Well, from an external view of an observer, the relativistic increase of mass is really the increase in the neergy-mass system, so the external observer will observer will see their spaceships increase... since acceleration through space causes a type of frame dragging, the more you increase the speed, the more gravitational acceleration which is directly equivalent to the distortions/curvature/drag is increased also. Analagous, and equivalant by Maxwells equations of a moving electron, will emit electromagnetic gamma rays, (the speed must also be equivalent to the speed at which the electron is moving at), and thus, gravitational mass (the kind of mass an electron is made of) will also radiate gravitational wave distortions.
.... this was from quantum quacks inetersting thread.
I ask a question; if we could make a photon have a rest mass (such as an interaction between a tachyon and a photon *), could the photon be perturbed into mass upon aloof interactions? (1)
I question this because of the following known (albiet, maybe, not very well-known) formulations of tachyonic existences and observable and measurable constituents:
1) Tachyons (root word from tachycardia) would generate Cherenkov radiation in a vacuum.
2) Adding energy to tacyons slowed them down with the velocity of light as the lower bound.
If tachyons are added with real energy (such as a photon), it will slow it down. If the lower limit of the tachyon is the speed of light, then what would happen if interaction between a photon and a tachyon under certain conditions, such as a high energy surrounding which is of real value, inexorably flux the photon into a particle of mass?
(1) Just an essay i wrote on tachyonic matter being possibly found from tritium decay:
Tachyonic Dynamics
We have all heard of the hypothetical particles called tachyons. They have a rest mass M that also has an imaginary value $$(M^2<0)$$. It turns out that $$(E=gM)$$, the observable mass-energy of these light weight particles, becomes ''real'' and ''positive''.
If a particle was able to defy the light-speed barrier so that v was greater than $$c$$ or $$(v>c)$$, then both g and E would become imaginary quantities, because $$\beta$$ would be larger than $$1$$ and $$(1 - \beta 2)$$ would be negative.
When using imaginary concepts, we must use complex numbers... nothing too complex about them, so don't be scared off! We need the calculus in concepts that are imaginary - not quite existing in the realms of the real - but are ''real'' nonetheless... we use it when calculating the imaginary dimension of time, and even concepts beyond ''$$c$$'' - imaginary mass.
-this small paragraph is for the layman, even though i am novice
To understand this better, we must consider the pyhagorean theorem.Complex numbers deal with square roots. Now, you might remember square roots from high school. A number that is multiplied by itself produces the square root - thus, the square root of $$4$$ is $$(2 x 2)$$. The square root of 9 is $$(3 x 3)$$. The square root of 16 is (4 x 4), ect. Note however, that the square root of 1, is (1 x 1). Complex numbers move into the negatives; thus, it helps mathematicians work out the improbable square root of -1, for instance, which is $$i x i = -1$$. The $$i$$ stands for ''imaginary'', and it helps us in calculating numbers that are not in the real world.
Another example is the square root of $$4$$, which is $$(i^2)^2 = -4$$. Quantum Physics and Relativity would be impossibility, without complex numbers, and so would our ability to calculate time as an imaginary dimension of space.
In a standard course of geometry, one will inventually learn the pythagorean theorem. As you will probably know, the theorem applies to length of the right sides of a right triangle.
It is a simple formula, and it tells us that if one was to work of the angles on the sides of the triangle, the sums of two of those angles will equal the sum of the remainding value angle. We say that the third angle is the one raised on the hypotenuse. The formula is:
$$a^2+b^2=c^2$$
The sides of the triangle are similar based to how we work out the lengths of space and time. Because time is a universal invariant, we say that the imaginary time dimension is an invariant relationship.
If we apply this triangle as an invariance of space, we find some interesting results... explanations to why time is relative and why we move so very slow through space, and so very fast through time; or it can be seen that time moves through is very fast - at the speed of light actually.
If you regard time as a dimension of space, you create, according to Minkowski, right triangles with one side adjacent corresponding to time and the other to space. Both legs of the space triangle remain in in ''real space'', whilst in the time triangle, its legs remain in ''imaginary space.''
So long as the imaginary side of the triangle remained longer than the real side, the hypotenuse will have a ''timelike'' order... But if one speeds up, then the traingle becomes warped, and if we where to reach ''c'' then both sides become exactly the same. In this sense, time stops and you aren't really moving at all!
If you exceed this value, then the real leg becomes longer than the imaginary leg, and you are now oscillating through the time dimension. This is what we mean by speeds that are bradynic, photonic or tachyonic. There is a boundary created at ''$$c$$'', and this is highlighted through the spacetime triangle.
Now, it has come to light (mind the pun) on the mass of the electron neutrino $$(Ve)$$, because it is a leading "dark matter" candidate... and we don't know the phsycial properties of dark matter. We have some examples of what some dark matter might be like, such as the axion particle which travels through material objects!
We can create neurtino's from the decay of tritium. The basic underlining rule is through the relativistic realtion between energy and momentum $$E^2 = P^2 + M^2$$... and we work out that it is mass squared that works out the neutrino mass from tritium decay... but this mass squared can be seen in light of either a positive reult or a negative result, and if it is a tachyon, containing a very light weight amount of imaginary matter of about $$i × 12 eV$$, there is the big problem that nothing fuitful will arise out of this... because the theorists do not believe its qualities would be observable or known.
But, i assume, that if we could harvest neutron energy, and also assuming that it is made of this imaginary stuff, then it might have profound implications for fuel... It might even produce the first spaceship that can jump into hyperspace!
.... this was from quantum quacks inetersting thread.
I ask a question; if we could make a photon have a rest mass (such as an interaction between a tachyon and a photon *), could the photon be perturbed into mass upon aloof interactions? (1)
I question this because of the following known (albiet, maybe, not very well-known) formulations of tachyonic existences and observable and measurable constituents:
1) Tachyons (root word from tachycardia) would generate Cherenkov radiation in a vacuum.
2) Adding energy to tacyons slowed them down with the velocity of light as the lower bound.
If tachyons are added with real energy (such as a photon), it will slow it down. If the lower limit of the tachyon is the speed of light, then what would happen if interaction between a photon and a tachyon under certain conditions, such as a high energy surrounding which is of real value, inexorably flux the photon into a particle of mass?
(1) Just an essay i wrote on tachyonic matter being possibly found from tritium decay:
Tachyonic Dynamics
We have all heard of the hypothetical particles called tachyons. They have a rest mass M that also has an imaginary value $$(M^2<0)$$. It turns out that $$(E=gM)$$, the observable mass-energy of these light weight particles, becomes ''real'' and ''positive''.
If a particle was able to defy the light-speed barrier so that v was greater than $$c$$ or $$(v>c)$$, then both g and E would become imaginary quantities, because $$\beta$$ would be larger than $$1$$ and $$(1 - \beta 2)$$ would be negative.
When using imaginary concepts, we must use complex numbers... nothing too complex about them, so don't be scared off! We need the calculus in concepts that are imaginary - not quite existing in the realms of the real - but are ''real'' nonetheless... we use it when calculating the imaginary dimension of time, and even concepts beyond ''$$c$$'' - imaginary mass.
-this small paragraph is for the layman, even though i am novice
To understand this better, we must consider the pyhagorean theorem.Complex numbers deal with square roots. Now, you might remember square roots from high school. A number that is multiplied by itself produces the square root - thus, the square root of $$4$$ is $$(2 x 2)$$. The square root of 9 is $$(3 x 3)$$. The square root of 16 is (4 x 4), ect. Note however, that the square root of 1, is (1 x 1). Complex numbers move into the negatives; thus, it helps mathematicians work out the improbable square root of -1, for instance, which is $$i x i = -1$$. The $$i$$ stands for ''imaginary'', and it helps us in calculating numbers that are not in the real world.
Another example is the square root of $$4$$, which is $$(i^2)^2 = -4$$. Quantum Physics and Relativity would be impossibility, without complex numbers, and so would our ability to calculate time as an imaginary dimension of space.
In a standard course of geometry, one will inventually learn the pythagorean theorem. As you will probably know, the theorem applies to length of the right sides of a right triangle.
It is a simple formula, and it tells us that if one was to work of the angles on the sides of the triangle, the sums of two of those angles will equal the sum of the remainding value angle. We say that the third angle is the one raised on the hypotenuse. The formula is:
$$a^2+b^2=c^2$$
The sides of the triangle are similar based to how we work out the lengths of space and time. Because time is a universal invariant, we say that the imaginary time dimension is an invariant relationship.
If we apply this triangle as an invariance of space, we find some interesting results... explanations to why time is relative and why we move so very slow through space, and so very fast through time; or it can be seen that time moves through is very fast - at the speed of light actually.
If you regard time as a dimension of space, you create, according to Minkowski, right triangles with one side adjacent corresponding to time and the other to space. Both legs of the space triangle remain in in ''real space'', whilst in the time triangle, its legs remain in ''imaginary space.''
So long as the imaginary side of the triangle remained longer than the real side, the hypotenuse will have a ''timelike'' order... But if one speeds up, then the traingle becomes warped, and if we where to reach ''c'' then both sides become exactly the same. In this sense, time stops and you aren't really moving at all!
If you exceed this value, then the real leg becomes longer than the imaginary leg, and you are now oscillating through the time dimension. This is what we mean by speeds that are bradynic, photonic or tachyonic. There is a boundary created at ''$$c$$'', and this is highlighted through the spacetime triangle.
Now, it has come to light (mind the pun) on the mass of the electron neutrino $$(Ve)$$, because it is a leading "dark matter" candidate... and we don't know the phsycial properties of dark matter. We have some examples of what some dark matter might be like, such as the axion particle which travels through material objects!
We can create neurtino's from the decay of tritium. The basic underlining rule is through the relativistic realtion between energy and momentum $$E^2 = P^2 + M^2$$... and we work out that it is mass squared that works out the neutrino mass from tritium decay... but this mass squared can be seen in light of either a positive reult or a negative result, and if it is a tachyon, containing a very light weight amount of imaginary matter of about $$i × 12 eV$$, there is the big problem that nothing fuitful will arise out of this... because the theorists do not believe its qualities would be observable or known.
But, i assume, that if we could harvest neutron energy, and also assuming that it is made of this imaginary stuff, then it might have profound implications for fuel... It might even produce the first spaceship that can jump into hyperspace!
