Exceptional!

So how can you tackle the question given in 17.7 without making use of the concept of Lorentz contraction? The question was: You travel to a star 10,000 light-years away (in Earth’s frame of reference) at a speed of 0.99c. How long does it take to get there from your perspective, and how far a distance is it? To get to the star will take 10000/0.99 years = 10101 years. However on the rocket ship you experience time slower so you need to adjust to the time you experience by dividing gamma (equivalent to multiplying by sqrt (1 - (v/c)^2) = sqrt (1-0.99^2) = 0.141. 10101 * 0.141 = 1424.8 years

So how can you tackle the question given in 17.7 without making use of the concept of Lorentz contraction? The question was: You travel to a star 10,000 light-years away (in Earth’s frame of reference) at a speed of 0.99c. How long does it take to get there from your perspective, and how far a distance is it? To get to the star will take 10000/0.99 years = 10101 years as experienced from the Earth. However on the rocket ship you experience time slower so you need to adjust to the time you experience by dividing by gamma (equivalent to multiplying by sqrt (1 - (v/c)^2) = sqrt (1-0.99^2) = 0.141. 10101 * 0.141 = 1424.8 years What is happening is the physical distance we are assigning to a meter is changing. We measure fewer meters but we should not draw the conclusion that the actual physical distance is shorter. So suppose we were to attach a tape measure to the rocket. What would people on Earth measure and what would people on the rocket measure? Would the lengths be different? The answer is that physical length is identical for both situations however the people on the rocket will not agree with the people on Earth that the markings on the tape measure off a meter. The people on the rocket will say the meter markings are far too short. They will both agree about the amount (mass) of tape between the Earth and the star and they will both agree that the mass of tape uniquely determines the physical distance so they will both agree that the physical distance covered is the same. A meter is defined as the physical distance that is covered by light in a single second divided by 299 792 458. If a second is longer then clearly light will cover more distance in that second and that physical distance will then have less meters. However it is the meter unit that is getting physically longer, the measured distance expressed in meters will be shorter but the physical distance stays the same.

Nothing with space is happening. In my view, space is not contracting, distances are not shortening, objects do not get shorter. Yet we domeasure shorter distances and we do measure objects to be shorter. What is changing is not the physical distance but the metric we are using to measure that distance. When our time "slows down" what this means is that the amount of time between two clock ticks increases and as light has a constant speed in physical space so too does the physical distance covered between the two ticks. Since a meter is defined as the physical distance light travels in 1/299 792 458 of a second then if that second is longer clearly the meter will end up being longer as light will travel further in the additional time between the two clock ticks. If meters become longer then fewer meters will fit into any given physical distance and so the measurement of the distance (using meters) will end up giving a smaller value for the measured distance. This is no different to the case of changing from a millimetre to a centimetre metric or from grams to kilograms. In both cases we will measure smaller values (10 times respectively 1000 times smaller) for the same distance or mass. In short, it is not space that is adjusting itself but the metric is (by definition) adjusting itself because it is based on a time unit that is variable. As time slows down the meter by its very definition becomes physically longer. Again, it is simply the metric that is changing, nothing is happening to physical space. Because the metric changes we measure different values for the same physical entities. This interpretation immediately resolves a number of difficulties described below that would need to be explained if true physical distance shortening (Lorentz contraction) took place. If it really is physical distance that is shortened then one would need to account for apparent size. Apparent size is a property of distance: when you get closer to an object that object will appear larger. If Lorentz contraction really shortens the physical distance then as Lorentz contraction takes place we would get physically closer to the object. By travelling ever closer to the speed of light we could get arbitrarily close. We should then see the object at the distance dictated by the Lorentz contraction. If Lorentz contraction really equates to shorter distances then theoretically, we could even observe a star as being a mile away or even closer (with all its detail!) that is a billion years distant in the rest frame. Something that is very difficult to accept. There are also other properties affected by physical distance. Radiation intensity and gravitational pull to name two. If we are truly at just 1 kilometre distance from a star if we accelerate to the appropriate velocity then if we believe in true space Lorentz contraction we will experience the star just as if it were 1 kilometre away in a non-accelerated situation. We would experience an extremely strong gravitational pull which would give us a “free” ride to the star with intense acceleration but unfortunately we wouldn’t be able to enjoy it for long because we would be fried by the intense radiation 1 kilometre above the surface of the star.

Lorenz contractions allow for shorter distances. The distances between objects are the same, when occuring in perception of the one moment.