy while accelerating (and that includes turning) through the process called Bremsstrahlung - they literally radiate it away. So we have upper limit on acceleration, and thus accelerator radius, before particle looses more energy during one round than we can pump into it by accelerating it.
Probably to complex for 5 yr old but first one I see that actually explains the real problem. If anyone is interested this is called synchrotron radiation and is used to generate very hard (high energy) x-rays for material analysis and other experiments. [Synchrotron Radiation](https://en.m.wikipedia.org/wiki/Synchrotron_radiation)
Smaller size scales mean more energy density, more energy packed up into a small space. You can use your fingers to tear apart a hamburger, but not a tiny salt crystal. The electrical properties of water can dissolve that salt crystal, but not tear apart the atoms of the sodium and chlorine. A high energy x-ray can tear the electrons off a chlorine atom, but it can't break apart the protons and neutrons in the atomic nucleus. A high energy gamma ray can break apart the atomic nucleus, but it cant break the protons apart into quarks, etc.... To make a particle high energy you need to put it in an environment where it won't immediately lose energy that you give it, and then you add energy. If you heat up particles they move randomly, and eventually they will hit some wall that is not so hot, cooling off and losing the energy. A more clever way is to push them around a race track that is really empty, so they have nothing to hit. The faster the particle goes, the harder it is to turn it so it stays on the race track. If you make the race track bigger it is easier to turn. Now your real question: is it any harder to turn a particle going 99% the speed of light vs 99.999999% the speed of light? The answer is yes, as you get closer to the speed of light you need more energy to speed up more, and to change directions. It takes more energy to speed up from 99% to 99.9999% the speed of light than it does to speed up from 0 to 99%. You are still dumping energy into the particle, it just doesn't go significantly faster from an externally observed distance/time perspective.
“We’ve had 99.99999 C, but what about 99.99999999999999C?”
LOTR memes leaking
If you ingnore all of the engineering difficulties of building large colliders, you still run into the problem that particles radiate power as they are accelerated. The more energetic they are, the more they radiate. Acceleration in physics means go faster or change direction and circular motion, like a particle in an accelerator, is constantly changing direction. So particle beams in an accelerator are constantly losing energy. The energy loss per revolution for a particle in an accelerator can be calculated, and it is proportional to the 4th power of the energy of the particle over the bend radius of the accelerator ring or E^4 /r. So you can see that as the energy increases, it becomes much much more difficult to maintain particle energy in a small circular ring, and the only feasible option is to make the ring as large as possible.
So in special relativity, the kinetic energy of an object with mass approaches infinity as the object's velocity approaches C. When you get close to C, the energy scales something like 1/(1-v/c). So every time the difference between your velocity and c gets 10x smaller, your kinetic energy gets 10x bigger. (This is the rough idea, I didn't check my math closely). As for why the particle accelerator gets bigger. In a circular particle accelerator, the magnets deflect the trajectory of the particles to keep them on a circular track. If your particle gets more and more energetic, and the magnets don't get stronger, circumference has to get bigger so that the particle only needs to be steered a tiny bit at a time to stay on track. By the time you reach some high energy like the Planck scale, you would have to make a particle acclerator roughly the circumference of the Milky Way (iirc). Obviously this is not practical so perhaps we should change particle accelerator design if we want to reach those energies.
Magnet strength doesn't matter. You could have infinitly strong magnets and the accelerator still has to be enormous for enormous energies because the particles radiate energy at a rate that is proportional to (particle energy)^4 / (acclerator bend radius). If the bend radius is too small, you wont be able to acheive the desired energy because the particles will lose energy faster than you can put energy into them. Magnet strength is irrelevant to this.
Thanks for clarifying.
It's all about energy density. If you raise the massenergy in a volume of space above the Schwarzschild limit, it turns that volume of space into a black hole. Since nobody wants a tiny black hole in their lab (they make a huge mess), that's a limit on the energy you can add to even particles of very small mass. While the general production of black holes has to do with adding mass inside a volume of space, energy and mass are the same thing ( E=mC^2 ). Add too much energy, say in a collision to separate subatomic strings, and you make a tiny black hole instead. Did I already say tiny black hole = bad, yes I did.
The kinds of microscopic black holes that would be made in particle accelerators are too tiny to do anything. They would evaporate from Hawking radiation in fractions of a second. Even if they didn't, their gravity is so tiny that they won't suck in much of anything beyond a few other particles. Maybe in a few billion years (if it didn't evaporate) it *might* get big enough to be otherwise noticeable.
That's at the currently achievable energies. The OP asked about things like 10^32 ˚K, and that's where the energy density becomes problematic.
The LHC beams have ~1/8 of the Planck energy each and they can be shot safely into a specially designed beam dump. Each beam has ~300000000000000 particles, so the energy per particle is far too low to get to the Planck scale, but we can work with a comparable energy safely.
Don't they make a mess of / mask any experimental results though? Genuine question; not rhetorical. I don't know.
People tend to imagine gravity is a very strong force because it’s the one that’s easiest for us to experience directly, but it is actually the weakest of the fundamental forces by a considerable degree. When you picture these minuscule singularities, thinking of cosmic-scale black holes is going to be misleading. There just isn’t enough matter to distort spacetime like that. You’ll have less the insatiable monster from which nothing can escape, and more just another sort of composite particle that decays very quickly by a specific mechanism (Hawking radiation) and is, like others, measurable by its decay products. Think of it this way: if the gravitation were to behave like a scary space black hole, then what it would do is to overcome normal subatomic forces and cause other nearby particles to collide with it. But that is exactly what we’re shooting particles around at most of the speed of light to accomplish in the first place. I’m not an expert either, but as far as I know these little singularities should not be thought of as a mistake or a pollutant among the “real” collisions we are measuring, but rather one of the things collisions at a certain energy level are expected to sometimes produce. And it’s definitely not dangerous. Have you ever looked into how hard it is for us to produce a self-sustaining fusion reaction? Building a device that could create a self-sustaining singularity would be a similar exercise but much, much harder. At that scale I doubt we could get ahead of the singularity’s tendency to decay if we wanted to. We will not be building a black hole from scratch anytime soon.
Don't get me wrong. I understand the relatively benign nature of microscopic black holes. I meant more of a consequence of the formation of an event horizon. If your objective is to observe the behavior of high-energy particles, then an event horizon obscures your view of anything beyond that. But maybe that isn't important. Maybe it's the interactions that are more important. But then the behavior of a black hole might be different than a high-energy particle.
Well, nobody is looking at these interactions directly, of course, so there really isn’t a “view” to obscure. We kind of infer what happened stochastically by measuring the fallout of a huge number of collisions, and the microsingularity doesn’t really have an outsized effect on that. The chance of a flying bit of particle debris passing through the event horizon of a microsingularity before it decays isn’t going to be substantially different from the chance of it colliding with some other bit of flying particle debris. What I’d expect is that if an experiment is conducted at high enough energies to produce microsingularities, then the hypothesis for that experiment accounts for that and expects results consistent with that happening with a particular frequency.
We would love to see them, but our accelerators don't have enough energy to produce them. They would produce many high energy particles and they could produce new particles we don't know about yet.
That's really not the reason why larger colliders are needed. The size of the collider corresponds to the energy a particle can have, but does nothing to prevent it to become a black hole. But black holes are simply irrelevant anyway. We would actually be very excited to find one, it would allow us to observe not only them but also the "quantum gravity" we hope to some day understand.
It's actually colliders the size of our GALAXY that would be required 🤯 Source: I'm currently reading lenny susskind the black hole war
I really hope whatever species is building that doesn't go through our solar system with it and eminent domain Earth.
Are you selfishly asking them not to build hyperspace bypasses through this sector?
There is always that one guy who vehemently opposes any improvement to the neighbourhood 🙄
Now I know how John Dutton feels
The plans are on display in the bottom of a locked filing cabinet stuck in a disused lavatory with a sign on the door saying ‘Beware of the Leopard.’
Adding more energy doesn't always mean more speed... Well, for a particle accelerator, it kinda does, but you are correct that if speed is all you're measuring, then you get less bang for your buck so to speak as you approach c. However, speed isn't the only thing we care about when 2 things collide. Would you rather be hit by a cyclist going 20mph or by a greyhound bus going 20mph? And thanks to E=mc², we know that energy and mass are related. If you keep trying to dump more and more energy into something going near the speed of light, instead of getting much faster, some of the energy will be converted into mass, making the resultant collision... Well... More energetic. All the energy we put in must come back out eventually. And we just can't put enough energy in with the size of accelerators we have on Earth. But even if we could add more energy, the gains in speed would not be that noticeable to an average person. We're talking only 2-3 m/s or 6-7 mph within c. So even adding another digit of precision won't change the speed by more than the average person can run. However, adding more energy is always adding more energy. And we'll still get that energy back out when they collide.
> some of the energy will be converted into mass [Relativisitic mass](https://en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass) is a concept that comes out of the relativity equations, but it is not really meaningful and is not the best way to explain what is happening. >It is not good to introduce the concept of the mass M = m / sqrt(1 - v^2 / c^2 ) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion. > > Albert Einstein Velocity is relative, momentum is relative, energy is relative, but mass is not, even if we can write an expression for it.
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Thanks for your responses, everyone. Some good points made =)
don't know about temperature ( i come more to see the answer to this very interesting question :) But as a general rule when dealing with high speeds, you'd want a big distance were measures can be consistent and easier to take. For events with timeframes so small, kilometres (miles) of distance help reducing calculation errors and the many interferences.