Help, I am trying to find someone who can help me with the following, as I am a simple chap who is struggling with a question: here go's (sorry If I bore anyone)
The speed of Light is a key element of the e=mc2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends. But is light not the visible element of energy. Nothing can be destroyed only converted from one form of energy to another, therefore is light not simply a visible form of energy. If there is no light, time still continues to past, we still age, etc etc. therefore should the theory no be
E=mass x speed of (energy) squared? all forms of energy must emit some form of light?in whatever spectrum...remove light no time.
This is bugging me , can enyone explain what I am obviously missing.
thanks
QUOTE (simonrach+Nov 15 2007, 06:23 PM)
Help, I am trying to find someone who can help me with the following, as I am a simple chap who is struggling with a question: here go's (sorry If I bore anyone)
The speed of Light is a key element of the e=mc2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends. But is light not the visible element of energy. Nothing can be destroyed only converted from one form of energy to another, therefore is light not simply a visible form of energy. If there is no light, time still continues to past, we still age, etc etc. therefore should the theory no be
E=mass x speed of (energy) squared? all forms of energy must emit some form of light?in whatever spectrum...remove light no time.
This is bugging me , can enyone explain what I am obviously missing.
thanks
Anyone with a better knowledge of SR, feel free to correct me if I'm wrong, but I think I can help. (I've claimed to be an amateur many times before, and here's my chance to prove it
)
Well first, if all stars were to disappear, time would not stop. There would still be matter left in the form of planets, asteroids, comets, nebulae etc... As long as there is matter, there is time, and space.
I'm not sure exactly what your question is beyond that, but maybe this helps.
In E=mc2, the constant c represents the speed at which a massless particle moves through space. This equation shows the relation between mass and energy by correctly determining the amount of energy released (in joules) by multiplying the object's mass (in kilograms) by the constant c (in meters per second, so c in this case is 299,792,458.)
Mass-energy equivalence
For instance, in a proton/anti proton annihilation, we use the formula to determine the amount of energy produced.
0.00000000000000000002941272=m (I'm not 100% sure I got this number right, I had to look it up online on the fly)
299,792,458=c
so E=mc2 comes out to
0.00000000000000000002941272(299,792,458x299,792,458)=0.00264348344207359709363808 joules or 9.516540391464949537097088 kilowatt-hours, which in this case is the rest energy of a proton plus the rest energy of an anti proton. In comparison, the average home uses (I think, I live in Florida, so this may be a bit high) about 1900 kilowatt-hours per month.
Before anyone gets any free energy ideas; Yes, we can produce antimatter. No it will not make a good power source. Why? Because we use up more power producing the antimatter than it would release when annihilated.
Antimatter as fuel
So how'd I do? Maybe not up to the standards of some people on this site, but I like to think I do know a little thing or two.
The speed of Light is a key element of the e=mc2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends. But is light not the visible element of energy. Nothing can be destroyed only converted from one form of energy to another, therefore is light not simply a visible form of energy. If there is no light, time still continues to past, we still age, etc etc. therefore should the theory no be
E=mass x speed of (energy) squared? all forms of energy must emit some form of light?in whatever spectrum...remove light no time.
This is bugging me , can enyone explain what I am obviously missing.
thanks
Anyone with a better knowledge of SR, feel free to correct me if I'm wrong, but I think I can help. (I've claimed to be an amateur many times before, and here's my chance to prove it
)Well first, if all stars were to disappear, time would not stop. There would still be matter left in the form of planets, asteroids, comets, nebulae etc... As long as there is matter, there is time, and space.
I'm not sure exactly what your question is beyond that, but maybe this helps.
In E=mc2, the constant c represents the speed at which a massless particle moves through space. This equation shows the relation between mass and energy by correctly determining the amount of energy released (in joules) by multiplying the object's mass (in kilograms) by the constant c (in meters per second, so c in this case is 299,792,458.)
Mass-energy equivalence
For instance, in a proton/anti proton annihilation, we use the formula to determine the amount of energy produced.
0.00000000000000000002941272=m (I'm not 100% sure I got this number right, I had to look it up online on the fly)
299,792,458=c
so E=mc2 comes out to
0.00000000000000000002941272(299,792,458x299,792,458)=0.00264348344207359709363808 joules or 9.516540391464949537097088 kilowatt-hours, which in this case is the rest energy of a proton plus the rest energy of an anti proton. In comparison, the average home uses (I think, I live in Florida, so this may be a bit high) about 1900 kilowatt-hours per month.
Before anyone gets any free energy ideas; Yes, we can produce antimatter. No it will not make a good power source. Why? Because we use up more power producing the antimatter than it would release when annihilated.
Antimatter as fuel
So how'd I do? Maybe not up to the standards of some people on this site, but I like to think I do know a little thing or two.
Good answer, that does help, this issue was blocking me from understanding this field and while it was I suppose a simple question, it was preventing me from comprehending(if this is possible) the theory and and its relativity (pun unintentional) and impact. Thanks very much for the explaination.
QUOTE (simonrach+Nov 16 2007, 03:23 PM)
Good answer, that does help, this issue was blocking me from understanding this field and while it was I suppose a simple question, it was preventing me from comprehending(if this is possible) the theory and and its relativity (pun unintentional) and impact. Thanks very much for the explaination.
I'm glad I could help, however, I must in all conscience advise you to wait for someone like BenTheMan, AlphaNumeric, Euler, Dallas or NeoDevin to contribute before running with what I've told you. I have no education in physics beyond a reading of pop-science books and what people such as they have explained to me. My answer may be 100% correct, but I cannot guarantee that it is.
Good luck to you
I'm glad I could help, however, I must in all conscience advise you to wait for someone like BenTheMan, AlphaNumeric, Euler, Dallas or NeoDevin to contribute before running with what I've told you. I have no education in physics beyond a reading of pop-science books and what people such as they have explained to me. My answer may be 100% correct, but I cannot guarantee that it is.
Good luck to you
hello simonrach. here is another point of view
i do not think the progression of
i do not think the progression of
QUOTE
Posted on Nov 16 2007, 09:23 AM e=mc2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends
is sound. the c in e=mc2 is a physical constant and a physical limit of velocity that acts as a conversion factor. if all stars, or more to your point, if all photons ceased to exist, c would still exist as a physical constant and as a physical limit of velocity. QUOTE (->
| QUOTE |
| Posted on Nov 16 2007, 09:23 AM e=mc2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends |
is sound. the c in e=mc2 is a physical constant and a physical limit of velocity that acts as a conversion factor. if all stars, or more to your point, if all photons ceased to exist, c would still exist as a physical constant and as a physical limit of velocity.
all forms of energy must emit some form of light?
all forms of energy must emit some form of light?
have you thought about gravitational energy ?
QUOTE
remove light no time.
one interpretation of time relies on motion. about one-third down the page the two rows of dominoes analogy http://www.ws5.com/spacetime/ if there were no light, motion of the moon around the earth, for example, would still require a 4th dimension i.e. time, to describe the changing distance between the earth and the moon.
QUOTE (simonrach+Nov 16 2007, 11:23 AM)
therefore if light is removed
How?
Sounds like a meaningless question to me.
How?
Sounds like a meaningless question to me.
in Maxwells equations, which describe electromagnetism, the constant c stands for the speed of electromagnetic radiation. It was learned that c is related to magnetic constant μ0 and permittivity of free space ε0 by:
c= 1/sqrt(μ0ε0).
c= 1/sqrt(μ0ε0).
Even if there was no light, the speed of light, c, is a parameter with units of distance over time, which appears to be fundamental in any description about how two observers who are moving with respect to one another describe the relationships between the events they observe.
http://forum.physorg.com/index.php?showtop...ndpost&p=246365
I reproduce this to spare you the pain of reading the nearby posts.
On Time Dilation (corrected and updated)
Time Dilation, as was shown shortly after Einstein's 1905 papers, is a natural result which arises from testable intuitive statements of the nature of space and time and physics.
First of all, assuming God doesn't write a physics textbook, man will be forever ignorant of the actual mechanisms of the universe. Even if Professor Y comes up with the mechanistic ONE TRUE THEORY OF EVERYTHING, there will be no way to distinguish the universe of the mechanistic theory from another universe where everything conspires to act just like Y's mechanistic model. That's why physicists (as opposed to philosophers) use mathematical models to avoid talking about the mechanism and only the behavior. Our everyday experience of the universe has taught us a lot of everyday assumptions. The following 4 should be non-controversial when you neglect gravity. They are all statements about observed symmetries of the universe -- so all of them are falsifiable if you found a counter-example.
Four everyday assumptions
Let us assume the laws of physics are translationally invariant in space. Then it follows a statement about a experiment happening in an arbitrary place will work the same if we center our coordinate basis with it. This also implies that we can calculate what's happening in an arbitrary place and apply a translation transform to it, and the physics is the same.
x' = x + T_x ; y' = y + T_y ; z' = z + T_z ;
Let us assume the laws of physics are translationally invariant in time. Then it follows a statement about a experiment happening in an arbitrary time will work the same if we center our basis of "now" with it. This also implies that we can calculate what's happening in an arbitrary time and apply a translation transform to it, and the physics is the same.
t' = t + T_t ;
Let us assume the laws of physics are rotationally invariant. Then it follows a statement about a experiment oriented in an arbitrary direction will work the same if rotate our coordinate basis to be aligned with it. This also implies that we can calculate what's happening in an arbitrary aligned experiment and apply a rotation transform to it, and the physics is the same.
x' = R_xx x + R_xy y + R_xz z ;
y' = R_yx x + R_yy y + R_yz z ;
z' = R_zx x + R_zy y + R_zz z ; Where R is a proper orthogonal matrix, which can be parameterized in various ways by 3 rotation angles.
Let us assume the laws of physics are invariant with respect to inertial frame. Then it follows a statement about a experiment with a freely moving center of mass moving in an arbitrary direction will work the same if set up our coordinate basis to be co-moving with it with it. But clearly any corresponding change-of-frame transform must tie velocity, time and space together. Since we already assumed we are rotationally invariant and translationally invariant, let us work with v in the x direction and just coordinate differences.
Δx' = F_xx Δx + F_xy Δy + F_xz Δz + F_xt Δt + F_x1 ;
Δy' = F_yx Δx + F_yy Δy + F_yz Δz + F_yt Δt + F_y1 ;
Δz' = F_zx Δx + F_zy Δy + F_zz Δz + F_zt Δt + F_z1 ;
Δt' = F_tx Δx + F_ty Δy + F_tz Δz + F_tt Δt + F_t1 ;
where F is a function of v, which we have agreed to consider in the x direction.
Limiting the form of the velocity transform
Since it makes no sense to talk about (Δx,Δy,Δz,Δt) = (0,0,0,0) which says that the two events happened in the same time and place in one frame transforming into other than (0,0,0,0) in the primed frame, it follows that (F_x1, F_y1, F_z1, F_t1) = (0,0,0,0). Thus F(v) represents a homogeneous transform.
If you think you know of a reason why a v in the x direction should involve displacements in the y or z direction, please let me know. I think that the rotational invariance we assumed earlier means that if v is in the +x direction, then it cannot have a reason to prefer +y or -y, and so the effect on y must be zero, and vice-versa, and the same for z.
Then F_yy = F_zz = 1 and F_xy = F_xz = F_yx = F_yz = F_yt = F_zx = F_zy = F_zt = F_ty = F_tz = 0. So we are over half done.
Δx' = F_xx Δx + F_xt Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= F_tx Δx + F_tt Δt ;
Since two events one frame which don't move at all have Δx = 0, but in the other frame Δx'/Δt' = v, then F_xt = v F_tt. Since if two events in one frame are connected by a particle moving at speed -v, and not moving in the other frame then Δx = -v Δt => Δx' = 0 = -F_xx v Δt + F_xt Δt => F_xt = v F_xx => F_xx = F_tt. Let's call that A(v).
Δx' = A(v) Δx + v A(v) Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= F_tx Δx + A(v) Δt ;
For the same reason that length-contraction must be in the direction of movement, we expect two observers to experience the same relative time dilation. Since there are no preferred directions, then nothing but convention distinguished -x from +x and so nothing distinguished -v from +v and so we expect that the time dilation to be the same for two observers in relative motion, if there is any time dilation.
Consider a motionless clock. Two tick of the clock are separated by Δt, but Δx = 0.
so Δt' = A(v) Δt . Now let's move the clock at -v so it is motionless for Δx' = 0. So we want to solve Δt = A(v) Δt', Δx = - v Δt, and Δt'= F_tx Δx + A(v) Δt
So Δx = - v A(v) Δt', Δt' = F_tx Δx + A(v) A(v) Δt' and so
Δt' = - v F_tx A(v) Δt' + A(v) A(v) Δt' and so
F_tx = ( A(v)A(v) - 1 ) / ( v A(v) ) = (1/v) ( A(v) - 1/A(v))
Δx' = A(v) Δx + v A(v) Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= (1/v) ( A(v) - 1/A(v)) Δx + A(v) Δt ;
At this point both the Newtonian and the Relativist should be happy. The Newtonian assumes that A(v) is a constant with value 1, while the Relativist sees that our four initial assumptions do not yet force that choice. A(v), based on our four assumptions, is just a number and may yet turn out to be a non-constant function of v.
http://www.courses.fas.harvard.edu/~phys16..._appendices.pdf
Working with the velocity transformation
Now with translations or rotations, they form a group. (A group is a mathematical way of talking about symmetries.) So that if you apply T1 and then T2, you get T3 which is also in the form of a translations. (Same for rotations.) This should be the same for two transforms related to velocity.
Δx' = A(v1) Δx + v1 A(v1) Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= (1/v1) ( A(v1) - 1/A(v1)) Δx + A(v1) Δt ;
Δx'' = A(v2) Δx' + v2 A(v2) Δt' ;
Δy'' = Δy' ;
Δz'' = Δz' ;
Δt''= (1/v2) ( A(v2) - 1/A(v2)) Δx' + A(v2) Δt' ;
Δx'' = A(v3) Δx + v3 A(v3) Δt = A(v2) (A(v1) Δx + v1 A(v1) Δt ) + v2 A(v2) ( (1/v1) ( A(v1) - 1/A(v1)) Δx + A(v1) Δt ) ;
Δy'' = Δy ;
Δz'' = Δz ;
Δt''= (1/v3) ( A(v3) - 1/A(v3)) Δx + A(v3) Δt = (1/v2) ( A(v2) - 1/A(v2)) (A(v1) Δx + v1 A(v1) Δt ) + A(v2) ( (1/v1) ( A(v1) - 1/A(v1)) Δx + A(v1) Δt ) ;
When we equate our expressions of the double-primed coordinates in terms of the unprimed coordinates, we have the following relations in v and A(v):
A(v3) = A(v2) A(v1) + (v2/v1) A(v2) A(v1) - (v2/v1) A(v2)/A(v1) = A(v3) = (v1/v2) A(v1) A(v2) - (v1/v2) A(v1)/A(v2) + A(v2) A(v1) ;
or
(v2/v1) A(v2) A(v1) - (v2/v1) A(v2)/A(v1) = (v1/v2) A(v1) A(v2) - (v1/v2) A(v1)/A(v2) ;
or
(v2 v1/v1²) A(v2) A(v1) - (v2 v1/v1²) A(v2) A(v1) / A(v1)² = (v1 v2 /v2²) A(v1) A(v2) - (v1 v2/v2²) A(v1) A(v2)/ A(v2)² ;
or, for generic v1 and v2,
(1/v1²) (1 - 1 / A(v1)² ) = (1/v2²) ( 1 - 1 / A(v2)² ) ;
But since this is true for any v, then there is some constant K = (1/(v²)) (1 - 1 / ( A(v)² ) ) for all v. This means A can be written in the form A(v) = 1/√(1 - K v²) ; Using the binomial theorem, we can show that when K v² << 1, A(v) is approximately: 1 + 1/2 K v² + 3/8 (K v²)² + 5/16 (K v²)^3 + 35/128 (K v²)^4 + 63/256 (K v²)^5 + 231/1024 (K v²)^6 + ... ; so the Newtonian will always appear correct as long as |v| is "small," or K << 1/v².
Only at high speed would there be evidence that K is not zero. (If K is zero, then A(v) = 1, just like the Newtonian assumed.)
http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf
http://arxiv.org/abs/physics/0302045
The generic velocity addition law
From equation 2 we see something that with a little algebraic reworking can become our velocity addition law from our four assumptions.
v3 A(v3) = (v2 + v1) A(v2) A(v1) ;
or
v3 / √(1 - K v3²) = (v2 + v1)/( √(1 - K v2²) √(1 - K v1²) ) ;
or
v3² /(1 - K v3²) = (v2 + v1)²/( (1 - K v2²) (1 - K v1²) ) ;
or
v3² = [ (v2 + v1)²/( (1 - K v2²) (1 - K v1²) ) ] [ ( (1 - K v2²) (1 - K v1²) ) / ( K(v2 + v1)² + (1 - K v2²) (1 - K v1²) ) ]
or
v3² = (v2 + v1)² / ( K (v2 + v1)² + (1 - K v2²) (1 - K v1²) ) ;
or
v3² = (v1 + v2)² / ( K v2 ² + 2 K v1 v2 + K v1² + 1 - K v2² - K v1² + K² v1² v2² ) ;
or
v3² = (v1 + v2)² / ( 1 + 2 K v1 v2 + K² v1² v2² ) ;
or
v3 = (v1 + v2) / ( 1 + K v1 v2 ) ;
Clearly if K is measured to be zero, then A(v) = 1 and there is no time dilation. However the results of an 1859 experiment (among thousands of others) are inconsistent with K = 0.
Fresnel and Fizeau's measured value of K
In the discredited dragged-ether theory of Fresnel, light is "slowed" and "dragged" by a transparent dielectric with dielectric constant n. It is slowed to V=c/n, but if the medium is moving at speed v, it is dragged and the measured speed is about U = c/n + v(1 - 1/n²). The amount of "ether dragging" by a moving dielectric is measured as the unexplained Frensel drag coefficient, 1 - 1/n². The result eventually help caused the downfall of the dragged-ether model, for where a physical medium can support a wide variety of waves, the phenomenon of dispersion shows that n is a function of wavelength, and so the Fresnel drag coefficient must also be a function of wavelength, and so there must be a different ether to drag for every wavelength of light.
But let's just take V=c/n the experimental velocity of light in stationary medium, and apply our generic velocity addition law to it and see how it predicts an observer moving relative to the medium measure its speed at.
v3 = (v1 + v2) / ( 1 + K v1 v2 ) = (v + V) / ( 1 + K v V ) = (v + c/n) / ( 1 + K v c/n )
if we assume K v c/n << 1, then we can use the binomial theorem to approximate v3 as (v + c/n) - (K v c/n) (v + c/n) + (K v c/n)² (v + c/n) + ...
= c/n + v - K v² c/n - K v c²/n² + K² v^3 c²/n² + K² v² c^3/n^3 ... or, if you drop the terms which aren't linear in v, v3 = c/n + v (1 - K c²/n²)
If v3 is close to the observed value U, then K c² = 1, or K = 1/c²
http://en.wikipedia.org/wiki/Aether_drag_hypothesis
http://en.wikipedia.org/wiki/Fizeau_experiment
Epilogue
This was written for Bryn, who hasn't explained why he doesn't believe in time dilation. It was written to show that time dilation, by which I mean that observers who differ in velocity must have A(v) different than 1, is the only physical result if you accept the four assumptions. The other consequences of this idea have been well-developed. K is very close to zero in ordinary units, but we have thousands of experimental results which suggest that it is much closer to 1/c² than to zero.
For simonrach, this should show that if the four assumptions are good, then even experiments not involving light will show that c is an physically important speed in our universe. Further E = m_0 A(v) c² gives us E = m_0 c² + 1/2 m_0 v² + ... which has been used to relate Newton's approximate formula for kinetic energy to Einstein's Relativity.
http://relativity.livingreviews.org/Articl...05-5/index.html
According to http://arxiv.org/abs/0708.0929 people have shown this to be true with various degrees of rigor since at least 1910.
W. A. von Ignatowsky, “Einige allgemeine Bemerkungen zum Relativitatsprinzip,” Phys. Z. 11, 972-976 (1910).
Following Einstein, Minkowski (1908) showed that algebraically this was the same as saying space and time were not separate things, which is how all physicists work today. Both Length contraction and time dilation arise from treating space and time as separate things with separate meanings, which is the Newtonian and intuitionist view. In Minkowski space-time, these are trivial (boring!) effects.
http://forum.physorg.com/index.php?showtop...ndpost&p=246365
I reproduce this to spare you the pain of reading the nearby posts.
On Time Dilation (corrected and updated)
Time Dilation, as was shown shortly after Einstein's 1905 papers, is a natural result which arises from testable intuitive statements of the nature of space and time and physics.
First of all, assuming God doesn't write a physics textbook, man will be forever ignorant of the actual mechanisms of the universe. Even if Professor Y comes up with the mechanistic ONE TRUE THEORY OF EVERYTHING, there will be no way to distinguish the universe of the mechanistic theory from another universe where everything conspires to act just like Y's mechanistic model. That's why physicists (as opposed to philosophers) use mathematical models to avoid talking about the mechanism and only the behavior. Our everyday experience of the universe has taught us a lot of everyday assumptions. The following 4 should be non-controversial when you neglect gravity. They are all statements about observed symmetries of the universe -- so all of them are falsifiable if you found a counter-example.
Four everyday assumptions
Let us assume the laws of physics are translationally invariant in space. Then it follows a statement about a experiment happening in an arbitrary place will work the same if we center our coordinate basis with it. This also implies that we can calculate what's happening in an arbitrary place and apply a translation transform to it, and the physics is the same.
x' = x + T_x ; y' = y + T_y ; z' = z + T_z ;
Let us assume the laws of physics are translationally invariant in time. Then it follows a statement about a experiment happening in an arbitrary time will work the same if we center our basis of "now" with it. This also implies that we can calculate what's happening in an arbitrary time and apply a translation transform to it, and the physics is the same.
t' = t + T_t ;
Let us assume the laws of physics are rotationally invariant. Then it follows a statement about a experiment oriented in an arbitrary direction will work the same if rotate our coordinate basis to be aligned with it. This also implies that we can calculate what's happening in an arbitrary aligned experiment and apply a rotation transform to it, and the physics is the same.
x' = R_xx x + R_xy y + R_xz z ;
y' = R_yx x + R_yy y + R_yz z ;
z' = R_zx x + R_zy y + R_zz z ; Where R is a proper orthogonal matrix, which can be parameterized in various ways by 3 rotation angles.
Let us assume the laws of physics are invariant with respect to inertial frame. Then it follows a statement about a experiment with a freely moving center of mass moving in an arbitrary direction will work the same if set up our coordinate basis to be co-moving with it with it. But clearly any corresponding change-of-frame transform must tie velocity, time and space together. Since we already assumed we are rotationally invariant and translationally invariant, let us work with v in the x direction and just coordinate differences.
Δx' = F_xx Δx + F_xy Δy + F_xz Δz + F_xt Δt + F_x1 ;
Δy' = F_yx Δx + F_yy Δy + F_yz Δz + F_yt Δt + F_y1 ;
Δz' = F_zx Δx + F_zy Δy + F_zz Δz + F_zt Δt + F_z1 ;
Δt' = F_tx Δx + F_ty Δy + F_tz Δz + F_tt Δt + F_t1 ;
where F is a function of v, which we have agreed to consider in the x direction.
Limiting the form of the velocity transform
Since it makes no sense to talk about (Δx,Δy,Δz,Δt) = (0,0,0,0) which says that the two events happened in the same time and place in one frame transforming into other than (0,0,0,0) in the primed frame, it follows that (F_x1, F_y1, F_z1, F_t1) = (0,0,0,0). Thus F(v) represents a homogeneous transform.
If you think you know of a reason why a v in the x direction should involve displacements in the y or z direction, please let me know. I think that the rotational invariance we assumed earlier means that if v is in the +x direction, then it cannot have a reason to prefer +y or -y, and so the effect on y must be zero, and vice-versa, and the same for z.
Then F_yy = F_zz = 1 and F_xy = F_xz = F_yx = F_yz = F_yt = F_zx = F_zy = F_zt = F_ty = F_tz = 0. So we are over half done.
Δx' = F_xx Δx + F_xt Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= F_tx Δx + F_tt Δt ;
Since two events one frame which don't move at all have Δx = 0, but in the other frame Δx'/Δt' = v, then F_xt = v F_tt. Since if two events in one frame are connected by a particle moving at speed -v, and not moving in the other frame then Δx = -v Δt => Δx' = 0 = -F_xx v Δt + F_xt Δt => F_xt = v F_xx => F_xx = F_tt. Let's call that A(v).
Δx' = A(v) Δx + v A(v) Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= F_tx Δx + A(v) Δt ;
For the same reason that length-contraction must be in the direction of movement, we expect two observers to experience the same relative time dilation. Since there are no preferred directions, then nothing but convention distinguished -x from +x and so nothing distinguished -v from +v and so we expect that the time dilation to be the same for two observers in relative motion, if there is any time dilation.
Consider a motionless clock. Two tick of the clock are separated by Δt, but Δx = 0.
so Δt' = A(v) Δt . Now let's move the clock at -v so it is motionless for Δx' = 0. So we want to solve Δt = A(v) Δt', Δx = - v Δt, and Δt'= F_tx Δx + A(v) Δt
So Δx = - v A(v) Δt', Δt' = F_tx Δx + A(v) A(v) Δt' and so
Δt' = - v F_tx A(v) Δt' + A(v) A(v) Δt' and so
F_tx = ( A(v)A(v) - 1 ) / ( v A(v) ) = (1/v) ( A(v) - 1/A(v))
Δx' = A(v) Δx + v A(v) Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= (1/v) ( A(v) - 1/A(v)) Δx + A(v) Δt ;
At this point both the Newtonian and the Relativist should be happy. The Newtonian assumes that A(v) is a constant with value 1, while the Relativist sees that our four initial assumptions do not yet force that choice. A(v), based on our four assumptions, is just a number and may yet turn out to be a non-constant function of v.
http://www.courses.fas.harvard.edu/~phys16..._appendices.pdf
Working with the velocity transformation
Now with translations or rotations, they form a group. (A group is a mathematical way of talking about symmetries.) So that if you apply T1 and then T2, you get T3 which is also in the form of a translations. (Same for rotations.) This should be the same for two transforms related to velocity.
Δx' = A(v1) Δx + v1 A(v1) Δt ;
Δy' = Δy ;
Δz' = Δz ;
Δt'= (1/v1) ( A(v1) - 1/A(v1)) Δx + A(v1) Δt ;
Δx'' = A(v2) Δx' + v2 A(v2) Δt' ;
Δy'' = Δy' ;
Δz'' = Δz' ;
Δt''= (1/v2) ( A(v2) - 1/A(v2)) Δx' + A(v2) Δt' ;
Δx'' = A(v3) Δx + v3 A(v3) Δt = A(v2) (A(v1) Δx + v1 A(v1) Δt ) + v2 A(v2) ( (1/v1) ( A(v1) - 1/A(v1)) Δx + A(v1) Δt ) ;
Δy'' = Δy ;
Δz'' = Δz ;
Δt''= (1/v3) ( A(v3) - 1/A(v3)) Δx + A(v3) Δt = (1/v2) ( A(v2) - 1/A(v2)) (A(v1) Δx + v1 A(v1) Δt ) + A(v2) ( (1/v1) ( A(v1) - 1/A(v1)) Δx + A(v1) Δt ) ;
When we equate our expressions of the double-primed coordinates in terms of the unprimed coordinates, we have the following relations in v and A(v):
- A(v3) = A(v2) A(v1) + (v2/v1) A(v2) A(v1) - (v2/v1) A(v2)/A(v1) ;
- v3 A(v3) = A(v2) v1 A(v1) + v2 A(v2) A(v1) = (v2 + v1) A(v2) A(v1) ;
- (1/v3) ( A(v3) - 1/A(v3)) = (1/v2) ( A(v2) - 1/A(v2)) A(v1) + A(v2) (1/v1) ( A(v1) - 1/A(v1)) ;
- A(v3) = (v1/v2) A(v1) A(v2) - (v1/v2) A(v1)/A(v2) + A(v2) A(v1) ;
A(v3) = A(v2) A(v1) + (v2/v1) A(v2) A(v1) - (v2/v1) A(v2)/A(v1) = A(v3) = (v1/v2) A(v1) A(v2) - (v1/v2) A(v1)/A(v2) + A(v2) A(v1) ;
or
(v2/v1) A(v2) A(v1) - (v2/v1) A(v2)/A(v1) = (v1/v2) A(v1) A(v2) - (v1/v2) A(v1)/A(v2) ;
or
(v2 v1/v1²) A(v2) A(v1) - (v2 v1/v1²) A(v2) A(v1) / A(v1)² = (v1 v2 /v2²) A(v1) A(v2) - (v1 v2/v2²) A(v1) A(v2)/ A(v2)² ;
or, for generic v1 and v2,
(1/v1²) (1 - 1 / A(v1)² ) = (1/v2²) ( 1 - 1 / A(v2)² ) ;
But since this is true for any v, then there is some constant K = (1/(v²)) (1 - 1 / ( A(v)² ) ) for all v. This means A can be written in the form A(v) = 1/√(1 - K v²) ; Using the binomial theorem, we can show that when K v² << 1, A(v) is approximately: 1 + 1/2 K v² + 3/8 (K v²)² + 5/16 (K v²)^3 + 35/128 (K v²)^4 + 63/256 (K v²)^5 + 231/1024 (K v²)^6 + ... ; so the Newtonian will always appear correct as long as |v| is "small," or K << 1/v².
Only at high speed would there be evidence that K is not zero. (If K is zero, then A(v) = 1, just like the Newtonian assumed.)
http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf
http://arxiv.org/abs/physics/0302045
The generic velocity addition law
From equation 2 we see something that with a little algebraic reworking can become our velocity addition law from our four assumptions.
v3 A(v3) = (v2 + v1) A(v2) A(v1) ;
or
v3 / √(1 - K v3²) = (v2 + v1)/( √(1 - K v2²) √(1 - K v1²) ) ;
or
v3² /(1 - K v3²) = (v2 + v1)²/( (1 - K v2²) (1 - K v1²) ) ;
or
v3² = [ (v2 + v1)²/( (1 - K v2²) (1 - K v1²) ) ] [ ( (1 - K v2²) (1 - K v1²) ) / ( K(v2 + v1)² + (1 - K v2²) (1 - K v1²) ) ]
or
v3² = (v2 + v1)² / ( K (v2 + v1)² + (1 - K v2²) (1 - K v1²) ) ;
or
v3² = (v1 + v2)² / ( K v2 ² + 2 K v1 v2 + K v1² + 1 - K v2² - K v1² + K² v1² v2² ) ;
or
v3² = (v1 + v2)² / ( 1 + 2 K v1 v2 + K² v1² v2² ) ;
or
v3 = (v1 + v2) / ( 1 + K v1 v2 ) ;
Clearly if K is measured to be zero, then A(v) = 1 and there is no time dilation. However the results of an 1859 experiment (among thousands of others) are inconsistent with K = 0.
Fresnel and Fizeau's measured value of K
In the discredited dragged-ether theory of Fresnel, light is "slowed" and "dragged" by a transparent dielectric with dielectric constant n. It is slowed to V=c/n, but if the medium is moving at speed v, it is dragged and the measured speed is about U = c/n + v(1 - 1/n²). The amount of "ether dragging" by a moving dielectric is measured as the unexplained Frensel drag coefficient, 1 - 1/n². The result eventually help caused the downfall of the dragged-ether model, for where a physical medium can support a wide variety of waves, the phenomenon of dispersion shows that n is a function of wavelength, and so the Fresnel drag coefficient must also be a function of wavelength, and so there must be a different ether to drag for every wavelength of light.
But let's just take V=c/n the experimental velocity of light in stationary medium, and apply our generic velocity addition law to it and see how it predicts an observer moving relative to the medium measure its speed at.
v3 = (v1 + v2) / ( 1 + K v1 v2 ) = (v + V) / ( 1 + K v V ) = (v + c/n) / ( 1 + K v c/n )
if we assume K v c/n << 1, then we can use the binomial theorem to approximate v3 as (v + c/n) - (K v c/n) (v + c/n) + (K v c/n)² (v + c/n) + ...
= c/n + v - K v² c/n - K v c²/n² + K² v^3 c²/n² + K² v² c^3/n^3 ... or, if you drop the terms which aren't linear in v, v3 = c/n + v (1 - K c²/n²)
If v3 is close to the observed value U, then K c² = 1, or K = 1/c²
http://en.wikipedia.org/wiki/Aether_drag_hypothesis
http://en.wikipedia.org/wiki/Fizeau_experiment
Epilogue
This was written for Bryn, who hasn't explained why he doesn't believe in time dilation. It was written to show that time dilation, by which I mean that observers who differ in velocity must have A(v) different than 1, is the only physical result if you accept the four assumptions. The other consequences of this idea have been well-developed. K is very close to zero in ordinary units, but we have thousands of experimental results which suggest that it is much closer to 1/c² than to zero.
For simonrach, this should show that if the four assumptions are good, then even experiments not involving light will show that c is an physically important speed in our universe. Further E = m_0 A(v) c² gives us E = m_0 c² + 1/2 m_0 v² + ... which has been used to relate Newton's approximate formula for kinetic energy to Einstein's Relativity.
http://relativity.livingreviews.org/Articl...05-5/index.html
According to http://arxiv.org/abs/0708.0929 people have shown this to be true with various degrees of rigor since at least 1910.
W. A. von Ignatowsky, “Einige allgemeine Bemerkungen zum Relativitatsprinzip,” Phys. Z. 11, 972-976 (1910).
Following Einstein, Minkowski (1908) showed that algebraically this was the same as saying space and time were not separate things, which is how all physicists work today. Both Length contraction and time dilation arise from treating space and time as separate things with separate meanings, which is the Newtonian and intuitionist view. In Minkowski space-time, these are trivial (boring!) effects.
QUOTE (simonrach+Nov 15 2007, 11:23 PM)
Help, I am trying to find someone who can help me with the following, as I am a simple chap who is struggling with a question: here go's (sorry If I bore anyone)
The speed of Light is a key element of the e=mc2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends. But is light not the visible element of energy. Nothing can be destroyed only converted from one form of energy to another, therefore is light not simply a visible form of energy. If there is no light, time still continues to past, we still age, etc etc. therefore should the theory no be
E=mass x speed of (energy) squared? all forms of energy must emit some form of light?in whatever spectrum...remove light no time.
This is bugging me , can enyone explain what I am obviously missing.
thanks
"During any wave interference the shape of the medium is determined by the sum of the separate amplitudes of each wave. We often say that when waves interfere, amplitudes add. During destructive interference, since the positive amplitudes from one crest are added to the negative amplitudes from the other trough, this addition can look like a subtraction."
- footnote Internet go ogle
This is the cause of relativity, it is the cause of relative time and space- a wave synchronization of emitted gravitational waves from all matter. Time, space and wave synchronization are three actions of the fundamental laws of nature. All matter has both individual absolute clocks and relative clocks. Think of how sound waves are both absolute and relative. Absolute for the object originating the constant wave and relative for the speeding observer because the frequency changes to to movement relative to the stationary originate of the sound. As sound is a function of a point of origin, mass to energy transfer into a sound wave, Time and space are functions of a point of origin, mass to energy transfer into a gravitational wave. It is wave synchronization then that takes over and is running the entire show! This is the cause of relativity- Matter does not warp time and space, matter creates time and space via the gravitational wave and it is the gravitational waves interference patterns that synchronize which is responsible for running everything from gravity to the acceleration increasing in the universe as it is flattening. F=ma F- CONSTANT, M- DECREASING, A- INCREASING
- C. M. T.
The speed of Light is a key element of the e=mc2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends. But is light not the visible element of energy. Nothing can be destroyed only converted from one form of energy to another, therefore is light not simply a visible form of energy. If there is no light, time still continues to past, we still age, etc etc. therefore should the theory no be
E=mass x speed of (energy) squared? all forms of energy must emit some form of light?in whatever spectrum...remove light no time.
This is bugging me , can enyone explain what I am obviously missing.
thanks
"During any wave interference the shape of the medium is determined by the sum of the separate amplitudes of each wave. We often say that when waves interfere, amplitudes add. During destructive interference, since the positive amplitudes from one crest are added to the negative amplitudes from the other trough, this addition can look like a subtraction."
- footnote Internet go ogle
This is the cause of relativity, it is the cause of relative time and space- a wave synchronization of emitted gravitational waves from all matter. Time, space and wave synchronization are three actions of the fundamental laws of nature. All matter has both individual absolute clocks and relative clocks. Think of how sound waves are both absolute and relative. Absolute for the object originating the constant wave and relative for the speeding observer because the frequency changes to to movement relative to the stationary originate of the sound. As sound is a function of a point of origin, mass to energy transfer into a sound wave, Time and space are functions of a point of origin, mass to energy transfer into a gravitational wave. It is wave synchronization then that takes over and is running the entire show! This is the cause of relativity- Matter does not warp time and space, matter creates time and space via the gravitational wave and it is the gravitational waves interference patterns that synchronize which is responsible for running everything from gravity to the acceleration increasing in the universe as it is flattening. F=ma F- CONSTANT, M- DECREASING, A- INCREASING
- C. M. T.
QUOTE (insight+Dec 16 2007, 09:12 AM)
"During any wave interference the shape of the medium is determined by the sum of the separate amplitudes of each wave. We often say that when waves interfere, amplitudes add. During destructive interference, since the positive amplitudes from one crest are added to the negative amplitudes from the other trough, this addition can look like a subtraction."
- footnote Internet go ogle
This is the cause of relativity, it is the cause of relative time and space... and so on and so forth...
No, it isn't. Do you want me to email you einstein's pop-science work on relativity?
- footnote Internet go ogle
This is the cause of relativity, it is the cause of relative time and space... and so on and so forth...
No, it isn't. Do you want me to email you einstein's pop-science work on relativity?
QUOTE (simonrach+Nov 15 2007, 11:23 PM)
Help, I am trying to find someone who can help me with the following, as I am a simple chap who is struggling with a question: here go's (sorry If I bore anyone)
The speed of Light is a key element of the e=MC2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends. But is light not the visible element of energy. Nothing can be destroyed only converted from one form of energy to another, therefore is light not simply a visible form of energy. If there is no light, time still continues to past, we still age, etc etc. therefore should the theory no be
E=mass x speed of (energy) squared? all forms of energy must emit some form of light?in whatever spectrum...remove light no time.
This is bugging me , can anyone explain what I am obviously missing.
thanks
All substance, including light (all radiation) has an electromagnetic field.
Future knowledge-
All electromagnetic fields decay into a monopole non binding gravitational wave. The essence of time is the decay rate of all electromagnetic fields into the gravitational wave, not just light. Light, or photons travel with in the gravitational wave blanket of space generated from all matter. The underlying equation is
Potential Energy decay= Kinetic energy formation times the speed of that formation squared. it is the same as area = Pi times r squared where r in this equation is defined as the radius of space formation and pi is defined as change in space and area is a two dimensional area because wave formation is combining and dimensions are decreasing. Time is the rate of the process. It is a simple two dimensional area problem that shows that space is elongating and flattening and the emission and synchronization of gravitational waves actually runs the show of the universe as energy is actually running out through this process. The universe has a beginning, middle, and end. You are in the middle, of the story of the universe.- insight
The speed of Light is a key element of the e=MC2 theory, therefore if light is removed (all the stars cease to exist, go with me here) then time also ends. But is light not the visible element of energy. Nothing can be destroyed only converted from one form of energy to another, therefore is light not simply a visible form of energy. If there is no light, time still continues to past, we still age, etc etc. therefore should the theory no be
E=mass x speed of (energy) squared? all forms of energy must emit some form of light?in whatever spectrum...remove light no time.
This is bugging me , can anyone explain what I am obviously missing.
thanks
All substance, including light (all radiation) has an electromagnetic field.
Future knowledge-
All electromagnetic fields decay into a monopole non binding gravitational wave. The essence of time is the decay rate of all electromagnetic fields into the gravitational wave, not just light. Light, or photons travel with in the gravitational wave blanket of space generated from all matter. The underlying equation is
Potential Energy decay= Kinetic energy formation times the speed of that formation squared. it is the same as area = Pi times r squared where r in this equation is defined as the radius of space formation and pi is defined as change in space and area is a two dimensional area because wave formation is combining and dimensions are decreasing. Time is the rate of the process. It is a simple two dimensional area problem that shows that space is elongating and flattening and the emission and synchronization of gravitational waves actually runs the show of the universe as energy is actually running out through this process. The universe has a beginning, middle, and end. You are in the middle, of the story of the universe.- insight
QUOTE (rpenner+Nov 20 2007, 02:34 PM)
I reproduce this to spare you the pain of reading the nearby posts.
....
In Minkowski space-time, these are trivial (boring!) effects.
Truly lovely! Mathless as I am, that bit sings to me! I have no words...
....
In Minkowski space-time, these are trivial (boring!) effects.
Truly lovely! Mathless as I am, that bit sings to me! I have no words...
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