A Common Scientific Belief

It is common scientific theory that when you approach the speed of light, you gain mass.

This is supported by Eintein's theory:

E = MC^2

which using simple algebra, you can isolate M (mass) to get:

M = E / C^2


However, how can this be? In school they always teach this:

Mass - measure of the amount of matter in a substance

Weight - the force of gravity acting upon the substance

So, using those, how can M = E / C^2?

Mass is the measure of the amount of matter in a substance. Therefore, how can you gain mass as you approach the speed of light? You do not gain matter, so therefore how do you gain mass without gaining matter?

So how would it effect mass? Mass should have no effect....

Maybe gravitational force increases...

that would increase weight, not mass...

it seems they are relating energy to mass, not velocity, so in fact it seems that 'approaching the speed of light' is not necessarily relevant, rather approaching that amount energy. [does not necessarily need to be kinetic].

uhh but then again, my field is calculus, not physics. :)

Does this help?
http://math.ucr.edu/home/baez/physic...oton_mass.html

The answer to that is more about time than energy. That equation is the final implication of the theory of relativity, to understand it you have to start at the beginning, with Galileo:
In Galileo’s day physicists were struggling with the problem of Earth rotating on its axis. The rotation meant that the Earth was continually moving and if that was true, then why, when a person dropped an object did it fall to ground exactly beneath the point where it was released. Shouldn’t the rotation have caused the Earth to have spun away from underneath it? Galileo was the first to answer this question, “before the object is released, it is travelling at he same speed as the Earth. When you release the object, it will continue to travel at the same horizontal speed, while accelerating downwards.” This was the first description of an inertial frame of reference.
An inertial frame of reference is one that is either at complete rest or moving with a constant speed. While you are within an inertial frame of reference, there is no possible mechanical experiment that can determine the speed of that frame of reference. In the example above, the earth is an inertial frame of reference. When the object is dropped it appears to fall straight to the ground. To an observer outside the frame of reference, it continues to move along with the frame of reference while it falls to the ground. The discovery of light as a wave seemed to introduce a loophole in this.
As the properties of a wave are dependent on its velocity, shouldn’t a ray of light from the lantern on a speeding train look different to the light given off by a lantern on the station it is approaching?
In 1801 Thomas Young devised an experiment that showed properties of light unique to waves. This presented problems for physicists as waves needed a medium to travel in. The proposed medium was that of aether, a transparent substance that was perfectly transparent and that filled all space. This meant that to determine your velocity, even in an inertial frame of reference, all you had to do was measure the speed of two light rays travelling at right angles. The aether would in theory affect the light differently depending on weather it was shone directly into the aether, or allowed to travel sideways, decreasing its effect on the light beam. This is what A. A. Michelson and E. W. Morley did in 1887. However they could not find a single difference in way each beam of light travelled, instead they found the speed of light to be constant. This is where Einstein steps in.
Consider a beam of light travelling from a light in the ceiling of a train carriage to the floor. As the speed of light is a constant, the time taken for this to happen must be the same for an observer inside the train and for another observer standing on an embankment outside the train. At low speeds this is quite normal, but imagine a super fast rocket train capable of travelling at half the speed of light. In the time the light takes for the passenger on the train to observe the light reaching the floor of the carriage, the person standing on the embankment would have also seen the train move forward a small distance. They therefore would not have seen the light travel straight down, but instead they would have witnessed the ray of light travelling diagonally as the train moves forward. The total effect of this is that in the same period of time the two observers witness the same ray of light travel two different distances. The only possible way for both observations to be correct is if the amount of time taken for this to occur on the train was less than that recorded by the person standing outside the train. That means as an object’s velocity increases the flow of time experienced by that object will decrease.
Now consider the reverse of the above situation. As the person in on the train is inside an inertial frame of reference, they cannot tell weather they are moving or at rest, with the entire planet moving around them. As a result, from their point of view, the person standing on the embankment is the one experiencing time dilation. In effect, the combination of these two factors essentially slows the train down, limiting its maximum velocity to the speed of light, when the time dilation becomes infinite. However speed alone can not alter something’s velocity, there has to be another factor at work here. That other factor is mass dilation. Here it is best to think of mass as not just the number of atoms inside an object but rather as an objects resistance to a change in its velocity. As shown before, as an objects mass increases so does its resistance to further acceleration so while the number of atoms within the object remains constant, its mass increases.
From that Einstein managed to derive a whole set of equations resulting in:
E = MC^2
Or factoring in mass increase:
E = E + MC^2
(I know that defies basic mathematics but just imagine the second E as having a subscript k attached to it, or Energy = Kinetic Energy + Rest Mass * The Speed of Light Squared)

A bit long winded I know, but there is no better way to explain it.

>It is common scientific theory that when you approach the
>speed of light, you gain mass.

Not only when approaching the speed of light. But when approaching the speed of light, the increment of mass is better to notice. For small speeds it is hard to measure.

m = m0 / sqrt (1 - v^2/c^2)

Since c (speed of light) is quite large and v (for example speed of a running person) quite small, the term v^2/c^2 is nearly 0. So

m = m0 / ~1 = ~m0

Where I use ~ as symbol for "almost".

This is an effect of relativity.

>This is supported by Eintein's theory:
>
>E = MC^2
>
>which using simple algebra, you can isolate M (mass) to get:
>
>M = E / C^2

This is a different theory, it's the equivalence of mass and engergy. It can be used to make basic calculations in nuclear reactions. In nuclear reactions the mass of the particles is converted to the energy. The mass of the particles is (almost exactly) known, so it's possible to calculate the energy which comes free after the reaction.

Quote:

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Here it is best to think of mass as not just the number of atoms inside an object but rather as an objects resistance to a change in its velocity.

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But by definition, mass is the measure of the number of atoms, particles, matter, etc. in an object.

So either they need to stop teaching the wrong definition of mass....or they need to change the variable name to something else....in my opinion of course...

>>But by definition, mass is the measure of the number of atoms, particles, matter, etc. in an object.

They do?
http://www.dictionary.com/search?q=mass
http://math.ucr.edu/home/baez/physic...oton_mass.html
http://physics.about.com/library/dict/bldefmass.htm
http://www.britannica.com/eb/article...d=0&query=mass

then again:
http://www.pas.rochester.edu/~ygao/p...e1/tsld008.htm
http://www.me.ttu.edu/faculty/jordan.../Mass/Mass.htm


Thats why I prefer chemistry.

[edit]
How could I forget Newton's definition:
F = ma
or m = F/a
Mass is simply how much an object can resist acceleration due to an external force. This is directly proportional to the amount of matter in an object.
[/edit]

>But by definition, mass is the measure of the number of atoms,
>particles, matter, etc. in an object.

I've not studied physics, but if I remember elementary phsyics well, a fundamental law of Newton was

F = m g

So

m = F / g

This is for calculations with relative low masses, speeds, forces etc, else you have to take relativity in acount.

Quote:

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Originally posted by DavidP
Mass is the measure of the amount of matter in a substance. Therefore, how can you gain mass as you approach the speed of light? You do not gain matter, so therefore how do you gain mass without gaining matter?

So how would it effect mass? Mass should have no effect....

---

Mass is not the same as matter. Energy is not matter, but does indeed have mass. In this case, a fast-moving object has a large amount of kinetic energy. This kinetic energy has its own associated mass, which in addition to the matter-based mass (rest mass) of the object makes the total effective mass of a moving object greater than that of a stationary object.