Where did we go wrong?
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Arthur Dent
Posted:
Wed Dec 07, 2005 5:37 pm
Joined: 26 Aug 2005
Posts: 7
Location: Ohio
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I was thinking about how Einstein said that nothing (save photons) can reach the speed of light. I wanted to do more reading on why this is believed to be truth and got a satisfactory explanation. I noticed though that all of the sites and books that I found never went into too much detail of the actual mathematics of the subject, assuming them self explanatory and too basic to waste time discussing.
So, I went into work in Excel trying to observe this phenomena through numbers, I knew that I would obviously need the formula E = MC² to do this, along with Ke = ½MV²
I came up with a chart listing the basic numerical behavior of four particles.
I will spend a brief moment going over the meanings behind the rows and columns in this Chart.
Particle:
This column just lists the name of the particle in question for later reference.
Mass: (M)
Describes the mass (in Kilograms) of the particle in a state of rest.
Velocity: (V)
Unlike the actual velocity (described below) this column announces the velocity we will attempt to accelerate the particle to.(M/s)
Kinetic Energy: (Ke)
The Kinetic Energy (in Joules) the particle will hold after we accelerate it.
Found by multiplying half the particle’s mass to the square of the velocity we will be accelerating it to.
Added Mass:
The Mass added to a particle by an increase of Kinetic Energy.
Found by dividing the Kinetic Energy of the particle by C² (9 times 10 to the power of 16)
Actual Velocity:
The Velocity a particle would reach with the current mass (Mass + Added Mass)
Assuming that V² = Ke / ½M it is found as the square root of the kinetic energy divided by half of the current mass.
| Code: |
Particle: Mass: Velocity: Kinetic Energy: Added Mass: Actual Velocity:
Par A: 10 3E+08 4.5E+17 5.00 244948974 M/s(.81C)
Par B: 15 3E+08 6.75E+17 7.50 244948974 M/s(.81C)
Par C: 22.5 3E+08 1.01E+18 11.25 244948974 M/s(.81C)
Par D: 10 6E+08 1.8E+18 20.00 346410161 M/s(1.15C)
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As you can see Par A through Par C all hold the expected values confirming Einstein’s statement, the universal speed limit is the speed of light. When we read further on to Par D it defies this as we add more kinetic energy than it needs and it exceeds the speed limit.
To simplify my question, what factor did I miss?
It is obvious that there are only two possible things to learn from the above and only one can be correct.
1.) Einstein is wrong
2.) I am wrong
I vote for the second possibility as it seems to hold alot more probability to be correct.
_________________
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Marc
Site Admin
Posted:
Wed Dec 07, 2005 9:11 pm
Joined: 24 Oct 2003
Posts: 108
Location: Ireland
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Arthur,
Interesting post but you've neglected to use the correct formula for relativistic kinetic energy.
The formula: KE = ½MV² applies at normal velocities but is slightly inaccurate. This inaccuracy becomes apparent close to the speed of light.
The formula you're looking for is: KE = mc^2 - m0c^2 where m0 is the rest mass of the particle.
For more information you can take a look at:
str_replace("\'","'","http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html")
- Marc
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Arthur Dent
Posted:
Wed Dec 07, 2005 11:27 pm
Joined: 26 Aug 2005
Posts: 7
Location: Ohio
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Marc,
Thank you very much, that helps quite a bit.
I don't have time at the moment to plug this into my Excel program, but I will try tomorrow maybe.
_________________
Trip to moon advertisment:
Lose 16.6% of your weight! Garanteed!
only about $100 million!
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SkyBoard
Site Admin
Posted:
Sat Dec 10, 2005 4:42 am
Joined: 05 Feb 2005
Posts: 24
Location: Los Angeles, CA
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Good clarification, Marc.
I would also like to point out the particle class that in theory does exist at speeds v>c. These particles, if they exist, are called tachyons. I cannot tell you there properties because I do not remember, but to me the mere classification is important.
More to the point, think of KE as Net Force, which is the absolute difference between parallel force (a component of gravity) and frictional force (that which impedes an object's path of motion). As you can see, the mathematical contructs are similar and though one is an energy and one is a force, the total KE is c^2 multiplied by the absolute difference of a particle's mass at two timepoints of reference.
_________________
"Your God may be in the details, but mine's in the process." - Ian Malcolm
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