Just been reading Use of Weapons by Iain M. Banks, and a description of a situation in there suddenly provoked a thought experiment in my mind:
Say I were travelling on my super-fast space ship at a fraction of the speed of light, from space station A to space station B, and am receiving constant communication from each of these stations, using electromagnetic radiation as the communication medium. Further, let’s assume that both A and B have synchronised clocks, and have complete knowledge of special relativity, of the distance between A and B, and of the constant velocity and the time of departure of my space ship from station A (They are able to calculate my position accurately at any time that they measure). Let’s say they have agreed to send a particular, identifiable signal at the same synchronised time, such that I will receive both these identical signals at the exact same time (i.e., when my space ship is exactly halfway between A and B). Clearly the signal from A will be red-shifted by a certain amount, and the signal from B will be blue-shifted by the same amount. Does this then imply that objects behind me will be measured, by me, to be longer than objects in front of me? (Length is being measured in the direction of my velocity vector)
Is this how the Lorentz contraction will affect my measurements? I’ve always been taught that Lorentz length contraction is just that: a contraction; a decrease, in the direction of the velocity vector, of the length measurement of other objects with a different relative velocity. Have I produced a contradiction, or is this all nonsense?
According to Lorentz’s formula here http://en.wikipedia.org/wiki/Length_contraction the length of the observed object is only dependent on its rest length and root(1 - v^2/c^2). It doesn’t matter whether you’re heading towards a space station with +ve velocity, or away from one with -ve velocity, because the velocity is squared.
As you approach the speed of light, you effectively compress your spacetime frame-of-reference in the direction that you are traveling, shortening all objects along that axis, both before and behind you. If the space station was, say, brick-shaped with its long axis at 45 degrees to your direction of travel, then it would appear to be a sheared parallelogram. Similarly, a circle would look like an oval.
Cool, man. I get what the formula is meant to do. I don’t get how red/blue-shifted light fits into it.
Light is meant to hit me with the same speed from all directions around me. That includes the radiation that makes up the communications I’m receiving from A and B. Say that the identical signal I’m receiving is some exact number of wavelengths of the radiation that was emitted with the same frequency from both A and B, and assume also that the time that I start receiving each message is identical. Then I will receive the blue-shifted message at a higher rate than the red-shifted one, and in fact will thus measure the actual length of the message from A (where I’m travelling from) to be quite a lot longer than normal. This change in time clearly is one-to-one with a change in length, i.e. lengths behind me are longer than lengths in front of me, and indeed longer than lengths of things that I am at rest relative to.
This part of your explanation is not logical (the “non-sense” part). A signal, or any information, requires length of message thus there cannot be a single moment of arrival for either and certainly not both together. Each message will take a length of time to be arriving from its fore edge to its aft edge. Because you are traveling faster toward one information stream, the length of one message must be experienced as shorter than the other (color shifting).
This red-blue shifting effect has nothing to do with the speed of the light travel but rather with how quickly the message pulses are perceived as changing. The traveler would perceive the aft sender as signaling at a slower rate than the forward sender until he calculated the relative motion effect. Without assuming constant speed of light travel and compensating, the traveler would assume that the aft message sender was merely sending at a slower rate.
From the traveler’s middle position, “M”, the entire forward approaching signal is captured within the distance of perhaps M to M+1 whereas the aft approaching signal is not fully captured until M+3. Because the traveler knows that he is moving away from A, he adjusts his perception of wavelength to account for red shift. Once that concern is included, he then measures both signals as well as any objects that he would be trying to measure as being the same length. Length can only be directly measured from a side. Length in the direction of travel must be calculated based on other observations and assumptions.
So by the end of all calculations and perception adjustments, there would not be any contradiction left. The point to such calculated measurements is to remove any possibility of contradiction, but the devil is in the detail, as always.
Not according to Special Relativity. Everything will seem different to the observer, but same to the people inside the space ship, because the time will change when one is moving, why we actually set the GPS sattelites’s clocks 45 mic sec forward according to SRT and 7 mic sec back according to GRT.