A Conceptual Alternative to Spacetime – Part 1
Minkowski interpreted time as a component of spacetime, in which it is comparable to the spatial dimensions. When applied to Einsteinian relativity, this allows the passage of time to differ for objects in different frames of reference, due to the Lorentz transformation. This is fundamental to both Special and General Relativity. One conclusion that may be drawn from this is that the description “now” can refer to any time in the past, present or future, as they are equally real. From a philosophic perspective, I find that view to be perplexing. However, I acknowledge that it is unavoidable within that context.
I therefore sought an alternative conceptual framework. The logical place to start was with Newtonian Relativity, as this preceded the Einsteinian form. Newtonian Relativity (which is also referred to as Galilean Invariance) was originated by Galileo. In this scenario:
- The relationships between frames of reference is defined by the Galilean Transformation (as opposed to the Lorentz Transformation of Special Relativity).
- There is no time dilation, nor spatial contraction.
- The existence of a physical space in which material objects exist is presumed.
However, Newtonian Relativity, alone, is not viable as an alternative to Special Relativity (SR). This is because it was defined before the discovery that the velocity of light is unaffected by the relative motion of the source and receiver. Thus it is less accurate than SR as a description of the behaviour of objects moving at near-light velocities. So I decided to investigate the possibility of incorporating the invariance of the velocity of light in an otherwise Newtonian environment. I did this by means of a thought experiment...
A Thought Experiment on Newtonian Relativity
In a region of space far away from other material objects there is a radio transmitter and two girls, Alice and Betty. The transmitter emits four time signals per second. Each girl has a device capable of displaying the time signals as they are received. At 10:00:00am the transmitter sends the time “10:00:00.00”. Alice and Betty have synchronized clocks co-located with them, but as there is no time dilation in this scenario, they always indicate the same time as the transmitter.
Alice is at rest with respect to the transmitter and 4 light seconds distant from it. So the time displayed on her device is always 4 seconds behind the actual time (as displayed on her clock). I.e. At 10:00:00 her device displays “09:59:56.00”. At 10:00:04 her device will display “10:00:00.00”, at 10:00:05 it will display “10:00:01.00”, and so on…
10:00:00.00_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _<-Betty Transmitter_ _ _ _ _ _ _ _ _ _ _ _ _ _ _Alice "09:59:56.00" 0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l secAt 10:00:00 Betty is 5 light seconds distant from the transmitter and approaching it at 0.2c. So in 5 seconds time (at 10:00:05) she will have travelled 1 light second and be adjacent to Alice. You might therefore expect that at 10:00:05 she too would receive the time signal “10:00:01.00”. However, Betty's observations require a little more thought. In her rest frame of reference, she is stationary and the transmitter is approaching her at 0.2c. At 10:00:00, when it is 5 light seconds distant from her, the transmitter emits the time signal "10:00:00.00" and continues on its way. The time signal approaches her at the velocity of light, so Betty will receive the time signal “10:00:00.00” at 10:00:05.
10:00:05.00_ _ _ _ _ _ _ _ _ _ _ _ _ _<-Betty "10:00:00.00" Transmitter_ _ _ _ _ _ _ _ _ _ _ _ _ _ _Alice "10:00:01.00" 0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l secSo at 10:00:05, even though they are adjacent, Alice (stationary in the frame of reference of the transmitter) receives the time signal "10:00:01.00" and Betty (stationary in her own rest frame) receives the time signal "10:00:00.00". Furthermore, Betty, will see Alice’s device displaying “10:00:01.00”, and Alice will see Betty’s device displaying “10:00:00.00”. Also, as five seconds have passed since the time signal “10:00:00.00” was transmitted, both their clocks will display “10:00:05.00”. So there is no discrepancy in how much time has actually passed for Alice and Betty (as indicated by their clocks), but the time signals received on adjacent devices from a distant transmitter are out of sync.
At this point you may be thinking “that cannot be”. If we imagine light as a particle or wave travelling through space, then when the girls are adjacent, they should receive the same time signal. It could therefore be argued that the prediction of the thought experiment is a paradox. If so, it invalidates the thought experiment. Which would leave us back where we started; with the current interpretation of spacetime as the only viable model. That is a perfectly legitimate argument, but if we pursue the model a little further, I hope to show that there is an alternative interpretation…