Naked Science Forum
General Science => General Science => Topic started by: Supervolant on 01/09/2018 22:47:10
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Hey people,
When an particle is approaching the speed of light. Is it gaining mass? Just like anything going fast? What amount of mass has something traveling at c?
Mass is gravity, right?
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Just wondering... so anyone?
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Yes.
Einstein's theory of special relativity helps here; he showed that E = mc2, meaning that as the energy of a body increases, so too does its mass. So as a particle accelerates it gains more kinetic energy; hence the "E" side of the equation increases. Since the speed of light (c) is a constant, the mass of the moving body (m) must increase to balance the equation.
This is the reason why travel at the speed of light is impossible for an object with mass (photons can do it because they are massless), because as the velocity increases so does the mass, meaning that you'd need an infinite amount of energy to continue to accelerate.
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Interesting. Just started reading Einstein's biography written by Walter Isaacson.
I have heard particle accelerators use particles and let them travel very close to the speed of light (c).
0,9999...% to (c) I once have seen.
Just hypothetical. What would happen if one of these particle travel at (c). Would the particle have an infinite amount of mass? I have so many questions but I am trying to hold this efficient.
Thanks for your answer Chris!
edit: These particles being accelerated there. Are no photos, or are they?
- Robert
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Hello People,
Not the best with numbers, more kind of a pictures person. I have a vivid picture about how to achieve traveling at the speed of light. Works out only if we (together) get down some numbers and facts. So common... you know what I mean! Let's go build these speed of light traveling space ships.
Anyone interested in a conversation about how to?!
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I have heard particle accelerators use particles and let them travel very close to the speed of light (c).
0,9999...% to (c) I once have seen.
The Large Hadron Collider (LHC) is currently the world's most powerful particle accelerator.
It can accelerate protons up to 99.999999% of c, or about 11 km/h slower than the speed of light (c).
One way physicists measure the mass of a particle is in units of GeV/c2.
A proton at rest has a mass of 0.938 GeV/c2.
When up to speed in the LHC, the proton has a mass of around 6500 GeV/c2.
See: https://en.wikipedia.org/wiki/Large_Hadron_Collider#Design
Just hypothetical. What would happen if one of these particle travel at (c). Would the particle have an infinite amount of mass?
Yes, it is just hypothetical, because we can never accelerate a massive particle to the speed of light in a vacuum, with a finite amount of energy, or in a finite amount of time.
There is one context where we can "bend the rules": Light travels slower in a material like water.
A nuclear reactor emits subatomic particles at almost the speed of light (in a vacuum), which is faster than the speed of light in water.
This results in Cherenkov radiation, the blue glow seen around water-cooled nuclear reactors.
See: https://en.wikipedia.org/wiki/Cherenkov_radiation
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Interesting. Just started reading Einstein's biography written by Walter Isaacson.
I have heard particle accelerators use particles and let them travel very close to the speed of light (c).
0,9999...% to (c) I once have seen.
Just hypothetical. What would happen if one of these particle travel at (c). Would the particle have an infinite amount of mass? I have so many questions but I am trying to hold this efficient.
Thanks for your answer Chris!
edit: These particles being accelerated there. Are no photos, or are they?
- Robert
The kinetic energy of an object with a rest mass of m can be calculated by the equation.
KE = mc^2(1/sqrt(1-v^2/c^2)-1)
As v approaches c, this approaches infinity. However, at v =c you get
KE = mc^2(1/sqrt(1-c^2/v^2)-1)
KE = mc^2(1/sqrt(1-1)-1)
KE = mc^2(1/sqrt(0)-1)
KE = mc^2(1/0-1)
1/0 is undefined . In other words, it has no answer. As a result, you can't say what the energy of a non-zero rest mass particle would have if it traveled at c. The universe just doesn't allow for such a scenario. ( And before you ask " But what if you did have a non-zero rest mass particle traveling at c?" the answer is: Then the rules by which we understand the universe as operating by are in error, which means we would need a new set of rules to answer that question. And since we have no idea what those new rules would be, we are at just as much a loss for an answer as before.)
But since the amount of energy needed to accelerate a particle approaches infinity as it approaches c, you can never achieve this in the first place. (No matter how close to c the particle is moving and how much energy you add to accelerate it, you only end up getting it a little closer to c, but never to c. )
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Evan_au
I am really appreciating your answer. Gained some insights I needed. But 6500 GTeV/c2 is as much as 6.5 flying mosquitos deliver while flying. That's not much. The particles travel 11 km/h under the speed of light?! Does that mean, there is a 11 km/h speed difference needed in order to let that particle reach a energy / mass of infinity?! My little sister is able to run this fast so common, really?
Janus
Wow. Didn't realize I am questioning the very foundation of how physics works. But yeah, I guess that's how progress occurs.
"As v approaches c, this approaches infinity. " Sry, but this blows my mind. Infinity?! I can't comprehend something not able to reach a certain speed (around 299.000 km/s) being the barrier straight to infinity.
Would a particle at c have infinity energy inside and infinite mass? Is the result of that a strong gravitational field around such a particle?
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Fact is. I would like to accelerate something to c. I believe the nature of how particle accelerator operate are the problem or challenge that needs to be overcome. Nature is working like a mathematician. Irrational numbers / ratios like pi (3,14...) and phi (1,618...) are the key factor and found everywhere.
So there are 11 km/h to infinity? The particle is already inside an extreme vacuum suspended by superconducting electro magnetic fields. The question is: What else in order to reduce friction enough to reach the speed of light?
Let's go back to 1,618... The most wonderful and important number inside our universe. Also called the golden section, divine proportion... found everywhere ranging to your body over seashells up to swirling galaxies in the very same pattern. Everything is revolving around this proportion where one geometric length is 1,618... times smaller or larger then the one geometric length before.
I could talk for days on this topic. Please visit the website below for more, it's worth it.
Visit https://www.goldennumber.net for a good first introduction to phi.
You recognize the golden spiral when you see it.
As Jay Harman from Pax Industries (interesting company) said: It's the path of least resistance. And that is absolutely true!
Nature is using this geometric proportion when the maximum energy efficiency is needed. Look at our bodies, a wonderful piece of biomachinery able to do great amount of physical and psychological labor. But in the end we only need to insert around 2000 calories a day. Every kcal is equal to 4200 joules of energy. Over the course of a day (86400 seconds) a person uses 97.2 joules a second which in turn averages 97.2 watts. As much as a strong light bulb. When you research the golden number you will see that our body is shaped from the most obvious to the least obvious ways according to the golden sections. The hyper efficient path of least resistance.
A little sidestep here. Imagine someone having a stone attached to a string swirling the stone around. Nice showcase for centrifugal forces. But now imagine the person pulling on the string making the lever effectively smaller. Just as a ice-skater doing a fast pirouette by pulling the arms in the overall circular rotation will accelerate, right?
Even tough not really understanding why, we all can accept that this is fact, ok?
Edit: Momentum. This law of physics explains why when a ice skater pulls in her arms when executing a turn, she spins more quickly. With arms outstretched, her mass is distributed over a greater space. When she draws her arms inwards, that distribution is reduced, so her speed must pick up to counteract this difference and keep her total momentum constant.
But why not doing the same with a particle inside an accelerator?
The hypothetical particle accelerator I propose uses this effect in combination with the path of least resistance in order to let a proton reach the speed of light.
On this theoretical particle accelerator we still can accelerate a particle around a circular path but once it reached 99.9999% or 11 km/h below (c) we derail inwards across a golden spiral where the particle impacts with another particle doing the very same but mirrored. I mean what about relativity here? Arn't these particles effectively colliding (even today) at speeds way over (c)?
When something at c would use up infinite amount of energy and becomes an infinite amount of mass the net result would be a black hole having it's own gravity? This is a key question. Theoretical technology like this is able to produce vast amounts of energy in excess of all we need, makes traveling at the speed of light possible but also allows for a weapon of mass destruction. I think we just shouldn't do the least option but the former ones sound very good indeed.
Would like to further communicate with you about what a particle does at the speed of light.
I like this topic and I have so many questions which result in a inner tension. If you do like this topic as well, please go ahead and be involved!
- Robert
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Time dilation is also a factor. The combustion of fuel is effectively slowed down due to time dilation. You get less bang for the buck. This of course is only observed by an observer who is stationary with respect to the dilated system. For an observer in the dilated frame his fuel consumption appears unaffected and length therefore appears contracted. Thus from a stationary observer's point of view the traveller requires more and more fuel to compensate. This is an alternative way to view the situation.
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jeffreyH
Thanks for the input, but please define fuel for me.
Inside the theoretical system mentioned before the fuel used would be electromagnetic waves wich travel as fast as (c). Time dilation to me describes the fact that something or even someone traveling at (c) is effectively doing time travel into the future. A traveler at (c) travels away from earth. His twin stays on earth. But who is really the one traveling? From the viewpoint of the traveler his twin on earth traveled at (c) while he was stationary. So why is it that he is doing time travel but not the one on earth? This is known as twin paradox and as far as I know that's one of Einsteins exciting thought experiments.
Does it really matter to the observer what amount of fuel the traveler requires for traveling?
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Evan_au
I am really appreciating your answer. Gained some insights I needed. But 6500 GTeV/c2 is as much as 6.5 flying mosquitos deliver while flying. That's not much.
But those 6.5 mosquitoes have something like 5e22 times the mass of the proton that the LHC is accelerating up to near c velocity. The energy given is per proton, while the LHC is actually accelerating packets of proton. So the total energy used by the LHC is much higher than this. The particles travel 11 km/h under the speed of light?! Does that mean, there is a 11 km/h speed difference needed in order to let that particle reach a energy / mass of infinity?! My little sister is able to run this fast so common, really?
But the amount of energy needed to get from that 11 km.sec short of c to c dwarfs the energy needed just to get it up to 11 km/sec short of c.
For example, let's say that you got a particle up to just 3 m/sec short of c. Now you double the amount of energy of the particle. This will get you to just 0.75 m/sec short of c. Double the energy again, and you will yet closer to c. But no matter how many times you keep doubling the energy, you just get closer to c, but never reach it.
Another way to look at it is that velocities don't add up the way they appear to do in everyday life. If your sister where in a train traveling at 20 km/hr relative to the tracks, and she ran forward at 11 km/hr relative to the train, we would say that she would then be traveling at 31 km/hr relative to the tracks. Now while this is so close to the correct answer to make no practical difference to us, it isn't exactly correct. The correct answer is 30.999999999999994... km/hr.
Now while this is a really small difference, when the speeds involved start keeping close to c, it starts to be more and more noticeable. For example, let's assume that our train is traveling at 11 km/hr short of c relative to the tracks and your sister again runs at 11 km/hr forward relative to the train. Her resulting speed relative to the tracks will now be 10.9999998808 km/hr short of c.
Janus
Wow. Didn't realize I am questioning the very foundation of how physics works. But yeah, I guess that's how progress occurs.
"As v approaches c, this approaches infinity. " Sry, but this blows my mind. Infinity?! I can't comprehend something not able to reach a certain speed (around 299.000 km/s) being the barrier straight to infinity.
Your ability to comprehend it or not has no bearing on the truth of it. It is an asymptotic function, just like 1/n=x.
as n gets larger, x gets smaller and smaller, but no matter how larger n gets, x never reaches zero.
With the c limit, you can try and look at it like this: The inertia of an object causes it to resist changes in its velocity. To overcome this, we apply energy to the object. But it turns out that adding energy also increases the object's resistance to further changes of velocity. So that means to speed the object up by the same amount, we have to add even more energy than we did the last time (or conversely, the same amount of applied energy will result in a smaller increase in speed.)
But more energy means an even further increase in the resistance to further speed increases.
Because of the relationship between the energy added and the increase in inertia, as the object increases in speed, less and less of the applied energy results in an increased speed. The result is an asymptotic relationship much like the 1/n example above, with the speed of c in the role of x=0.
Would a particle at c have infinity energy inside and infinite mass? Is the result of that a strong gravitational field around such a particle?
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Fact is. I would like to accelerate something to c. I believe the nature of how particle accelerator operate are the problem or challenge that needs to be overcome. Nature is working like a mathematician. Irrational numbers / ratios like pi (3,14...) and phi (1,618...) are the key factor and found everywhere.
What you would like or believe is of no consequence. It has nothing to do with the operating principles of the accelerator, but with limits imposed by the universe itself.
So there are 11 km/h to infinity? The particle is already inside an extreme vacuum suspended by superconducting electro magnetic fields. The question is: What else in order to reduce friction enough to reach the speed of light?
It has nothing to do with friction. It has to do with the fact that even at 100% efficiency it takes as much added energy to accelerate a particle form 11 km/hr short of c to 2.7 km/hr short of c, as it did to get it up to 11 km/hr short in the first place.
This is not like aircraft breaking the "sound barrier", which was a matter of solving engineering and aerodynamics problems; how do you build an aircraft that can hold up to the stress and be able to control it. (by the time the sound barrier was broken, we already had plenty of examples of things that traveled faster than sound.)
This is something quite different. This is built into the very operating principles of the universe itself.
Let's go back to 1,618... The most wonderful and important number inside our universe. Also called the golden section, divine proportion... found everywhere ranging to your body over seashells up to swirling galaxies in the very same pattern. Everything is revolving around this proportion where one geometric length is 1,618... times smaller or larger then the one geometric length before.
I could talk for days on this topic. Please visit the website below for more, it's worth it.
Visit https://www.goldennumber.net for a good first introduction to phi.
Completely off topic and has nothing to do with why c is the speed limit for the universe.
You recognize the golden spiral when you see it.
As Jay Harman from Pax Industries (interesting company) said: It's the path of least resistance. And that is absolutely true!
Nature is using this geometric proportion when the maximum energy efficiency is needed. Look at our bodies, a wonderful piece of biomachinery able to do great amount of physical and psychological labor. But in the end we only need to insert around 2000 calories a day. Every kcal is equal to 4200 joules of energy. Over the course of a day (86400 seconds) a person uses 97.2 joules a second which in turn averages 97.2 watts. As much as a strong light bulb. When you research the golden number you will see that our body is shaped from the most obvious to the least obvious ways according to the golden sections. The hyper efficient path of least resistance.
A little sidestep here. Imagine someone having a stone attached to a string swirling the stone around. Nice showcase for centrifugal forces. But now imagine the person pulling on the string making the lever effectively smaller. Just as a ice-skater doing a fast pirouette by pulling the arms in the overall circular rotation will accelerate, right?
Even tough not really understanding why, we all can accept that this is fact, ok?
Edit: Momentum. This law of physics explains why when a ice skater pulls in her arms when executing a turn, she spins more quickly. With arms outstretched, her mass is distributed over a greater space. When she draws her arms inwards, that distribution is reduced, so her speed must pick up to counteract this difference and keep her total momentum constant.
But why not doing the same with a particle inside an accelerator?
The hypothetical particle accelerator I propose uses this effect in combination with the path of least resistance in order to let a proton reach the speed of light.
On this theoretical particle accelerator we still can accelerate a particle around a circular path but once it reached 99.9999% or 11 km/h below (c) we derail inwards across a golden spiral where the particle impacts with another particle doing the very same but mirrored.
You are trying to apply Newtonian physics to a Relativistic universe. No matter what scheme you come up with, you are not going to "trick" the universe into allowing you to accelerate a particle up to c or greater. Besides, if such a simple trick would work, don't you think someone would have already tried it? . What is it that gives some people the idea that modern professional physicists are so thick that they couldn't see their own hand in front of their face without someone pointing it out to them? [/quote]
I mean what about relativity here? Arn't these particles effectively colliding (even today) at speeds way over (c)?
[/quote]This is "closing speed" as measured in the lab. But neither particle is traveling at greater than c relative to the lab. If you were riding with either particle, you would measure its relative velocity with respect to you as being less than c (another result of how velocities add in Relativity)
When something at c would use up infinite amount of energy and becomes an infinite amount of mass the net result would be a black hole having it's own gravity? This is a key question.
No. As far as the object itself is concerned, its mass and gravity remains unchanged. It can't turn into a black hole in one frame and not another Theoretical technology like this is able to produce vast amounts of energy in excess of all we need, makes traveling at the speed of light possible but also allows for a weapon of mass destruction. I think we just shouldn't do the least option but the former ones sound very good indeed.
There is no way to get more energy out of something than the sum of the energy it started with and the energy you added. If You accelerate an object up to 0.9999c, you can release a ton of energy by smacking it into something, but no more energy than you had to expend in order to accelerate it up to that speed in the first place. So no, this does not produce any excess energy.
Would like to further communicate with you about what a particle does at the speed of light.
I like this topic and I have so many questions which result in a inner tension. If you do like this topic as well, please go ahead and be involved!
- Robert
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Thanks for the reality! I am here to grow and you helped on that.
Really studied your answer for quite some time since you really seem to understand the topic. Appreciate your effort on educating me!
The fact that this knowledge exists really makes me appreciate humanity and the progress we, as a species, have made! It does seem to me that the speed of light is the very foundation everything is relying on...
You made a beautiful example of my sister running with 11km/h inside a train traveling at 20km/h. Relative velocity to the train tracks is 31 km/h.
Let's do another thought experiment.
What about someone riding on a light beam at the speed of light next to earth (being the observer) and turn on a flashlight.
Is as you have mentioned before (c) the very limit our universe is operating on? Or is the law of additional velocities still existent in this example?
In other words.
Will the flashlights light be 2x(c) seen as an observer on earth, or does nothing get past (c) and the observer would see the light not escaping out of the flashlight just like the traveler would see the beam of light he is riding on and the flashlights light as frozen?
In history people like Einstein have questioned everything. Even accepted set of law's like they are found in the rules (known to us) of how physics work. Why not questioning Einstein himself? We can not get past (c) when we accept what the Relativitätstheorie is telling us. The mission is to get on or even past the speed of light.
Imagine having a large enough spaceship to carry something as the LHC with it. After the protons circulated to 99.9999...% the speed of light we derail straight to the back and outwards of the spaceship and use the accelerated protons as a way of propulsion. In the vacuum of space would that mean that the theoretical high speed of the spaceship is 99.9999...% of (c)? Do we have to count in the mass of the space ship as well? Of course for the acceleration but the end velocity is only dependent on the speed at which the propellant is leaving the spaceship. Is there something wrong in my thinking here?
And I know this won't get us to the speed of light, but still the result to my question above and the facts including it are necessary to my understanding for further thinking.
Thanks already! Would really like to see another answer from you Janus.
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Thanks for the reality! I am here to grow and you helped on that.
Really studied your answer for quite some time since you really seem to understand the topic. Appreciate your effort on educating me!
The fact that this knowledge exists really makes me appreciate humanity and the progress we, as a species, have made! It does seem to me that the speed of light is the very foundation everything is relying on...
You made a beautiful example of my sister running with 11km/h inside a train traveling at 20km/h. Relative velocity to the train tracks is 31 km/h.
Let's do another thought experiment.
What about someone riding on a light beam at the speed of light next to earth (being the observer) and turn on a flashlight.
It's an invalid light experiment. You and your flashlight cannot be traveling at the same speed as that light beam. If you try to imagine such a thing you get nonsense as a result.
Instead, let's imagine that you are are traveling at 0.999999c relative to the Earth. In this case, when you turn on your flashlight, you will measure the light heading away from you at c. Someone on the Earth will measure the same light as traveling at c relative to them and thus the light beam traveling at 0.000001c with respect to you. This is one of the fundamental principles by which out universe works. c. the speed of light in a vacuum is invariant. You always measure it as having the same value with respect to yourself. Is as you have mentioned before (c) the very limit our universe is operating on? Or is the law of additional velocities still existent in this example?
In other words.
Will the flashlights light be 2x(c) seen as an observer on earth, or does nothing get past (c) and the observer would see the light not escaping out of the flashlight just like the traveler would see the beam of light he is riding on and the flashlights light as frozen?
This is the kind of nonsense answers that occur by assuming you can travel next to the light. According to the invariant nature of the speed of light, Both the speed of the light beam and your flashlight beam have to be moving at c relative to you as measured by you, but how can you be traveling right next to light beam that is traveling at c relative to you?
In history people like Einstein have questioned everything. Even accepted set of law's like they are found in the rules (known to us) of how physics work. Why not questioning Einstein himself?
Einstein did not question everything. He built on the work of others before him, and his theories are always being tested. It is just, to date, they keep passing the tests. Someday, that may be not the case, and at that time we may gain a clue as to go beyond Einstein We can not get past (c) when we accept what the Relativitätstheorie is telling us. The mission is to get on or even past the speed of light.
[/quote]No, the mission is to determine how the universe works, regardless of how we feel about the limitations it may put on us.
Imagine having a large enough spaceship to carry something as the LHC with it. After the protons circulated to 99.9999...% the speed of light we derail straight to the back and outwards of the spaceship and use the accelerated protons as a way of propulsion. In the vacuum of space would that mean that the theoretical high speed of the spaceship is 99.9999...% of (c)? Do we have to count in the mass of the space ship as well? Of course for the acceleration but the end velocity is only dependent on the speed at which the propellant is leaving the spaceship. Is there something wrong in my thinking here?
The final velocity of a rocket is not limited by its exhaust velocity (if that were the case, we would have never been able to even get satellites into orbit which requires a speed of ~7.9 Km/sec considering that the exhaust velocities of our launch vehicles is only ~4.5 km/sec.
However, that does not mean that the speed of a rocket is limitless.*
For a rocket bound by Relativity, you use the Relativistic rocket equation
Vf = c tanh(Ve/c ln(Mi/Mf))
Vf is the final rocket rocket velocity, c the speed light in a vacuum, tanh** is the hyperbolic tangent* Ve is the exhaust velocity ln is the natural log, Mi is the initial rocket mass (before fuel burn) and Mf the final mass (after fuel burn).
by this equation, Mi/Mf would need to equal ~14,142 in order for the rocket to reach 99.999999% of c with the same exhaust velocity. Trying to get to 99.9999999% of c ( just a few km/h faster) jumps this to ~44721 or an increase by a factor of 3.16
This means that for every kilogram you are trying to get up to 99.9999999% c by using this rocket method would require 44720 kg of proton mass to throw backwards, And that 1kg has to include the accelerator mass, and the mass of whatever power source you need to accelerate all those protons up to 99.999999% of c.
The upshot is that no matter how much fuel/protons you have to start with, the final velocity of your rocket will end up being less than c.
And I know this won't get us to the speed of light, but still the result to my question above and the facts including it are necessary to my understanding for further thinking.
Thanks already! Would really like to see another answer from you Janus.
* under Newtonian physics the final velocity of a rocket is theoretically limitless regardless of the exhaust velocity, however there are practical limits. For a typical chemical rocket with an exhaust velocity of 4500 m/sec, it takes about 10.5 kg of fuel for every kg you want to launch to escape velocity from the Earth even under ideal conditions. it would require an additional 12.42 km/sec to then escape the Sun, this jumps the required fuel up to 180 kg per kg. (You can see why NASA uses fly-by of planets to get a speed boost for so many of their deep space missions)
As you can see, this can get out of hand really fast with your rockets becoming almost all fuel tanks and the superstructure to support them.
** tanh(x) = (1-e^(-2x))/(1+e^(-2x), where e = ~ 2.71828
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No. A particle has a discrete atomic mass, defined as rest mass.
As the particle is accelerated the transfer of energy requires an increasing amount of time. It does acquires more KE.
I use the analogy of 'a diminishing return on your investment'.
This time dilation was originally interpreted as inertial resistance, but has become obsolete.
Current particle physics uses equivalent energy as a standard of measurement as mentioned here.
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en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass
read it for yourself.
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Janus, you are amazing and I am sure you know that yourself! Really good insight on what the light speed actually means to mass and how rocket propulsion works. I read you answer a few times and now try my best at the math parts...
Phyti. I am going ahead and read the wikipedia article. But for now I HAVE to start a new thread about another topic...