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e = MASS * c^2

Ren
Posts: 7,102
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11/12/2011 10:36:08 PM
Posted: 5 years ago
Something has always intrigued me about the equation e = mc^2 as it relates to time. People always seem to concentrate on only one of the variables -- velocity -- when considering the possibility of transversing time. However, no one ever considers the ramifications of inflating the other variable -- mass -- to achieve the same effect.

Of course, given that it's simply a variable that applies to the equation in the same way as velocity (via multiplication), I've always figured that inflating it should somehow produce the same effect as inflating velocity, and thus, should somehow have some effect on time.

Well, it turns out that mass does have an effect on time -- and literally, in the same way. Get this relativity -- the more massive something is, the slower time moves for that object. Literally.

So, no matter the source of the energy, energy itself literally slows the flow of time. Get that.

The implications of this is very serious. If we found a way to manipulate energy at will, we would literally have the same capacities for time.

However, only in one direction. It is physically impossible, as far as humanity knows right now, to move backward in time. It is a single-direction vector. We can only move forward by slowing it down for ourselves relative to everything around us, hence the term "relativity."

It also denotes that if we could build something that can somehow alter it's own mass or density or whatever, or the energy that it emits, while protecting ourselves from this effect, and that can also accelerate to speeds proportionate to light (that is, which can be expressed non-exponentially in relation to light), we can transverse significant distances throughout the universe within a human lifetime.

Thoughts?
Ore_Ele
Posts: 25,980
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11/14/2011 9:56:06 AM
Posted: 5 years ago
Just a quick glance at the basic equation for time dilation...

[delta]t` = [delta]t / ( 1 - v^2 / c^2)

I don't see mass having any effect on this at all.
"Wanting Red Rhino Pill to have gender"
Ren
Posts: 7,102
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11/14/2011 12:57:03 PM
Posted: 5 years ago
At 11/14/2011 9:56:06 AM, Ore_Ele wrote:
Just a quick glance at the basic equation for time dilation...

[delta]t` = [delta]t / ( 1 - v^2 / c^2)

I don't see mass having any effect on this at all.

Actually, the equation for time dilation requires that you find the square root of the bottom half of the right side of the equation, i.e., one minus the the square of the velocity of a casual observer divided by the square of the speed of light.

The reason why this point is crucial is because it reduces the quantity down to a measurement that is proportionate to measurements relating to a casual observer (as the equation requires that his or her velocity is squared so that it can interact functionally with the speed of light squared, consistent with the mass-energy equivalence equation).

The way this equation determines time dilation, which is the physical determination of the passage of time in mathematical terms, is by comparing the difference between the time elapsed for an observed object and that for a casual observer. It is essentially an alteration of the time equation, which is [delta]t = 2L/c, or, the change in time equals 2 periods of a clock (for example, a second, a minute, etc.) divided by the speed of light (or, the terminal velocity of all known things).

Therefore, the time dilation equation can apply to either an object affected by a given velocity, or an object that has a certain gravitational pull, or mass, and in fact, if you were to look it up, you'd see that the equation is often applied to both.

Don't you just love math? I fkking love math.

As it stands, whether mass affects time is not up for question. I have been mulling about this forever, but never mentioned it precisely because I wasn't sure whether mass affected time. But, now I have conclusive evidence that it does -- it is exactly what physicists are saying.

However, I did identify an inaccuracy in my post. I wrote that time is a variable, but made it seem as though it was a variable in relation to e = mc^2 -- I didn't mean this. I was referring to time as it applies to Einstein's ten relativity equations, summarized as an interaction between regular curvature, Ricci curvature, the cosmological constant, the acceleration of gravity, the speed of light, a given metric, and the aggregate forces applied to an object at a given velocity. E = mc^2 does not necessarily indicate that time moves slower in response to velocity and mass. It is a mathematical statement that proves mass and energy are interchangeable. The "c" in the equation is not a variable -- it is the contant known as the speed of light.
Chthonian
Posts: 247
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11/15/2011 12:50:21 PM
Posted: 5 years ago
Interesting discussion, Ren!

My understanding of the E=mc^2 equation is that as matter moves it gains momentum and energy, and thus becomes heavier as it moves. And apparently mass has an upper limited to how fast it can move, which is the speed of light; nothing can move past us faster than this limit.

So, we can only increase mass with motion. And I am not sure if time will change for increasing an object's mass-- inside or outside the inertia frame—if the object isn't moving, unless it is so massive that it's gravity can trap objects moving at the speed of light, ostensibly bending space-time.

Another intriguing thought here is that even if we can move at or near the speed of light, Hubble's law tells us that the universe is expanding faster than the speed of light. So to truly travel large galactic distances, we are going to have to find a way to warp space-time.

A while back I was watching a TV show were a guy proposed building a spaceship that can bend space directly in front of it and ride the ripple, decreasing the actually distance traversed. But if I remember correctly the energy to do this is close to infinite so looks like we are a long way off before humans embark on deep space travel.
Ren
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11/16/2011 4:30:48 AM
Posted: 5 years ago
At 11/15/2011 12:50:21 PM, Chthonian wrote:
Interesting discussion, Ren!

My understanding of the E=mc^2 equation is that as matter moves it gains momentum and energy, and thus becomes heavier as it moves. And apparently mass has an upper limited to how fast it can move, which is the speed of light; nothing can move past us faster than this limit.

Thanks.

E=mc^2 has nothing to do with weight -- it refers to relativistic mass. That is, the mass of an object based on its aggregate energy, without taking into account its invariant mass, which is its composite that is not transferable -- it's physical properties.

So, we can only increase mass with motion. And I am not sure if time will change for increasing an object's mass-- inside or outside the inertia frame—if the object isn't moving, unless it is so massive that it's gravity can trap objects moving at the speed of light, ostensibly bending space-time.

Based on your reasoning, matter would have a threshold to how massive it could be, and this threshold reduces in some proportion with its velocity. However, as far as we know, this isn't the case; there is no upper-margin to how massive something can be. Moreover, the reason why relativistic mass is distinguished from invariant mass is because relativistic mass results in part from kinetic energy, which derives from an outside source that applied work to the object. The reason why we have invariant mass--which is a constant based on the mass of an object at rest--is because mass exists despite motion.

In that regard, an object with a gravitational pull, which can result from either velocity, mass, or a combination of the two, experiences a slower rate of passing time than objects with much smaller masses or velocities relative to that object. This slower rate of passing time is always relative, though. In other words, time is always moving at the same rate, but due to physical limitations in the conveyance of energy and the interpretation of that energy, it appears as though time moves slower to an observer that is moving more slowly.

This is likely because all known forces bend and warp in response to gravity.

Another intriguing thought here is that even if we can move at or near the speed of light, Hubble's law tells us that the universe is expanding faster than the speed of light. So to truly travel large galactic distances, we are going to have to find a way to warp space-time.

I've never heard of Hubble's Law, could you quote/link it, please?

On the other hand, the Universe is conceivably expanding at the speed of light, given that the universe contains light and there is certainly light moving in that direction. That said, the reason why it may appear that the Universe is moving faster than the speed of light is because it moves at the same rate in which it can be detected, magnifying the time it takes to detect it proportionate to the distance of the observer, which increases exponentially each moment, as its a moving body. Therefore, from the perspective of someone watching the Universe expand from a given point within the Universe, the point at which the Universe is expanding is moving in fast-forward, meaning that it is going the speed of light within a warped interpretation of time as it applies to the constant C. This is because the light that's emanating from the margin of the Universe that makes it visible, and forces emanating from it that make it real, are travelling at or slower than the speed of light, although it is moving at that speed. Therefore, by the time these forces reach the observer, the margin of the Universe is no longer there.

However, from the perspective of the expanding margin of the Universe, time is moving at a normal rate, and it is moving at the speed of light. The observer, on the other hand, is frozen, because the light emanating from that observer that makes him visible, and the energy emanating from him that makes him real, is traveling from him at the same rate or slower than the speed at which the margin of the Universe is moving.

Ya feel me?

A while back I was watching a TV show were a guy proposed building a spaceship that can bend space directly in front of it and ride the ripple, decreasing the actually distance traversed. But if I remember correctly the energy to do this is close to infinite so looks like we are a long way off before humans embark on deep space travel.

I've never heard of any real physical or theoretical application that can result in "bending space..."

However, I do know that Stephen Hawking proposed that the tiny ripples in time-space, which are almost like cracks, wrinkles, or striations, appear and then almost instantly disappear from reality. These ripples are on the quantum level, and are too small for matter to pass through. However, if we figured out a way to magnify their size exponentially, we would, in turn (due to this mass-time relativity) increase the duration of their existence, effectively creating a wormhole through which we can pass into another point in time in the Universe (or, interchangeably, another place in the Universe).

On the other hand, whether or not we can traverse relatively significant distances throughout the Universe within a human lifetime, I believe, is still up for question. Time moves slower in proportion to an object's velocity (and mass) -- this is a general relativity, not just one that occurs at the speed of light. So, our solar system is something like 4 lightyears across. Therefore, travelling half the speed of light, we should be able to get to another solar system entirely within 8 years minus however much time slows due to the spaceship's relativistic mass.
Chthonian
Posts: 247
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11/16/2011 9:20:24 PM
Posted: 5 years ago
At 11/16/2011 4:30:48 AM, Ren wrote:
At 11/15/2011 12:50:21 PM, Chthonian wrote:
Interesting discussion, Ren!

My understanding of the E=mc^2 equation is that as matter moves it gains momentum and energy, and thus becomes heavier as it moves. And apparently mass has an upper limited to how fast it can move, which is the speed of light; nothing can move past us faster than this limit.

Thanks.

E=mc^2 has nothing to do with weight -- it refers to relativistic mass. That is, the mass of an object based on its aggregate energy, without taking into account its invariant mass, which is its composite that is not transferable -- it's physical properties.

In "The Character of Physical Law" Richard Feynman writes that "the energy associated with motion appears as an extra mass, so things get heavier when they move." http://www.weburbia.com... It appears to be an intuitive way to think about mass in motion without having to use complicated mathematics. Put another way, increasing mass makes an object more resistant to change. Fundamentally, mass is a measure of an object's inertia.

So, we can only increase mass with motion. And I am not sure if time will change for increasing an object's mass-- inside or outside the inertia frame—if the object isn't moving, unless it is so massive that it's gravity can trap objects moving at the speed of light, ostensibly bending space-time.

Based on your reasoning, matter would have a threshold to how massive it could be, and this threshold reduces in some proportion with its velocity. However, as far as we know, this isn't the case; there is no upper-margin to how massive something can be. Moreover, the reason why relativistic mass is distinguished from invariant mass is because relativistic mass results in part from kinetic energy, which derives from an outside source that applied work to the object. The reason why we have invariant mass--which is a constant based on the mass of an object at rest--is because mass exists despite motion.

Time can only appear to change based on an objects position and velocity relative to another. For the object in the inertial frame, time stays constant. The focus of this discussion is that you contend that increasing mass will change time for that object. I was suggesting that since you aren't including motion, the mass we are discussing is invariant mass, and thus is unlikely to change its reference of time. Also, I not implying that there is an upper limit to how massive an object can be, I am only suggesting that there is a limit to how fast an object can physically move.

In that regard, an object with a gravitational pull, which can result from either velocity, mass, or a combination of the two, experiences a slower rate of passing time than objects with much smaller masses or velocities relative to that object. This slower rate of passing time is always relative, though. In other words, time is always moving at the same rate, but due to physical limitations in the conveyance of energy and the interpretation of that energy, it appears as though time moves slower to an observer that is moving more slowly.

This is likely because all known forces bend and warp in response to gravity.

Another intriguing thought here is that even if we can move at or near the speed of light, Hubble's law tells us that the universe is expanding faster than the speed of light. So to truly travel large galactic distances, we are going to have to find a way to warp space-time.

I've never heard of Hubble's Law, could you quote/link it, please?

Hubble's Law states that the apparent recessional velocity of a galaxy is proportional to its distance from the observer. So they can appear to be receding faster than the speed of light. http://carma.astro.umd.edu... My understanding of Hubble's Law is that objects aren't really moving; the space around the objects is. The analogy often given is to think of the universe as a rubber band and the galaxies as dots on the rubber band. When the rubber band is stretched the dots appear to move away from one another but from the dots reference frame they haven't actually moved.

On the other hand, the Universe is conceivably expanding at the speed of light, given that the universe contains light and there is certainly light moving in that direction. That said, the reason why it may appear that the Universe is moving faster than the speed of light is because it moves at the same rate in which it can be detected, magnifying the time it takes to detect it proportionate to the distance of the observer, which increases exponentially each moment, as its a moving body. Therefore, from the perspective of someone watching the Universe expand from a given point within the Universe, the point at which the Universe is expanding is moving in fast-forward, meaning that it is going the speed of light within a warped interpretation of time as it applies to the constant C. This is because the light that's emanating from the margin of the Universe that makes it visible, and forces emanating from it that make it real, are travelling at or slower than the speed of light, although it is moving at that speed. Therefore, by the time these forces reach the observer, the margin of the Universe is no longer there.

However, from the perspective of the expanding margin of the Universe, time is moving at a normal rate, and it is moving at the speed of light. The observer, on the other hand, is frozen, because the light emanating from that observer that makes him visible, and the energy emanating from him that makes him real, is traveling from him at the same rate or slower than the speed at which the margin of the Universe is moving.

Ya feel me?

I am not sure time has a "normal rate". Time is always relative to the observer.

A while back I was watching a TV show were a guy proposed building a spaceship that can bend space directly in front of it and ride the ripple, decreasing the actually distance traversed. But if I remember correctly the energy to do this is close to infinite so looks like we are a long way off before humans embark on deep space travel.

I've never heard of any real physical or theoretical application that can result in "bending space..."

While it seems highly unlikely someone has patented the idea http://www.canada.com...


On the other hand, whether or not we can traverse relatively significant distances throughout the Universe within a human lifetime, I believe, is still up for question. Time moves slower in proportion to an object's velocity (and mass) -- this is a general relativity, not just one that occurs at the speed of light. So, our solar system is something like 4 lightyears across. Therefore, travelling half the speed of light, we should be able to get to another solar system entirely within 8 years minus however much time slows due to the spaceship's relativistic mass.

As an object moves faster, it will increase is mass. This will increases its inertia making it harder and harder to maintain super high speeds. So, any ship that would travel as fast as you suggest is going to need an enormous fuel supply.
Ren
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11/17/2011 1:24:24 PM
Posted: 5 years ago
At 11/16/2011 9:20:24 PM, Chthonian wrote:

While it seems highly unlikely someone has patented the idea http://www.canada.com...

Well, the article makes it clear that there's no real scientific foundation for the belief that one can build something that bends space-time. However, a physicist was quoting in that article as having stated, "Many physicists have said one can bend space-time, but one would need to fly in something far more massive than Earth, or nearly as fast as light, to make a big change."

...suggesting that relativity applies to mass in the same way it does velocity, as I proposed.

As an object moves faster, it will increase is mass. This will increases its inertia making it harder and harder to maintain super high speeds. So, any ship that would travel as fast as you suggest is going to need an enormous fuel supply.

Like I said -- there is a difference between relativistic and invariant mass. Physicists almost always refer to the latter, as kinetic energy and velocity require separate designations to make sense of all forces acting on a object. In that regard, E=mc^2 can almost be considered shorthand. The real equation is something like E=(m^2c^2)/1-v^2 * p^2...

Wait, is that right?

No, apparently its E^2 = (m0^2c^4) + (p^2c^2)

Where m is the object's (invariant) mass, c is the constant the speed of light, and P is the object's momentum.

That said, you're right -- the fuel supply is the most fantastical aspect of the supposition. Although, something truly massive enough may have the capacity to contain such a fuel supply...?
tBoonePickens
Posts: 3,266
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11/18/2011 11:38:57 AM
Posted: 5 years ago
An object's "weight" does not increase with its velocity, its mass does. This is why when it's usually stated in laymen's terms, they usually put quotes around weight. Weight and mass are not equivalent: your weight on the Moon is about 1/6th your weight on Earth however, your mass is the same in both places.

I have heard that the rate of expansion is increasing but NOT that it has exceeded or even matched the speed of light. I have heard of some theories (Inflation) where in the very early universe, it did expand at well above FTL speeds. Apparently, this theory claims that the FTL speed limit was not physically in effect.

As far as increasing an object's mass, there comes a point where said object would collapse under it's own weight! Regardless, I think that there is a limit as to how massive an object could be...let's say it was infinite (or close to it) there wouldn't be a need to travel anywhere as this object would already be everywhere!
WOS
: At 10/3/2012 4:28:52 AM, Wallstreetatheist wrote:
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