Hi all, Take a planet A and another one B, just a few million kilometres apart – they are NOT travelling relative to one another and are separated by billions of steel rulers, all lined up end to end, so that everybody can agree on the distance between the planets. Planet A fires a rocket at 0.5c directly towards planet B Planet B fires a laser beam at the speed of light (funnily enough) directly towards Planet A The initial blast off of the rocket and the laser beam are simultaneous based on someone standing exactly half way between the two planets. Now, to any observer, wherever they may be, and after taking into account the finite speed of light at velocity c, they will observe the rocket taking double the amount of time to reach it’s destination than the laser took to reach it’s destination. Based on this observation, I imagine everybody would agree that the rocket is travelling at 0.5c and in the opposite direction to the laser beam. I know that the blast-off may not always appear simultaneous to all observers, but I believe that all said and done, ALL observers should be able to agree on the distance between the planets and the fact that the rocket is travelling half the speed of the laser beam and in the opposite direction to it. This suggests to me that from this very simple experiment, the light beam MUST be travelling past the rocket at 1.5c, otherwise something is drastically wrong! I am sure that the rocket may well measure the speed of light as that of c, and this I do not dispute, but I believe there are some possible explanations for this. What I would like to point out is the REALITIES of this situation. Anyone care to comment? Please Register or Log in to view the hidden image!
To somebody in the frame of reference of the planets, the light travels in one direction at speed c, and the rocket travels in the other direction with speed 0.5 c. Nothing is going faster than light, so there's no problem. To somebody in the frame of reference of the rocket, the light is travelling towards the rocket at speed c, and the planets are moving at speed 0.5 c. Again, no problem. For the first observer, the <b>difference</b> in speeds between the light and the rocket is 1.5c, but that is fine. No object is observed going faster than c.
Hmmmm, it's your middle paragraph: "To somebody in the frame of reference of the rocket, the light is travelling towards the rocket at speed c, and the planets are moving at speed 0.5 c. Again, no problem." that I have a problem with. I know what the rocket will observe, but given the distances and times we ALL agree on, the laser beam surely MUST be travelling past the rocket at 1.5c:bugeye:
Observations are bases on light. How else do you propose to observe. With that said, how do you propose to observe what the laser beam is doing? (or the rocket, for that matter). If you're invoking omniscience, then this doesn't seem to be a scientific inspection.
I tell you what then Errandir, suppose you perform exactly the same experiment, but this time lets invoke sound rather than light to help with our observations. We’ll set the experiment up such that there are two hollow tunnels stretching from each planet to some remote observer and these tunnels are filled with air. We use very simple device,s which upon the launch and arrival of both the laser beam and rocket, produce a sound wave which travels through the tunnels and on to the observer. This time we’re not using light to measure with, but we can still arrive at the same conclusions with a few simple calcs – that is: the laser beam travelled the same distance as the rocket, in the opposite direction and therefore MUST have passed the rocket at 1.5 c, regardless of what the rocket THINKS it measures!
The issue is NOT what we would CALCULATE in this manner from the point of view of some third observer with air tubes for the purpose of measurement. The issue is the observation FROM THE SPACE SHIP. The problem is, if you connect air tubes to the ship, the ship will be traveling faster than the signal that is trying to reach it from the arrival of the light signal at the planet from which the ship left. The signal will certainly NOT arrive at the ship until well after it has reached its destination.
Dav I know what the rocket will observe, but given the distances and times we ALL agree on, the laser beam surely MUST be travelling past the rocket at 1.5c No, the light from the laser is traveling at c. The rocket is traveling at 0.5c. That is all. If he could, the observer on the rocket will measure the light at c, not 1.5c. Light is measured at c by all observers, regardless of reference frame.
There is some confusion here! I know and understand that the rocket measures the laser beam as having a velocity of no greater than c. I have no problem with accepting what an instrument would measure and that this is the case. My suggestion is that what the rocket is measuring is an illusion of what is happening in reality. I have outlined in the experiment above how you can determine the speeds of both the laser beam and the rocket. We also know that they are travelling in opposite directions to each other and a simple vector calculation tells us they are travelling at 1.5c towards each other. They MUST be travelling at 1.5c relative to each other, surely! Hold on a second, I've thought of something else: When the Planet A recieves the laser beam it measures a certain frequency of the beam, right? Now, I believe the rocket will measure an increased frequency due to it's speed relative to the beam, am I right? So the rocket must be travelling into the beam to create this effect. However, I can see why there might be no apparent measured change in velocity because as the frequency increases the wavelength decreases and so cancels out when applying v=f lambda
Surely, from the perspective of an observer at rest relative to the planets. Like how if you point flashlights in opposite directions, their beam fronts move apart at 2c. No laws of physics break, for, as James says, no object is exceeding c. What the rocket is measuring might be an illusion of what is happening in reality if the 1.5c was a measurement of an object’s velocity, but it’s not; it’s the difference of two objects’ velocities.
day57: <i>My suggestion is that what the rocket is measuring is an illusion of what is happening in reality. I have outlined in the experiment above how you can determine the speeds of both the laser beam and the rocket. We also know that they are travelling in opposite directions to each other and a simple vector calculation tells us they are travelling at 1.5c towards each other. They MUST be travelling at 1.5c relative to each other, surely!</i> The rocket's measurements are as real as any other measurements. There is no illusion happening here. What you have done is to specify a particular reference frame in advance. Naturally, both the people on the planets and the people in rocket agree that, <b>according to the rulers laid out</b> (i.e. stationary in the planets' frame of reference), the relative speed of the rocket and the light is 1.5c. But notice that to come to that conclusion the rocket people must do a calculation to transform to the other reference frame. In fact, what the rocket people directly observe is that the rulers shrink so that the distance between the planets is less than what it was before the rocket started. The measured speed of light is c in the rocket frame, and this is also the <b>observed</b> relative speed in that frame. The 1.5c figure, from the rocket's point of view, relies on a calculation.
Question James, I had started to enter this discussion and was working on a table showing the distance at various velocities etc. But you have introduced that variable. While working on the table I had a thought. During the time a rocket pilot would be accelerating he would also see distance changing. If I monitor my "g" forces I know my true acceleration but seeing the distance change means I would see a much higher acceleration than was real. For example say I take 90 days to reach 86.6% c. At that junction I would have reduced the distance to A.C. from 4.3 ly down to 2.15 ly and think I have gone 2.15 ly in 90 days. If I calculate the acceleration required to reach 86.6% c in 90 days I get approximatley 1,095 fps^2. The relavistic change in distance at 86.6% c tells me I had to accelerate at 1.71524E11 fps^2. What happened to conservation? The change in distance/time mandates a super high acceleration which is inconsistant with F=ma.? Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
MacM, The formulas of time dilatation and length contraction you use are derived from within the framework of special relativity. If you want to include acceleration, you'll need to enter the arena of the (more difficult) general relativity. Bye! Crisp
James This is the statement I don't like: " In fact, what the rocket people directly observe is that the rulers shrink so that the distance between the planets is less than what it was before the rocket started " I understand that distance *appears* to alter, but I can't/don't believe that the *real* distance changes, which leads me to believe there is an illusion going on and some kind of misinterpretation of observation has occured. I find it extrordinary that the laser beam is not travelling past the rocket at 1.5c given the circumstances set out in the experiment.
Crisp, Thanks. I don't disagree with your statement but it doesn't answer the question. I was looking for the relavistic answer to the question. Since you didn't give it I suspect you don't have a Relavistic answer. I was surprised by the magnitude of the shift error in acceleration in this case. It is approximately 170 million times greater!. Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
2Inquisitive, They are right. The measured velocity of light remains constant for a moving observer. That is why they call light invariant. I don't like it either but that seems to be the way it is and we are stuck with it. At the same time (and this is my personal view and they don't like that) is that the invariance of light is caused by light being a quantum energy process. That is it is caused by the manner in which light gets produced and re-produced. Being a quantum energy (a specific amount of energy) required to create a photon the observers motion becomes v+c and v-c relative to the source and shifts the creation of a photon. That means you are not looking at the same photon or you are looking at the same photon that has its re-production rate altered by the motion of the observer. Basically this view holds that Relativity is not required and is based on a false understanding of the production of light. One needs to keep in mind that for things to be as they are claimed in Relativity light is not constant but not only varies but does so for every observer simultaneously. That is light must have multiple velocites simultaneously. (Very simular to clock rates and time dilation). Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
James R, You speak of rulers appearing to shrink as the observer in the rocket increases velocity. In this case, is it not feasible for the wavelength of the laserbeam to *apparently* shrink too? And with an increase in frequency observed, the velocity of the laser would *appear* the same, regardless of your relative speed to it??????
The formulas for including acceleration into special relativity are here and fortunately are fairly simple.
MacM, It's sad to see that you sold out considering that the only place where the speed of light has been measured was on the surface of the Earth, stationairy in the Earth's gravitational field. Are you next going to suggest that 9.80665 m/s^2 is a universal constant??? Tom
Prosoothus, Didn't sell out Tom. It is still just an illusion of light production being a quantum energy affect where the observers velocity (energy) is v+c or v-c in the prodluction/reproduction of photons. Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius. .
<b>MacM</b>: <i>While working on the table I had a thought. During the time a rocket pilot would be accelerating he would also see distance changing.</i> Correct. <i>If I monitor my "g" forces I know my true acceleration but seeing the distance change means I would see a much higher acceleration than was real.</i> No. <i>For example say I take 90 days to reach 86.6% c. At that junction I would have reduced the distance to A.C. from 4.3 ly down to 2.15 ly and think I have gone 2.15 ly in 90 days.</i> No. As you accelerate, the distance continually changes for you. The total distance travelled must be obtained by integration in that case. (See the link above.) <i>If I calculate the acceleration required to reach 86.6% c in 90 days I get approximatley 1,095 fps^2.</i> At constant acceleration, I get 33.4 m/s<sup>2</sup> for the acceleration, or 109.6 feet per s<sup>2</sup>. <i>The relavistic change in distance at 86.6% c tells me I had to accelerate at 1.71524E11 fps^2.</i> I have no idea where you got that figure from. <i>What happened to conservation? The change in distance/time mandates a super high acceleration which is inconsistant with F=ma.?</i> Not according to me. (Conservation of what?) <i>At the same time (and this is my personal view and they don't like that) is that the invariance of light is caused by light being a quantum energy process. That is it is caused by the manner in which light gets produced and re-produced. Being a quantum energy (a specific amount of energy) required to create a photon the observers motion becomes v+c and v-c relative to the source and shifts the creation of a photon.</i> This makes no sense. Perhaps you could explain what you mean. <i>Basically this view holds that Relativity is not required and is based on a false understanding of the production of light.</i> Please give us your theory on the true understanding of the production of light. I can't wait. <i>One needs to keep in mind that for things to be as they are claimed in Relativity light is not constant but not only varies but does so for every observer simultaneously. That is light must have multiple velocites simultaneously.</i> The speed of light is always the same for all observers. It doesn't get much simpler than that. I have no clue as to why you claim light has multiple speeds, let alone why it has multiple speeds at the same time. I guess it must be part of your web of misconceptions about relativity. <b>dav57</b>: <i>I understand that distance *appears* to alter, but I can't/don't believe that the *real* distance changes, which leads me to believe there is an illusion going on and some kind of misinterpretation of observation has occured.</i> So, are you saying "real" distance is what we measure on Earth? But the Earth is travelling around the sun at 30 km/s, and the sun goes around the centre of the galaxy at 200 km/s. The galaxy itself moves relative to other galaxies. The reference frames of the rocket, the Earth, the sun and our galaxy all have different conceptions of distance. Which one do you think is the "real" distance, and why? <i>You speak of rulers appearing to shrink as the observer in the rocket increases velocity. In this case, is it not feasible for the wavelength of the laserbeam to *apparently* shrink too? And with an increase in frequency observed, the velocity of the laser would *appear* the same, regardless of your relative speed to it??????</i> Yes. That's exactly what happens.
