# Mass accelerator to light speed - how much energy is required?

#### RogueRose

Joined Oct 10, 2014
375
What I'm trying to figure out is how much energy would be needed to accelerate 454 grams (or 1kg would be interesting as well) to light speed? I've read that it would take almost an infinite amount, which doesn't quite make sense, as then that would mean that 500 tons would require the same "infinite" amount. I'd assume this takes place in a vacuum.

Is the equation e=mc^2?

(454)*(299 792 458)^2
(454) * 89,875,517,873,681,764 = 40,803,485,114,651,520,856

If this is what is required, what energy value is being used? Joules, watts?

This is just an exercise to see how much energy it would take to accelerate 1 lb to light speed.

#### nsaspook

Joined Aug 27, 2009
8,897
By special relativity, the energy needed to accelerate a particle (with mass) grows super-quadratically when the speed is close to c, and is ∞ when it is c. F=ma is false in SR near light speed. It's basically because your mass isn't constant, it varies based on your speed.

Since you can't supply infinite energy to the particle, it is not possible to get to 100% c.

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#### WBahn

Joined Mar 31, 2012
26,398
What I'm trying to figure out is how much energy would be needed to accelerate 454 grams (or 1kg would be interesting as well) to light speed? I've read that it would take almost an infinite amount, which doesn't quite make sense, as then that would mean that 500 tons would require the same "infinite" amount. I'd assume this takes place in a vacuum.
Part of your conceptual problem is the notion that the would be "the same" infinite amount. At any given speed (relative to the same observer) the amount of energy required to bring the two masses to that speed will be in proportion to their mass ratios.

Is the equation e=mc^2?

(454)*(299 792 458)^2
(454) * 89,875,517,873,681,764 = 40,803,485,114,651,520,856

If this is what is required, what energy value is being used? Joules, watts?
This is where these things called "units" come in handy. Track the units and that will answer your question. Though it will be helpful to understand what the units of energy are and are not. Is joules a unit of energy? Is watts a unit of energy?

#### djsfantasi

Joined Apr 11, 2010
7,911
Part of your conceptual problem is the notion that the would be "the same" infinite amount. At any given speed (relative to the same observer) the amount of energy required to bring the two masses to that speed will be in proportion to their mass ratios.
Uh oh... You had to bring that up. Two separate values that are infinite can be different. That is, they can be not equal.

One of my favorite concepts.

#### Papabravo

Joined Feb 24, 2006
17,235
What I'm trying to figure out is how much energy would be needed to accelerate 454 grams (or 1kg would be interesting as well) to light speed? I've read that it would take almost an infinite amount, which doesn't quite make sense, as then that would mean that 500 tons would require the same "infinite" amount. I'd assume this takes place in a vacuum.

Is the equation e=mc^2?

(454)*(299 792 458)^2
(454) * 89,875,517,873,681,764 = 40,803,485,114,651,520,856

If this is what is required, what energy value is being used? Joules, watts?

This is just an exercise to see how much energy it would take to accelerate 1 lb to light speed.
Kg m^2/sec^2 are Joules. This is not related to the energy required to accelerate the mass. This is the energy that would be released if all of the mass was converted to energy by some process.

The formula you are looking for is:

$$m\;=\;\frac{m_0}{\sqrt{1\;-\;\frac{v^2}{c^2}}}$$

where $$m_0$$ is the rest mass, v is the present velocity and c is the speed of light. As you can plainly see, when v=c the denominator goes to 0 and the mass, m, diverges to ∞. If you allow for a velocity greater than c, the mass becomes imaginary. You could also allow for an imaginary velocity.

#### crutschow

Joined Mar 14, 2008
28,156
Two separate values that are infinite can be different.
Infinity is infinity.
It's how fast you get there that's different.

#### Papabravo

Joined Feb 24, 2006
17,235
There are different cardinalities of infinity. For example the positive integers are countable, but the real numbers are uncountable. The reasoning is that you can establish a 1:1 correspondence between the positive integers and the positive integers. No such correspondence can be established between the positive integers and the real numbers.

From the wiki: https://en.wikipedia.org/wiki/Infinity

Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities).[1] For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.

#### Papabravo

Joined Feb 24, 2006
17,235
In this problem you have the following paradox:
1. You accelerate a bit and your velocity increases
3. Because your mass has increased, it is harder to accelerate and get to the next increment in velocity.
Wash, rinse, repeat.

#### RogueRose

Joined Oct 10, 2014
375
THANKS for the replies! Much of what was said I had heard before but never knew how they fit together and this was very helpful in putting the pieces together.

-So am I correct to say that as the mass reaches light speed, it looses all of it's mass?
-secondly, the amount of energy needed is basically infinite, but it reaches infinity faster than the 500 ton mass?
-UNITS! Yes, that was the brain block I had when I was struggling for "that value" - So what is the correct unit for E?

I was trying to compare the energy needed for the LHC to send the particle to near light speed to a 1 lb ofject reaching the same speed. I wanted to show the amounts currently being used for "particles" vs what it would take for 1lb at the same speed - if you see what I'm explaining, could anyone help with this? The speed of the LHC is ".999999990 c, or about 3.1 m/s (11 km/h) slower than the speed of light "

#### Papabravo

Joined Feb 24, 2006
17,235
THANKS for the replies! Much of what was said I had heard before but never knew how they fit together and this was very helpful in putting the pieces together.

-So am I correct to say that as the mass reaches light speed, it looses all of it's mass?
-secondly, the amount of energy needed is basically infinite, but it reaches infinity faster than the 500 ton mass?
-UNITS! Yes, that was the brain block I had when I was struggling for "that value" - So what is the correct unit for E?

I was trying to compare the energy needed for the LHC to send the particle to near light speed to a 1 lb ofject reaching the same speed. I wanted to show the amounts currently being used for "particles" vs what it would take for 1lb at the same speed - if you see what I'm explaining, could anyone help with this? The speed of the LHC is ".999999990 c, or about 3.1 m/s (11 km/h) slower than the speed of light "
One at a time
1. -So am I correct to say that as the mass reaches light speed, it looses all of it's mass? No, the mass increases without bound and the rate of increase gets larger as well.
2. -secondly, the amount of energy needed is basically infinite, but it reaches infinity faster than the 500 ton mass? I suppose, if only because for a given velocity the 500 ton mass has more kinetic energy.
3. The correct SI unit for energy is the Joule. The cgs unit is the erg (10^-7 J.), and the English unit is the foot-pound (1.3558 J.) Anything that has units of mass times velocity squared is measuring energy.

#### crutschow

Joined Mar 14, 2008
28,156
So am I correct to say that as the mass reaches light speed, it looses all of it's mass?
No, just the opposite.
At near the speed of light, the energy being added to accelerate the object adds only slightly to the velocity, the rest of the energy shows up as increased mass.
That's why an object can't reach the speed of light, because it's mass keeps increasing instead of its speed.

But interestingly, if you were riding on the object, you wouldn't notice that effect.
Due to the slowing of time relative to the rest of the universe, you would experience a continuous apparent increase in speed.
Because of this effect, someone calculated that, if you were on a spaceship that could continuously accelerate at the rate of 1G (32 ft/s/s), then you could reach the end of the known universe in less than one normal lifetime in that ship, even though, to the rest of the universe, you never traveled faster than light.
Here's a discussion on that.

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#### djsfantasi

Joined Apr 11, 2010
7,911
Infinity is infinity.
It's how fast you get there that's different.
Actually, my point is that infinity is NOT infinity. As @Papabravo pointed out, there are different cardinalities of infinity. This concept was my Ah hah! moment of my undergraduate studies in Applief Mathematics

#### MrSoftware

Joined Oct 29, 2013
2,015
Since velocity is relative, how does it work out when two particles with mass are traveling in opposite directions at .5c relative a 3rd party observer? Relaive the observer each particle is going .5c, but relative each other the particles should be traveling at c. But do the particles not see their velocity relative each other as c due to their own shift in time, which is also relative each other?

#### Kermit2

Joined Feb 5, 2010
4,162
The time is not the only thing that changes near light speed.

Everything grows shorter in the direction of travel. The rocket ship which was 100 feet long on earth would be much shorter near light speed, but an astronaut could measure it in flight and would not discern any changes because the measuring instruments would have contracted by the same amount.

#### BR-549

Joined Sep 22, 2013
4,938
In the future this equation will be proved false. Along with all of his other equations. The only reason it works today, is because we can not test it yet, and the equation is so sloppy.

There will be a limit to the mass gain. This is because, when a particle is accelerated, some of that force goes into moving the particle and some of that force goes into spinning the particle.

When a particle is first hit with an external force......it will NOT move at first. This is the reaction of inertia. The particle will first try to turn and orientate in reaction to the force. This causes the particle to line up with the force. A lot of external forces can be nullified just by turning or changing orientation, without moving. After the particle lines up....and if it still has a net force......then it will move. As it moves forward....another spin rotation will be super imposed on the already spinning particle. The spin is perpendicular to the forward motion.

The ratio of the forward motion and the spinning motion will depend on the velocity of the accelerating force. When the spinning rate gets to the next energy level......the particle will contract and will physically get smaller. This contraction has two results. First....the area of the particle has decreased. That means the target area for the external force has been reduced. Now it will take much more force to move the particle. And second...All of the particle flux is confined to a much smaller area. FLUX DENSITY happens to be what MASS is. So even though the size decreased, the mass has increased. Also....each successive contraction takes magnitudes more acceleration.

There will be a limit to this contraction, because flux must have area. When this limit is reached.....there will be no more mass gains and all of the acceleration will go into forward motion. In other words.....no more inertia to overcome........and unlimited velocity.

The property of inertia comes from 2 perpendicular, rotating fluxes. Mass is the density of that flux.

#### nsaspook

Joined Aug 27, 2009
8,897

#### nsaspook

Joined Aug 27, 2009
8,897
Since velocity is relative, how does it work out when two particles with mass are traveling in opposite directions at .5c relative a 3rd party observer? Relaive the observer each particle is going .5c, but relative each other the particles should be traveling at c. But do the particles not see their velocity relative each other as c due to their own shift in time, which is also relative each other?
It's tricky.
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel2.html

#### BR-549

Joined Sep 22, 2013
4,938
That is so lame. The length of length does not change. The rate of time does not change.

The frequency of a dipole changes in a electric field gradient or a magnetic field gradient. All of your machines and all of your measuring tools use dipoles.

A gravity gradient can change the frequency of a dipole also. Accelerating a "mass" can change dipole frequency. In other words.....just changing direction, can change dipole frequency.

There is no mystery or magic here. Time and length do not change. Nature is very firm.

#### BR-549

Joined Sep 22, 2013
4,938
Our clocks are based on dipole or atomic vibrations. This is a terrible idea.

If we used the frequency of an electron for a clock, we could keep perfect synced time everywhere.

Then you would see time (and length) does not change. All electrons in the universe have a common time.