The derivation of the equations in the link is based on the accelerating observer experiencing constant acceleration, while mine (2nd post in this thread) is based on the non-accelerating observer seeing constant acceleration for the accelerating observer.
Therefore the situations are different.
Special Relativity
yes
indeed, special and relativity have extremely varied equations
by the way, the uncertainty period only becomes very very apparent when either the position or velocity or energy and time is reduced very close zero. so in the case of the rocket, since none of these conditions are satisfied, the uncertainty principle isn't of much of an issue
indeed, special and relativity have extremely varied equations
by the way, the uncertainty period only becomes very very apparent when either the position or velocity or energy and time is reduced very close zero. so in the case of the rocket, since none of these conditions are satisfied, the uncertainty principle isn't of much of an issue
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zong
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I think I have much to talk about, after the forum is now finally up again.. Thanks yong quan for upping the forum again!
Destructos: so, if one is travelling faster than c would time turn on it's head?
carlogambino: One of the laws of special relativity states that c is a constant. This constant can never be reached by moving objects. Thus, time cannot "stop" for you and me, which is why we cant travel back to the past either
yes, c is a constant that currently cannot be reached or breached, except in very special cases (read up on Hawking Radiation). But in the case that we can travel faster than c (suppose), then we have the time cone idea to talk about. In a way, we can travel to the future, because if we travel at speed c, then we would experience no time lag while the world moves forward. If we exceed c, then we would exit this time cone, and we may either reach a parallel universe, or traverse to any "time-period" we like, even in the past. Which one is true, no one knows. All these are hypotheses. For more info about this, read up on time cones, I think Stephen Hawking would talk about it in his brief history of time.
Destructos: God is light so therefore time does not apply to him, so i'm wondering, if particles(or God for that matter) is/are travelling at c, will it observe the universe 3 dimensionally or 4 dimensionally?
God is light?! Never heard that before. But then again, if we consider that to be so, then he can traverse thru all time, so he can control everything and not grow old! Haha maybe this MIGHT be true, too?
QuantumGravity: For example, the expansion of the universe during the inflation period caused the universe to expand much faster than c. This is possible as the universe as a whole is massless.
ARGH WRONG CONCEPT!! The currently accepted reason for the inflation of the universe being faster than the speed of light, is that AT THAT 3 MINUTES OF EXPANSION, relativity cannot explain what happens, and string/superstring/M Theory must take over. This is because all or some of the forces have been unified, and since the energy can take one form or another and not a definite type, relativity cannot tell what is happening.
Gwenyi: How can an object exist without having any mass ? according to e=mc^2, you'll need infinite mass and infinite energy to travel at c. If the universe were to be massless , then how can it travel at c since energy would be 0 when u sub m=0 into the equation ?
For this question exists a simple answer. Look into Quantum Mechanics. It will tell you that for LIGHT, E=hf, where E is energy of photon, h is planck's constant, and f is its frequency. E=mc^2 cannot be applied here, or if it can be, I do not yet know.
I'm not all-knowing, okay..
Sam Lee: You would want to think that the item that is expanding is the empty space within the universe itself, and not the particles flying away from each other at faster than the speed of light. Since, Einstein theory refers to only objects with mass, this might be possible for empty space to expand.
Er, well the universe is not massless.. If it were, this means there is no universe, because even energy constitutes mass. Although if you want I have a quote about it that can make you laugh and think: God made everything out of nothing, but the nothingness shows through. -- Paul Valery
weixing: Normally, photon is consider to have no mass.
Yep, you may think of a photon as massless. But they do have a mass, just so small we think of it as nearly nothing. But they are not the smallest things in the universe! Or so I heard. There are some particles in a black hole that are very much smaller than a photon, thought to hold information about matter that fell into the black hole. But that is another thing altogether.
weixing: Question to think about (saw this on one website, quite interesting):
A higher frequency photon have more energy than a lower frequency photon, so can we say that a higher frequency photon is more "massive" than a lower frequency photon??
Quite interesting, yes. If you're talking relativistic mass, yes. Because E=hf for a photon. And a higher frequency photon has more energy, thus more relativistic mass. That's my opinion only though, don't quote me for this!
shoelevy: in relativity, the mass you state must be specified as rest mass or relativistic mass
so when u say photons have mass that are so small we refer to them as massless, you are wrong. photons are described as massless means they have no REST mass. but they have relativistic mass.
this is very easy to understand.
1)if they had rest mass, then they can't travel at the speed of c.
2)from the above post by me, you can easily see from the equation that a photon has momentum. as a result, it behaves like a particle and when it hits something, it'll transfer some momentum to the target object. therefore, a photon behaves as though it has mass. so, to makes things coherent, physicists asign photons with a mass specifically called imaginary mass or relativistic mass. its called relativistic mass because its mass is a result of relativity
Your causality is wrong. Physicists postulated a photon as a packet of energy that acts as though it has mass, THAT is why those equations came about. You're using the equations derived from those assumptions, and then telling me that the assumptions are true. It's like telling me that 1+1=2 because 2-1=1. Makes not much sense..
But you're correct to some extent, Photons have mass and have velocity, so they do have momentum. But i think, this momentum is more appropriately addressed by quantum mechanics in the de broglie wavelength equation, (lambda) = h/mv, where mv = momentum of photon, h = planck's constant, and lambda is the wavelength of the photon. Again, I am not sure if this equation can be applied, because I have not fully understood the basic assumptions of quantum mechanics.
To the rocket question: eeek, so many formulae! Don't wanna look at them.. had enough of them in school!
All these are very arguable, and I admit I do not know everything, so part of these may be wrong. Tell me if this is so! I'm not all-knowing, nor am i infallible.. and my english sucks, so clarify if i didn't say anything properly.. thanks.
Destructos: so, if one is travelling faster than c would time turn on it's head?
carlogambino: One of the laws of special relativity states that c is a constant. This constant can never be reached by moving objects. Thus, time cannot "stop" for you and me, which is why we cant travel back to the past either
yes, c is a constant that currently cannot be reached or breached, except in very special cases (read up on Hawking Radiation). But in the case that we can travel faster than c (suppose), then we have the time cone idea to talk about. In a way, we can travel to the future, because if we travel at speed c, then we would experience no time lag while the world moves forward. If we exceed c, then we would exit this time cone, and we may either reach a parallel universe, or traverse to any "time-period" we like, even in the past. Which one is true, no one knows. All these are hypotheses. For more info about this, read up on time cones, I think Stephen Hawking would talk about it in his brief history of time.
Destructos: God is light so therefore time does not apply to him, so i'm wondering, if particles(or God for that matter) is/are travelling at c, will it observe the universe 3 dimensionally or 4 dimensionally?
God is light?! Never heard that before. But then again, if we consider that to be so, then he can traverse thru all time, so he can control everything and not grow old! Haha maybe this MIGHT be true, too?
QuantumGravity: For example, the expansion of the universe during the inflation period caused the universe to expand much faster than c. This is possible as the universe as a whole is massless.
ARGH WRONG CONCEPT!! The currently accepted reason for the inflation of the universe being faster than the speed of light, is that AT THAT 3 MINUTES OF EXPANSION, relativity cannot explain what happens, and string/superstring/M Theory must take over. This is because all or some of the forces have been unified, and since the energy can take one form or another and not a definite type, relativity cannot tell what is happening.
Gwenyi: How can an object exist without having any mass ? according to e=mc^2, you'll need infinite mass and infinite energy to travel at c. If the universe were to be massless , then how can it travel at c since energy would be 0 when u sub m=0 into the equation ?
For this question exists a simple answer. Look into Quantum Mechanics. It will tell you that for LIGHT, E=hf, where E is energy of photon, h is planck's constant, and f is its frequency. E=mc^2 cannot be applied here, or if it can be, I do not yet know.
I'm not all-knowing, okay..Sam Lee: You would want to think that the item that is expanding is the empty space within the universe itself, and not the particles flying away from each other at faster than the speed of light. Since, Einstein theory refers to only objects with mass, this might be possible for empty space to expand.
Er, well the universe is not massless.. If it were, this means there is no universe, because even energy constitutes mass. Although if you want I have a quote about it that can make you laugh and think: God made everything out of nothing, but the nothingness shows through. -- Paul Valery
weixing: Normally, photon is consider to have no mass.
Yep, you may think of a photon as massless. But they do have a mass, just so small we think of it as nearly nothing. But they are not the smallest things in the universe! Or so I heard. There are some particles in a black hole that are very much smaller than a photon, thought to hold information about matter that fell into the black hole. But that is another thing altogether.
weixing: Question to think about (saw this on one website, quite interesting):
A higher frequency photon have more energy than a lower frequency photon, so can we say that a higher frequency photon is more "massive" than a lower frequency photon??
Quite interesting, yes. If you're talking relativistic mass, yes. Because E=hf for a photon. And a higher frequency photon has more energy, thus more relativistic mass. That's my opinion only though, don't quote me for this!
shoelevy: in relativity, the mass you state must be specified as rest mass or relativistic mass
so when u say photons have mass that are so small we refer to them as massless, you are wrong. photons are described as massless means they have no REST mass. but they have relativistic mass.
this is very easy to understand.
1)if they had rest mass, then they can't travel at the speed of c.
2)from the above post by me, you can easily see from the equation that a photon has momentum. as a result, it behaves like a particle and when it hits something, it'll transfer some momentum to the target object. therefore, a photon behaves as though it has mass. so, to makes things coherent, physicists asign photons with a mass specifically called imaginary mass or relativistic mass. its called relativistic mass because its mass is a result of relativity
Your causality is wrong. Physicists postulated a photon as a packet of energy that acts as though it has mass, THAT is why those equations came about. You're using the equations derived from those assumptions, and then telling me that the assumptions are true. It's like telling me that 1+1=2 because 2-1=1. Makes not much sense..
But you're correct to some extent, Photons have mass and have velocity, so they do have momentum. But i think, this momentum is more appropriately addressed by quantum mechanics in the de broglie wavelength equation, (lambda) = h/mv, where mv = momentum of photon, h = planck's constant, and lambda is the wavelength of the photon. Again, I am not sure if this equation can be applied, because I have not fully understood the basic assumptions of quantum mechanics.
To the rocket question: eeek, so many formulae! Don't wanna look at them.. had enough of them in school!
All these are very arguable, and I admit I do not know everything, so part of these may be wrong. Tell me if this is so! I'm not all-knowing, nor am i infallible.. and my english sucks, so clarify if i didn't say anything properly.. thanks.
yes, i know my casaulity is wrong but you have to understand that its for the sake of explaining. if you want me to avoid casaulity i'll just have to start everything from the 2 postulates, go through lorentz transformation, through principle of equivalence then through quantum mechanics. you want that?...i think not....so sacrifice of casaulity is necessary in this case.
and u said "this momentum is more appropriately addressed by quantum mechanics in the de broglie wavelength equation, (lambda) = h/mv, where mv = momentum of photon, h = planck's constant, and lambda is the wavelength of the photon"
your application of the equation is correct but definition for the photon's momentum is WRONG. mv is a classical definition, not quantum nor relativistic. forget your jc lecture notes. they're not deep enough. using mv to define the photons momentum is very very tricky business. NEVER do that. the method used by einstein himself for showing that photons have momentum is again E^2=m^2 c^4 + p^2c^2 and substitude
and for the part where u said "For this question exists a simple answer. Look into Quantum Mechanics. It will tell you that for LIGHT, E=hf, where E is energy of photon, h is planck's constant, and f is its frequency. E=mc^2 cannot be applied here, or if it can be, I do not yet know. I'm not all-knowing, okay.. "
yes, e=mc^2 can be used but you must use its original form.
and for this "Quite interesting, yes. If you're talking relativistic mass, yes. Because E=hf for a photon. And a higher frequency photon has more energy, thus more relativistic mass. That's my opinion only though, don't quote me for this! "
you missed out hf=pc ==>p=hf/c ==> greater freq=greater momentum
paiseh shoot you but i did alot of intensive reading on relativity and i feel i should share what i know
and u said "this momentum is more appropriately addressed by quantum mechanics in the de broglie wavelength equation, (lambda) = h/mv, where mv = momentum of photon, h = planck's constant, and lambda is the wavelength of the photon"
your application of the equation is correct but definition for the photon's momentum is WRONG. mv is a classical definition, not quantum nor relativistic. forget your jc lecture notes. they're not deep enough. using mv to define the photons momentum is very very tricky business. NEVER do that. the method used by einstein himself for showing that photons have momentum is again E^2=m^2 c^4 + p^2c^2 and substitude
and for the part where u said "For this question exists a simple answer. Look into Quantum Mechanics. It will tell you that for LIGHT, E=hf, where E is energy of photon, h is planck's constant, and f is its frequency. E=mc^2 cannot be applied here, or if it can be, I do not yet know. I'm not all-knowing, okay.. "
yes, e=mc^2 can be used but you must use its original form.
and for this "Quite interesting, yes. If you're talking relativistic mass, yes. Because E=hf for a photon. And a higher frequency photon has more energy, thus more relativistic mass. That's my opinion only though, don't quote me for this! "
you missed out hf=pc ==>p=hf/c ==> greater freq=greater momentum
paiseh shoot you but i did alot of intensive reading on relativity and i feel i should share what i know
let me tell you, alot of people misuse E=mc^2
people always duan zhang qu yi~!
you MUST start from its original long form, appreciate and understand it Then can you truely know its applications.
don't start with E=mc^2 then not know when to use or blame anything when it fails to explain what it is supposed to
people always duan zhang qu yi~!
you MUST start from its original long form, appreciate and understand it Then can you truely know its applications.
don't start with E=mc^2 then not know when to use or blame anything when it fails to explain what it is supposed to
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zong
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and u said "this momentum is more appropriately addressed by quantum mechanics in the de broglie wavelength equation, (lambda) = h/mv, where mv = momentum of photon, h = planck's constant, and lambda is the wavelength of the photon"
your application of the equation is correct but definition for the photon's momentum is WRONG. mv is a classical definition, not quantum nor relativistic. forget your jc lecture notes. they're not deep enough. using mv to define the photons momentum is very very tricky business. NEVER do that. the method used by einstein himself for showing that photons have momentum is again E^2=m^2 c^4 + p^2c^2 and substitude
Don't underestimate even jc level physics. I've checked on the net, and confirmed that this topic is still under scrutiny. Neither my answer nor yours is "correct", and there are supporters on each side, and more supporters of many other "answers". And also that's why I include the disclaimer, those were my "ideas", as to how to answer the question.
yes, e=mc^2 can be used but you must use its original form.
Sorry, I admit, I think E=mc^2 can be used. but using the original form, yes.
you missed out hf=pc ==>p=hf/c ==> greater freq=greater momentum
And what do you want to show by this? All I can make of why you added this is that greater momentum contributes to greater relativistic mass. Is that what you need to show? If so, thanks, I think I forgot to prove that part. As usual, because I never explain enough...
paiseh shoot you but i did alot of intensive reading on relativity and i feel i should share what i know
Don't worry about shooting me, sometimes my explanations are not enough or inconsistent too.
let me tell you, alot of people misuse E=mc^2
people always duan zhang qu yi~!
you MUST start from its original long form, appreciate and understand it Then can you truely know its applications.
don't start with E=mc^2 then not know when to use or blame anything when it fails to explain what it is supposed to
Sometimes, it's enough to just use this formula to derive everything. And there ARE really cases where relativity does not apply. The first 3 minutes of the big bang is one example. And yes I do not know all there is about relativity, especially when we start extending it into whatever tensors. But I'm sure in the cases we talk about above we're only treading the basics of relativity. No need for such crazy equations.
your application of the equation is correct but definition for the photon's momentum is WRONG. mv is a classical definition, not quantum nor relativistic. forget your jc lecture notes. they're not deep enough. using mv to define the photons momentum is very very tricky business. NEVER do that. the method used by einstein himself for showing that photons have momentum is again E^2=m^2 c^4 + p^2c^2 and substitude
Don't underestimate even jc level physics. I've checked on the net, and confirmed that this topic is still under scrutiny. Neither my answer nor yours is "correct", and there are supporters on each side, and more supporters of many other "answers". And also that's why I include the disclaimer, those were my "ideas", as to how to answer the question.
yes, e=mc^2 can be used but you must use its original form.
Sorry, I admit, I think E=mc^2 can be used. but using the original form, yes.
you missed out hf=pc ==>p=hf/c ==> greater freq=greater momentum
And what do you want to show by this? All I can make of why you added this is that greater momentum contributes to greater relativistic mass. Is that what you need to show? If so, thanks, I think I forgot to prove that part. As usual, because I never explain enough...
paiseh shoot you but i did alot of intensive reading on relativity and i feel i should share what i know
Don't worry about shooting me, sometimes my explanations are not enough or inconsistent too.
let me tell you, alot of people misuse E=mc^2
people always duan zhang qu yi~!
you MUST start from its original long form, appreciate and understand it Then can you truely know its applications.
don't start with E=mc^2 then not know when to use or blame anything when it fails to explain what it is supposed to
Sometimes, it's enough to just use this formula to derive everything. And there ARE really cases where relativity does not apply. The first 3 minutes of the big bang is one example. And yes I do not know all there is about relativity, especially when we start extending it into whatever tensors. But I'm sure in the cases we talk about above we're only treading the basics of relativity. No need for such crazy equations.
you missed out hf=pc ==>p=hf/c ==> greater freq=greater momentum
And what do you want to show by this? All I can make of why you added this is that greater momentum contributes to greater relativistic mass. Is that what you need to show? If so, thanks, I think I forgot to prove that part. As usual, because I never explain enough...
its just for people to see easily the relationship because your original explanation of E=hf doesn't relate back to momentum
Don't underestimate even jc level physics. I've checked on the net, and confirmed that this topic is still under scrutiny. Neither my answer nor yours is "correct", and there are supporters on each side, and more supporters of many other "answers". And also that's why I include the disclaimer, those were my "ideas", as to how to answer the question.
that's why i said using mv to define the photons momentum is very very tricky business. NEVER do that. in my own opinion, i think its wrong to us e mv because it neglects relativistic effects. if u wanna include relativistic effects, you're better of doing E^2=m^2 c^4 + p^2c^2
And what do you want to show by this? All I can make of why you added this is that greater momentum contributes to greater relativistic mass. Is that what you need to show? If so, thanks, I think I forgot to prove that part. As usual, because I never explain enough...
its just for people to see easily the relationship because your original explanation of E=hf doesn't relate back to momentum
Don't underestimate even jc level physics. I've checked on the net, and confirmed that this topic is still under scrutiny. Neither my answer nor yours is "correct", and there are supporters on each side, and more supporters of many other "answers". And also that's why I include the disclaimer, those were my "ideas", as to how to answer the question.
that's why i said using mv to define the photons momentum is very very tricky business. NEVER do that. in my own opinion, i think its wrong to us e mv because it neglects relativistic effects. if u wanna include relativistic effects, you're better of doing E^2=m^2 c^4 + p^2c^2
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weixing
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Hi,
General Relativity and Special Relativity are subject that are very difficult to understand and I believe that not many people out there really understand it.... remember Einstein nearly spend his whole life study it. And there are so many books on this subject, so I was wondering how many author really understand the subject. Even the author understand the subject very well, but do you really understand what the author trying to said???
Anyway, it is good to have interest in this subject... hope someone here will do his PhD on this in the future.
Have a nice day.
General Relativity and Special Relativity are subject that are very difficult to understand and I believe that not many people out there really understand it.... remember Einstein nearly spend his whole life study it. And there are so many books on this subject, so I was wondering how many author really understand the subject. Even the author understand the subject very well, but do you really understand what the author trying to said???
Anyway, it is good to have interest in this subject... hope someone here will do his PhD on this in the future.
Have a nice day.
Yang Weixing
"The universe is composed mainly of hydrogen and ignorance."
"The universe is composed mainly of hydrogen and ignorance." -
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