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eNathan
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How does [tex]E = mc^2 [/tex] imply that no object with rest mass can ever reach the speed of light?
eNathan said:How does [tex]E = mc^2 [/tex] imply that no object with rest mass can ever reach the speed of light?
anyone correct me if I am wrong, but isn't it because when a particle approaches the speed of light its mass increases towards infinity, and when it hits the speed of light its mass is infinity, so according to E=mc^2 you would need an infinite amount of energy, which u can't geteNathan said:How does [tex]E = mc^2 [/tex] imply that no object with rest mass can ever reach the speed of light?
Honorable_Death said:Ok i have a question that's a little off topic but its been on my mind for a long time and would much appreciate an anwser, here it goes. According to past forums i have read relatavistic mass does not create warps in space-time, in other words energy does not create warps in space-time, but instead it is rest mass that effects gravity, now in a nuclear reaction it is rest mass that is used as m in E=mc^2 right? and if this is right then that means that rest mass equals energy, so energy would effect gravity also right?
pervect said:Energy, momentum, and pressure all cause gravity via the "stress-energy tensor".
I'm not sure where you read that relativistic mass does not warp space-time. The phrase is unclear enough that I'm not sure quite what it means.
Some examples might (or might not) help clarify the situation.
Suppose you have a cold object. From an external source, you heat it up. The cold object now has a greater gravitational field. It also has a greater invariant mass. The two are closely related by the equivalence principle - so gravitatioanl mass will always be equal to inertial mass, or just invariant mass.
Suppose you have a massive object, and you either a) increase it's velocity or b) increase your velocity relative to it. The gravitational field of the moving object is different from that of the non-moving ones in many ways (it's not spatially uniform, for one thing), but a rapidly moving object will never (for instance) turn into a black hole.
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The last point to consider is a combination of the first two points above. Suppose we have a gas in a container, and we heat the gas up while keeping it contained.
Then the difference between the hot container and the cold container is just the fact that the gas molecules are moving around, in all directions.
We've already argued that the mass (and gravity) of the system with the hot gas is (very slightly!) greater than the mass of the system with the cold gass. As long as the gravity is "weak-field", we can decompse the total gravitational field of the system into the sum of the fields due to each particle. Thus we can argue that in some sense the field of an individual particle is "stronger" when it is moving, but this is an average sort of field over many directions, since the field of a moving particle is definitely not uniform.
This approach eventually breaks down - eventually, the entire idea of gravity "as a field" starts to have problems. This occurs when the space-warping effects of gravity start to become important. At this point, a uniform treatment that treats gravity as a curvature of space-time becomes necessary. To fully explain the math of this concept is difficult, about all I can say is that it is important to know that the idea of gravity as a "field" eventually gets replaced by the notion of curvature.
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pervect said:I'm not sure where you read that relativistic mass does not warp space-time. The phrase is unclear enough that I'm not sure quite what it means.
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I think you may have misunderstood what other members on physicsforums.com said, I remember you made a similar accusation of people contradicting each other on this thread but in that case you were misunderstanding, and nothing said on that thread contradicts what pervect said above. Can you point to a specific post that you think does contradict it?eNathan said:I am beginning to question everything I know about physics. I have knows several physisics, and things I hear from them and physicsforums.com often contradict each other. This case in particular. I am not critisizing what you wrote, I am just saying some things you said contradict other things I have heard.
Hi pervect. You're one sharp dude and I consider myself honored that you referred to my previous discussions.pervect said:Yes - AFAIK the only time E is not equal to Mc^2 is the case Pete likes to bring up that occurs when a system is not isolated (i.e. when there are forces acting on it from the "outside world").
For an isolated system, the concept of the relativistic mass of a system can be replaced by the concept of the energy of the system.
I miss these arguements. Perhaps I'll get my ISP back today.Honorable_Death said:i was talking about relativistic mass does not effect gravity and has no gravitational force
Its important to keep in mind what the term "covariant" meas in this quote. It refers to the components of tensors and how they change upon change in coordinates. Quantities/numbers which have this property are called "covariant" while those which don't change are called "invariant." There are many different uses of the term "covariant" so best to keep them distinct.With Mach's solution of the problem of rotation, the gravitational field is deprived of its absolute character and recognized as a covariant magnitude which varies from coordinate system to coordinate system.
Its rarely the case that a body does not interact with the outside world. Consider a uniform E-field. Place a dumbell in the field and its mass won't be related to the energy by E = mc^2. The dumbell being a rod with a -q charge on one end and +q charge on the other end. The rod won't accelerate. It will move at constant velocity in all inertial frames. But the mass won't read as E = mc^2.pervect said:Yes - AFAIK the only time E is not equal to Mc^2 is the case Pete likes to bring up that occurs when a system is not isolated (i.e. when there are forces acting on it from the "outside world").
The equation E=mc^2 is a fundamental equation in physics that relates energy (E) to mass (m) and the speed of light (c). It states that the energy of an object is equal to its mass multiplied by the speed of light squared.
The speed of light (c) is a fundamental constant in the universe and is the fastest possible speed at which any object can travel. In the equation E=mc^2, it shows the relationship between mass and energy, indicating that even a small amount of mass can produce a large amount of energy when multiplied by the speed of light squared.
According to Einstein's theory of relativity, as an object approaches the speed of light, its mass increases and requires more and more energy to continue accelerating. At the speed of light, an infinite amount of energy would be needed to accelerate an object with rest mass, making it impossible to reach that speed.
According to the theory of relativity, nothing can travel faster than the speed of light. This is because as an object approaches the speed of light, its mass and energy requirements become infinite. Additionally, the laws of physics as we know them break down at such high speeds.
E=mc^2 revolutionized our understanding of energy and mass by showing that they are two forms of the same thing. It also introduced the concept of mass-energy equivalence, which states that mass can be converted into energy and vice versa. This equation has been instrumental in the development of modern physics and has had numerous practical applications, such as in nuclear energy and nuclear weapons.