Explaining without using the Lorentz contraction:

The number of Earth years needed to get to Zakstar is 10^9/ v where v is the speed of the rocket. Divide by the time dilation factor to get to rocket years (equal to multiplying by the square root of (1 – v^2). We take units where c is 1 (light years per year). So 10^9 * sqrt( 1 – v^2) = 1 or
10^18 * (1 – v^2) = 1. Solving this gives the required answer. This speed is just about 1 billionth of a meter less than the speed of light.

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

Here is the point: we have discovered that simultaneity differs for people depending on their relative movement and the next thing we do is to go on to use a measurement technique that precisely makes use of the concept of simultaneity?. Worse yet, we even stop using the technique that we were already using to measure length which involved no simultaneity for the stationary train even though it can be perfectly validly extended to moving trains. In the stationary case, George walks past the front (or the back) of the train and as he passes the front (or back) he attaches the tape measure to the front (or back) of the train and reads of the value as he passes the back (or front) of the train. If the train is moving (assume towards him) he can carry out the identical measurement as he walks past the front (or the back) of train as he passes the front (or back) he attaches the tape measure to the front (or back) of the train and reads of the value as he passes the back (or front) of the train. Does anyone doubt that the value he reads off his identical whether the train is moving or not?

From a physics viewpoint it simply does not make sense to replace what we believe is a perfectly good measurement technique which gives the same value whether the train is moving or not with respect to the measurer with a different technique that does not. There is no reason, as a thought experiment , that if we have clocks and rods that we cannot also have measuring tapes (even if they are hundreds of light years long).

That measurement techniques involving relativity of simultaneity gives weird results is clear but it is nonsensical to ascribe these results to actual properties of space: simply use a measurement technique that is invariant to movement such as the measuring tape.

Moving objects appear or are measured to be shorter along the direction of motion only if a time dependent measurement technique is used.
“The notion of length itself requires simultaneity.” I disagree with this. You can measure length using other time independent methods. These do not require simultaneity.

Moving objects appear or are measured to be shorten along the. direction of motion only if a time dependent measurement technique is used.

There is no question that if Gracie uses the measurement method in question – which involves time – she will measure a different (shorter) length than George. Greene goes on to state that space itself is contracting in the direction of motion “space is adjusting for time” as Greene puts it. The (undiscussed) assumption here is is that a time-dependent measurement method continues to remain valid when relative motion is involved. It is by no means the case that Gracie has to use a time-dependent measurement method. For example, she could have set up a series of light beams projecting over the track, one every 10 cm for the length of the platform, as the train passes by a counter records the number of light beams being blocked by the train. This will initially be zero and then start climbing as the train blocks more and more light beams reaching some maximum value and then decreasing as the train starts pulling past the station (I am assuming here that the train is shorter than the station platform) finally falling back to zero as the train leaves the station completely. Gracie can simply read off the maximum value to determine the length of the train.

The length value Gracie measures will be the same as George’s. No Lorentz contraction takes place and space does not have “to adjust to time”. Just as with the time-dependent measurement method, the measurement is made from the platform. So if Gracie has two measurement methods available which give different results (outside of experimental error) can we consider both methods to be measuring the same thing if they are applied under the same circumstances? The time independent method described above will measure what is called the “proper” or “rest” length but what is the time dependent measurement actually measuring?

There is a lot of discussion about what Loentz contraction really is, with a significant group claiming that actual contraction of distance takes place (it is a space-like phenonemon) and another significant group stating that what is really happening (and being described) is that time dilation is taking place (it is a time-like phenomenon).

Speed = Distance/Time is something everyone agrees on. What is apparently up for grabs is whether it is valid to invert the expression in order to define distance as Distance = Speed x Time or whether this inversion breaks down in a relativistic context where time is dilating.

If it really is distance 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 distance (that is, it is a space like phenomenon and not a time-like phenomenon) 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. I do not accept that this is possible so I do not accept that length contraction equates to physical distance shortening.

There are also other properties affected by (true) distance. Radiation intensity and gravitational pull to name two. If we are truly at just 1 mile distance from a star if we accelerate to the appropriate velocity then if we believe the space-like interpretation of Lorentz contraction we will experience the star just as if it were 1 mile away in a non-accelerated situation. We would be both fried and experience an extremely strongly gravitational pull.

Note that the apparent size phenomenon is not the same as magnification. A space-like interpretation of the Lorentz contraction postulates that at the right velocity (very close to light) the distance will really be one mile and the observer (in the rocket presumably) will observe exactly the same thing as we would here on Earth if the star were 1 mile away. Magnification presents resolution issues which do not play a role in the apparent size case. If resolution issues are raised to prevent being able to see the star up close then the Lorentz contraction cannot be true distance shortening.

In my view, Lorentz contraction is a (highly) useful mathematical method for manipulating time dilation (which is a real physical phenomenon) but the Lorentz contraction does not result in actual shortening of the physical distance. Objects and distances do not physically shrink (in the direction of motion or any other direction), a photon is not “everywhere in the universe” and we cannot define Distance to be Speed x Time in a relativistic context.

Since we haven’t bothered to try to define what “past” and “future” is then we all using our own (and possibly) different interpretations of those concepts which can bring us to different conclusions/insights. I would propose that the concepts of past and future need to be tied to the concept of causality. Events that have occurred that can affect what I am doing now can be said to be in the past. Events that can be affected by what I am doing now can be considered to be in the future.