now back to the original question about registering the beams from A and B on the rocket moving at speed 0.8c
Imagine observer B issueing one photon each second packing one second of his life on that photon.
So as i imagine rocket observer moving towards B will register 3 photons per second each packed with one second of B's life. So in one second of rocket observer he will be able to see 3 seconds of observer's B life.
Or will he register just one photon per second packed with 3 seconds of B's life ?
I can logically understand what the person standing at A measure here. The hard thing to understand is that on the rocket, according to the theory, the clock will show the same time elapsed in both case.
rocket observer thinks the light has reached the mirror when observer A still thinks light is moving towards the mirror and has not reached it yet. The fact is neither of them knows if mirror is there (maybe it was broken already or removed by some alien?). In other words the moment at which you think light has reached the mirror is your speculation about what there now is and you base your guess on the time light will need to cover the distance (it is your imaginary 3D space you think to be simultanious with you)- whether it is true you will only know when the light comes from there and tells you what really happened.
When observer A thinks light reached the mirror, the rocket observer thinks light is already for some time on its way back after the event.
rocket observer and observer A have different understanding of what the "simultanious with me" reality is. One defines the moment of a distant event based on the distance and the time light needs to cover it so no wonder it depends on your relative motion to/from that event
Regarding the beam traveling in the same direction as the rocket A will see a that 2 years elapse between the reflection from from the detector in the back to the refection from the detector in the front. 1 year is the time the light will take fore traveling from B to A. So according to A it took the light beam 1 year to go from the detector in the back to the detector in the front.
In this case you can explain the much shorter time shown by the detector clock on the rocket by stating that the time was moving slower on the moving rocket but that explanation will not hold fore the light beam traveling at the opposite direction to the rocket so what is the explanation in that case?
now back to the original question about registering the beams from A and B on the rocket moving at speed 0.8c
Imagine observer B issueing one photon each second packing one second of his life on that photon.
So as i imagine rocket observer moving towards B will register 3 photons per second each packed with one second of B's life. So in one second of rocket observer he will be able to see 3 seconds of observer's B life.
Or will he register just one photon per second packed with 3 seconds of B's life ?
In this case I can only say that he will se 3 seconds of B's life during 1 second measured at A. Is there a fundamental differens in this case?
Two events in a frame moving relative to an observer ( but measured/transformed to an observer's frame ) which respectively define the start and end of a clock 'tick' will have a greater time separation with higher relative speed, and independent of direction.
Quite rightly the frequency of each light signal recieved will have Doppler shifting though. That would occur even if the observer made only a single measurement of only one event in the other frame. That signal will have Doppler shifting as described. If you compare two such shifted signals you'll get the time dilation/slowing.
Is that the physical slowing of time that occures on a moving object, same as the case with the experiments with muon decay ?
Is that the physical slowing of time that occures on a moving object, same as the case with the experiments with muon decay ?
Ok let's say you are at point A and i am at point B which is 8 l.y (light years) away from A. Now you through at me the muon (or launch the rocket) at speed of 0.8c
What you will see with your own eyes is that during 18 years of your life the life on the rocket will pass 6 years and cover distance of 8 l.y so when you see rocket arrived at point B the rocket clock will show 6 years passed , my clock will show 18 years passed (you need really huge telescope to see that :) ) and your clock will show 18 years passed. You wonder how is that possible for the rocket to pass 8 l.y distance and having only 6 years passed onboard ?
I don't know if you can call it faster than light travel or rephrase it by saying that for rocket moving at 0.8c the space has contracted by 60% from 8 l.y to 4.8 l.y so that at speed of 0.8c it only required 6 years (instead of 10 years) to pass those 4.8 l.y (instead of original 8 l.y)
Now what i would see from my point B is that during my and your 2 years time rocket passes 6 years in traveling 8 l.y. distance from A to B
Again 6 years time to pass 8 l.y. distance from whatever point you look
Bear in mind that muon/rocket-driver could say the same thing about you - namely that not the muon/rocket life is slowed but it is your life slowed and your space is contracted :) or that it is mine time is slowed and my space is contracted
Now if you ask me if a muon whose whole life-span (before decaying) is let's say 6 years only - will it be able to cover distance of 8 l.y ? the answer is yes, absolutely - you just need to through it at speed of 0.8c or higher
life extention of fast-decaying particles is well established fact.
For example in 1952 a beam of pions with half life of 1.8*10^-8 sec was being launched at speed of 0.99995c and well detectable at several hundred meters distance. If for no time dilation effect half of them would be decayed already at 5.4 meters distance, the next half on the next 5.4m and so on so hardly any would be observed at several hundred (the amount of pions beamed would have to be unimaginably high then to explain the detection results)
But each photon detection is a distinct event which either happens or it doesn't ( no 'fractional' events ), and so is particulate. We don't actually 'view' the oscillation of the electric/magnetic field as it cycles with the photon phases - so there is no counting 'up...down....up....down...up....down...' of any field strength rhythm.
I understand that the frequency can increase if the wavelength decreases, but does this mean that there is no 'highest frequency' since the wavelength can be shorter? If the oscillation also can't propagate faster than c, then what effect does this have on the fastest possible oscillation for a single cycle? How would this constraint be applied to the oscillation? What would be the frequency of a cycle of 'up-down-up' that has a limit of propagating at c? Gravity, like relative motion, will shift the frequency up or down, but two objects can't recede from each other faster than c, and photons can't climb out of a black hole, so doesn't this also suggest that there is a maximum frequency?
I understand that the frequency can increase if the wavelength decreases, but does this mean that there is no 'highest frequency' since the wavelength can be shorter?
There is no known highest frequency, nor shortest wavelength.
Quote:
If the oscillation also can't propagate faster than c, then what effect does this have on the fastest possible oscillation for a single cycle?
We never measure any phase as an absolute, only the difference between phases of one thing and some other. You seem to be thinking of some 'velocity' or rate of change of the field transverse to the photon's direction? It's not a measurable quantity, even as a 'gedanken'. For a single photon how could you make two measurements of phase at distinct times? You only ever measure a photon by absorbing/deflecting/emitting/whatever - so now it's different or not there. That's what I mean when we have deduced wave behaviour from interference, which compares phases in some group of photons, we never have the pleasure of seeing the 'waves' per se like we do at the sea-shore. Text books are replete with such diagrams however.
Quote:
How would this constraint be applied to the oscillation? What would be the frequency of a cycle of 'up-down-up' that has a limit of propagating at c?
Not applicable. In fact no quantum phase is measurable quantity of itself - it is perhaps combined with some other object's phase - and you 'square' an associated amplitude to yield the probability of some event. With a bunch of photons you gain patterns in the behaviour of the herd which reflect said probability predictions, and with remarkable accuracy for quantum electrodynamics ( QED ). The more quanta/particles involved the closer the fit.
It's worth mentioning the 'shot' noise error with LIGO is a reflection of the random fluctuation of photon behaviour in this fashion. With higher laser power more photons are involved, and such shot behaviour as a fraction of the total statistic declines. The 7 or so Watt power with current LIGO setup is going to be dwarfed by the several hundred odd Watt power for Advanced LIGO design! :-)
Quote:
Gravity, like relative motion, will shift the frequency up or down, but two objects can't recede from each other faster than c, and photons can't climb out of a black hole, so doesn't this also suggest that there is a maximum frequency?
No, a minumum frequency ( zero ), as the photon loses all of it's energy and via E = hv ( E = energy, h = Planck's constant, v = frequency ). So a photon emitted from just on the outside of the event horizon is going to be barely detectable at a distance. It will have a frequency in fractions of a Hertz, an humungously long wavelength, and stuff all momentum. Any object descending toward the event horizon, while emitting radiation, is going to gradually fade 'to the red' and beyond as seen by a distant observer. This is a classical view to a point in that it has yet to be devised the behaviour of gravity in the small with large field strengths - a quantum/gravity mix. QED is solid though.
Gravity is only attractive, so it creates potential wells not hills. It will only down-shift radiation frequencies as you get further from the mass not upshift.
More generally, when c as an absolute speed limit is mentioned, it is important to grasp that it applies to measurable quantities and not necessarily to some underlying model. ( Feymnan diagrams are a good example of where many things can be done, as long as no measurable violation of various principles is predicted ).
Cheers, Mike.
( edit ) This raises some tricky questions like: if a photon descends to the singularity of a black hole what energy/frequency shifts occur, and what is 'measurable' there anyway given the one way nature of the spacetime situation?
A dearth of experimental data to guide theory here..... :-)
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
More generally, when c as an absolute speed limit is mentioned, it is important to grasp that it applies to measurable quantities and not necessarily to some underlying model. ( Feymnan diagrams are a good example of where many things can be done, as long as no measurable violation of various principles is predicted ).
Ah, thanks Mike. Consideration of the Feynman diagrams (and the many quantum possibilities that must be accounted for when a photon goes simply from A to B) helps me to see the distinction. I think I was a bit stuck on words like 'absolute' and 'invariant'...
Ok. one last question guys. Does frequency or dopler effect have anyting att all to do with how the speed of light will messured or detected by the photo detector? I cant see that thay have but I might be wrong.
Ok. one last question guys. Does frequency or dopler effect have anyting att all to do with how the speed of light will messured or detected by the photo detector? I cant see that thay have but I might be wrong.
[short answer]
Speed is always a constant in free space - no matter who/what/when/where - and independent of anything at all, frequency included.
Frequency will depend on various relative motions etc.
[/short answer]
[long answer]
It can be easier to think of frequency as the amount of 'punch' a photon has. While it always travels at a given speed, it doesn't always deliver the same energy or momentum:
for a photon:
Energy = h * frequency
( h = Planck's constant )
Energy = momentum * c
and since speed of light = c = frequency * wavelength
then
Energy = h * c / wavelength
So higher frequency ( shorter wavelength ) gets more punch, with lower frequency ( longer wavelength ) is less punch. Thus Doppler shifting implies a greater punch for light from an approaching source, than light from a receding source. We have an everyday expectation that it would be the velocity that would vary in that manner - as it does for bullets/baseballs/whatever - but not so for light.
If you throw a ball up in the air ( away from the ground ) then it's kinetic energy diminishes with height as it slows down before it falls back. A photon going up will also do something similiar - again, not by varying it's speed - but by lowering it's energy/frequency. This is gravitational redshift.
A black hole is a region where no matter what energy a photon has, it cannot climb out of the gravity well ( if within the event horizon ). The only objects that 'in theory' escape from a black hole are those going faster than light - so the constancy of light speed implies that photons can't go even faster to achieve that! Cuts both ways ...... :-)
Constancy of light speed is one of the hardest, and most counter-intuitive, parts of relativity. You are not alone in this. Many famous physicists are/were similiarly afflicted.
Try and think of 'ordinary' mechanics as a low speed approximation of relativity, rather than relativity as a 'special' extension of Newtonian stuff.
Generally, for any particle:
Energy = 'rest' amount + 'kinetic' amount
for bodies with mass:
'rest' amount = m * c * c ( ie. 'em cee squared' )
kinetic amount = some_function(varies with velocity)
For massless particles:
'rest' amount = zero, or irrelevant because travelling at light speed.
'kinetic' amount = some_function(doesn't vary with velocity)
[/long answer]
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
now back to the original
)
now back to the original question about registering the beams from A and B on the rocket moving at speed 0.8c
Imagine observer B issueing one photon each second packing one second of his life on that photon.
So as i imagine rocket observer moving towards B will register 3 photons per second each packed with one second of B's life. So in one second of rocket observer he will be able to see 3 seconds of observer's B life.
Or will he register just one photon per second packed with 3 seconds of B's life ?
RE: RE: I can logically
)
Regarding the beam traveling in the same direction as the rocket A will see a that 2 years elapse between the reflection from from the detector in the back to the refection from the detector in the front. 1 year is the time the light will take fore traveling from B to A. So according to A it took the light beam 1 year to go from the detector in the back to the detector in the front.
In this case you can explain the much shorter time shown by the detector clock on the rocket by stating that the time was moving slower on the moving rocket but that explanation will not hold fore the light beam traveling at the opposite direction to the rocket so what is the explanation in that case?
RE: now back to the
)
In this case I can only say that he will se 3 seconds of B's life during 1 second measured at A. Is there a fundamental differens in this case?
RE: Two events in a frame
)
Is that the physical slowing of time that occures on a moving object, same as the case with the experiments with muon decay ?
RE: Is that the physical
)
Ok let's say you are at point A and i am at point B which is 8 l.y (light years) away from A. Now you through at me the muon (or launch the rocket) at speed of 0.8c
What you will see with your own eyes is that during 18 years of your life the life on the rocket will pass 6 years and cover distance of 8 l.y so when you see rocket arrived at point B the rocket clock will show 6 years passed , my clock will show 18 years passed (you need really huge telescope to see that :) ) and your clock will show 18 years passed. You wonder how is that possible for the rocket to pass 8 l.y distance and having only 6 years passed onboard ?
I don't know if you can call it faster than light travel or rephrase it by saying that for rocket moving at 0.8c the space has contracted by 60% from 8 l.y to 4.8 l.y so that at speed of 0.8c it only required 6 years (instead of 10 years) to pass those 4.8 l.y (instead of original 8 l.y)
Now what i would see from my point B is that during my and your 2 years time rocket passes 6 years in traveling 8 l.y. distance from A to B
Again 6 years time to pass 8 l.y. distance from whatever point you look
Bear in mind that muon/rocket-driver could say the same thing about you - namely that not the muon/rocket life is slowed but it is your life slowed and your space is contracted :) or that it is mine time is slowed and my space is contracted
Now if you ask me if a muon whose whole life-span (before decaying) is let's say 6 years only - will it be able to cover distance of 8 l.y ? the answer is yes, absolutely - you just need to through it at speed of 0.8c or higher
life extention of fast-decaying particles is well established fact.
For example in 1952 a beam of pions with half life of 1.8*10^-8 sec was being launched at speed of 0.99995c and well detectable at several hundred meters distance. If for no time dilation effect half of them would be decayed already at 5.4 meters distance, the next half on the next 5.4m and so on so hardly any would be observed at several hundred (the amount of pions beamed would have to be unimaginably high then to explain the detection results)
RE: But each photon
)
I understand that the frequency can increase if the wavelength decreases, but does this mean that there is no 'highest frequency' since the wavelength can be shorter? If the oscillation also can't propagate faster than c, then what effect does this have on the fastest possible oscillation for a single cycle? How would this constraint be applied to the oscillation? What would be the frequency of a cycle of 'up-down-up' that has a limit of propagating at c? Gravity, like relative motion, will shift the frequency up or down, but two objects can't recede from each other faster than c, and photons can't climb out of a black hole, so doesn't this also suggest that there is a maximum frequency?
RE: I understand that the
)
There is no known highest frequency, nor shortest wavelength.
We never measure any phase as an absolute, only the difference between phases of one thing and some other. You seem to be thinking of some 'velocity' or rate of change of the field transverse to the photon's direction? It's not a measurable quantity, even as a 'gedanken'. For a single photon how could you make two measurements of phase at distinct times? You only ever measure a photon by absorbing/deflecting/emitting/whatever - so now it's different or not there. That's what I mean when we have deduced wave behaviour from interference, which compares phases in some group of photons, we never have the pleasure of seeing the 'waves' per se like we do at the sea-shore. Text books are replete with such diagrams however.
Not applicable. In fact no quantum phase is measurable quantity of itself - it is perhaps combined with some other object's phase - and you 'square' an associated amplitude to yield the probability of some event. With a bunch of photons you gain patterns in the behaviour of the herd which reflect said probability predictions, and with remarkable accuracy for quantum electrodynamics ( QED ). The more quanta/particles involved the closer the fit.
It's worth mentioning the 'shot' noise error with LIGO is a reflection of the random fluctuation of photon behaviour in this fashion. With higher laser power more photons are involved, and such shot behaviour as a fraction of the total statistic declines. The 7 or so Watt power with current LIGO setup is going to be dwarfed by the several hundred odd Watt power for Advanced LIGO design! :-)
No, a minumum frequency ( zero ), as the photon loses all of it's energy and via E = hv ( E = energy, h = Planck's constant, v = frequency ). So a photon emitted from just on the outside of the event horizon is going to be barely detectable at a distance. It will have a frequency in fractions of a Hertz, an humungously long wavelength, and stuff all momentum. Any object descending toward the event horizon, while emitting radiation, is going to gradually fade 'to the red' and beyond as seen by a distant observer. This is a classical view to a point in that it has yet to be devised the behaviour of gravity in the small with large field strengths - a quantum/gravity mix. QED is solid though.
Gravity is only attractive, so it creates potential wells not hills. It will only down-shift radiation frequencies as you get further from the mass not upshift.
More generally, when c as an absolute speed limit is mentioned, it is important to grasp that it applies to measurable quantities and not necessarily to some underlying model. ( Feymnan diagrams are a good example of where many things can be done, as long as no measurable violation of various principles is predicted ).
Cheers, Mike.
( edit ) This raises some tricky questions like: if a photon descends to the singularity of a black hole what energy/frequency shifts occur, and what is 'measurable' there anyway given the one way nature of the spacetime situation?
A dearth of experimental data to guide theory here..... :-)
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
RE: More generally, when c
)
Ah, thanks Mike. Consideration of the Feynman diagrams (and the many quantum possibilities that must be accounted for when a photon goes simply from A to B) helps me to see the distinction. I think I was a bit stuck on words like 'absolute' and 'invariant'...
Ok. one last question guys.
)
Ok. one last question guys. Does frequency or dopler effect have anyting att all to do with how the speed of light will messured or detected by the photo detector? I cant see that thay have but I might be wrong.
RE: Ok. one last question
)
[short answer]
Speed is always a constant in free space - no matter who/what/when/where - and independent of anything at all, frequency included.
Frequency will depend on various relative motions etc.
[/short answer]
[long answer]
It can be easier to think of frequency as the amount of 'punch' a photon has. While it always travels at a given speed, it doesn't always deliver the same energy or momentum:
for a photon:
Energy = h * frequency
( h = Planck's constant )
Energy = momentum * c
and since speed of light = c = frequency * wavelength
then
Energy = h * c / wavelength
So higher frequency ( shorter wavelength ) gets more punch, with lower frequency ( longer wavelength ) is less punch. Thus Doppler shifting implies a greater punch for light from an approaching source, than light from a receding source. We have an everyday expectation that it would be the velocity that would vary in that manner - as it does for bullets/baseballs/whatever - but not so for light.
If you throw a ball up in the air ( away from the ground ) then it's kinetic energy diminishes with height as it slows down before it falls back. A photon going up will also do something similiar - again, not by varying it's speed - but by lowering it's energy/frequency. This is gravitational redshift.
A black hole is a region where no matter what energy a photon has, it cannot climb out of the gravity well ( if within the event horizon ). The only objects that 'in theory' escape from a black hole are those going faster than light - so the constancy of light speed implies that photons can't go even faster to achieve that! Cuts both ways ...... :-)
Constancy of light speed is one of the hardest, and most counter-intuitive, parts of relativity. You are not alone in this. Many famous physicists are/were similiarly afflicted.
Try and think of 'ordinary' mechanics as a low speed approximation of relativity, rather than relativity as a 'special' extension of Newtonian stuff.
Generally, for any particle:
Energy = 'rest' amount + 'kinetic' amount
for bodies with mass:
'rest' amount = m * c * c ( ie. 'em cee squared' )
kinetic amount = some_function(varies with velocity)
For massless particles:
'rest' amount = zero, or irrelevant because travelling at light speed.
'kinetic' amount = some_function(doesn't vary with velocity)
[/long answer]
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal