Synopsis
A thought experiment is used to investigate the effects of the invariance of the velocity of light in a Newtonian environment. This reveals an apparent inconsistency, in that two observers can receive different time signals from a distant transmitter, even though they are adjacent at that moment. The inconsistency is resolved by adopting a novel conceptual framework, a simultaneity-time continuum, in which the physical relationships between macroscopic objects remain Newtonian but the observed relationships can, and will, differ.
Introduction
Galilean Invariance (which is also referred to as Newtonian Relativity) is a form of relativity that 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.
I would direct anyone who is not familiar with this form of relativity to Wikipedia, which contains an article called “Galilean Invariance”.
Special Relativity is regarded as a more accurate description of the behaviour of objects moving at near-light velocities, but Newtonian Relativity is sufficiently accurate for most practical purposes, and is easier to use. However, Newtonian Relativity pre-dated the discovery that the velocity of light is unaffected by the relative motion of the source and receiver. I therefore decided to use a thought experiment to examine the effects the invariance of the velocity of light would have in a Newtonian environment. I.e. if you do not introduce the concepts of time dilation and spatial contraction of Special Relativity.
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 synchronised 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 sec
At 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 sec
So 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. We will come back to that. For the moment, we will re-run the experiment, starting again at 10:00:00. This time, moments before they are adjacent, both girls step sideways such that at 10:00:05 each is at the exact position occupied by the other in the first experiment.
10:00:05.00_ _ _ _ _ _ _ _ _ _ _ _ _ _ _Alice "10:00:01.00"
Transmitter_ _ _ _ _ _ _ _ _ _ _ _ _ _<-Betty "10:00:00.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
The small transverse movements should have no effect on when the girls receive the time signals, so Alice’s device will still show “10:00:01” whilst Betty’s will show “10:00:00”. The girls are at the exact positions occupied by each other in the first run, yet each still receives the time signals according to their own relationship to the transmitter.
Also, if we assume that the girls could see the transmitter, at 10:00:05 Alice would see it as being 4 light seconds distant, whilst Betty would see it as being 5 light seconds distant. Is there an actual difference in the distance? No. The girls see the transmitter as being at different distances because they are seeing it where it was (with respect to themselves) when the light that each receives was emitted. So even though the actual physical relationships are unaffected, the apparent relationships to a distant object can, and will, differ.
We can describe this effect more fully by using a sequence of “snapshots”. For brevity, I will refer to Alice, Betty and the Transmitter as A, B and T. The actual time at which each “snapshot” is taken is shown on the left. This matches the time signal emitted by the transmitter at that moment, and the times displayed on Alice and Betty’s clocks. For clarity, Betty’s distance from the transmitter is given in brackets after the time. The time displayed on the receiving devices is shown in quotes against the respective observer.
If at 10:00:00.00 Betty was 5 light seconds distant from the transmitter, then 1.25 seconds earlier (at 09:59:58.75) she was 1.25 x 0.2 light seconds further away. I.e. 5.25 light seconds distant. Therefore she will receive the time signal “09:59:58.75” 5.25 seconds later, at 10:00:04. At that time (10:00:04) she is 5.25 x 0.2 light seconds nearer than at 09:59:58.75, ie. 5.25 - 1.05 = 4.2 light seconds distant from the transmitter. Whereas, at 10:00:04, Alice receives the time signal “10:00:00.00” and remains 4 light seconds distant from the transmitter.
10:00:04.00 (4.2)_ _ _ _ _ _ _ _ _ _ _ _<-B "09:59:58.75"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:00.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
Using this logic, we can work back to the time signal that Betty received at 10:00:00 when she was 5.0 light seconds distant. However, there is an easier way to work out the steps. Alice receives 4 time signals per second, because that is the frequency they are emitted at and she is stationary with respect to the transmitter. However, Betty, because of her relative velocity, receives 5 time signals per second. Also Betty moves 0.2 light seconds nearer the transmitter. This is a linear relationship, So we can work back second by second deducting 1 second from the time displayed by Alice’s device, and 1.25 seconds from the time displayed on Betty’s device, and adding 0.2 light seconds to her distance. Thus we determine that at 10:00:00 Betty’s device displayed “09:59:53.75” when she was 5 light seconds distant from the transmitter. The complete sequence is:
10:00:00.00 (5.0)_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _<-B "09:59:53.75"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "09:59:56.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:01.00 (4.8)_ _ _ _ _ _ _ _ _ _ _ _ _ _ _<-B "09:59:55.00"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "09:59:57.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:02.00 (4.6)_ _ _ _ _ _ _ _ _ _ _ _ _ _<-B "09:59:56.25"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "09:59:58.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:03.00 (4.4)_ _ _ _ _ _ _ _ _ _ _ _ _<-B "09:59:57.50"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "09:59:59.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:04.00 (4.2)_ _ _ _ _ _ _ _ _ _ _ _<-B "09:59:58.75"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:00.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:05.00 (4.0)_ _ _ _ _ _ _ _ _ _ _<-B "10:00:00.00"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:01.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
Similarly, we can project forwards by adding 1 second to Alice‘s display, 1.25 seconds to Betty‘s display, and deducting 0.2 light seconds from Betty’s distance from the transmitter. Thus at 10:00:09 both devices display “10:00:05.00” (the time when the girls were adjacent):
10:00:06.00 (3.8)_ _ _ _ _ _ _ _ _ _<-B "10:00:01.25"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:02.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:07.00 (3.6)_ _ _ _ _ _ _ _ _<-B "10:00:02.50"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:03.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:08.00 (3.4)_ _ _ _ _ _ _ _<-B "10:00:03.75"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:04.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
10:00:09.00 (3.2)_ _ _ _ _ _ _<-B "10:00:05.00"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:05.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
Similarly, at 10:00:25 Betty arrives at the transmitter, and her device (not surprisingly) shows “10:00:25.00”. Betty’s device shows “10:00:21.00”.
10:00:25.00 (0.0)
B "10:00:25.00"
T_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _A "10:00:21.00"
0_ _ _ _ _1_ _ _ _ _2_ _ _ _ _3_ _ _ _ _4_ _ _ _ _5 l sec
We have followed Betty’s progress over a 25 second period. The timings of her receipt of the time signals follow a consistent pattern. The only apparent illogicality is that, when the girls are adjacent, they receive different time signals. If this is correct, then we can draw an important conclusion from these results:
As was mentioned earlier, if space were a physical entity, these results could not arise. Light would travel at a fixed velocity with respect to space, and when the girls were adjacent they would receive the same time signal. This suggest that, in this scenario, space does not exist as a physical entity, at least, so far as light is concerned. Yet it is fundamental to Newtonian mechanics that material objects behave as if space exists physically. We will deal with this apparent contradiction in the next section…
Note: You may have noticed that the Doppler effect has not been mentioned. Because of her relative velocity, Betty will see the time signals as being Doppler shifted. However, that does not affect the times encoded in the signals, nor when they will be received. Therefore, the Doppler effect can be ignored for these purposes.
A Simultaneity-Time Framework for Cosmology
The problem identified with the invariance of the velocity of light in a Newtonian scenario is that two observers can receive different time signals from a distant transmitter, even though they are adjacent at that moment. Furthermore, when the experiment is re-run and the observers swap places, they still receive the time signals related to their own relationship to the transmitter. If you regard space as a physical entity, and light as particles or waves travelling through that space, then this is impossible. It simply could not happen.
So how do we resolve this? Well, if material objects behave as if space exists as a physical entity, but light behaves as if it isn’t, then it’s as if there are two different universes that interact and affect one another. I say as if because I do not mean to imply that this is actually the case. Merely that the universe appears to be different to different types of entities. Hence the nature of the actual universe (according to this scenario) must support both views.
I would also add as axioms that:
The universe obeys causality.
The past, present and future do not co-exist. Time is not a dimension, at least, not in the same sense that the spatial ones are.
Note: Every scientific model of the universe (that I am aware of) treats time as a dimension. This is necessary if we are to model change, cause and effect, and the way that entities interact. This does not invalidate the models, but it is important to recognise that this feature of a model may have no corollary in the actual universe.
Also, I propose to focus on two classes of entities:
Massless entities that can travel at the velocity of light, and whose velocity is unaffected by the relative velocity of the source and the observer. For brevity I refer specifically to photons.
Macroscopic objects that have mass, cannot travel at the velocity of light, and whose velocity is affected by the relative velocity of the source (if any) and the observer. For brevity I refer to “macro objects”.
So how do we put together a framework for a cosmology that meets these criteria? Well, firstly, if space does not exist as a physical entity in the universe experienced by photons, then it cannot exist in the actual universe. But if that is so, what meaning can we attribute to spatial distances, and what causes the delay between photons being emitted by one object and being received by another? It cannot be the time taken for the photon to “travel” through space from one to the other, as space does not exist to photons in this scenario.
We can resolve this by adapting an idea suggested by Einstein; that of differences in simultaneity. Einstein suggested that simultaneity was dependent on the frame of reference. I.e. That two events which are simultaneous when seen from one frame of reference may not be so from a different frame of reference. Lets take this idea, but instead of attributing the effect to the relative motions of the frames of reference, what if it is an inherent property of macro objects?
Putting this another way… Conventionally we would say that where an object is determines when it experiences events. But if space does not actually exist, what determines where an object is? So, instead, let us reverse this causal relationship and state that when an object experiences events determines where it is. Thus we may say that if there is a delay of five seconds between the emission of light by one body, and it’s reception by another, it is because there is five seconds difference in their view of when that event occurred, I.e. their view of simultaneity differs by five seconds. So we may say that those two objects are five light seconds apart, which, using c, translates into a spatial distance of one and a half million kilometres (or thereabouts).
Of course space is not one dimensional, it is three dimensional, and this suggests that the differences in simultaneity are three dimensional. This does not explain why space is three dimensional, it merely acknowledges that it is. Put simply, if this were not so, the universe would not be as it is. So instead of a space-time universe, we end up with a simultaneity-time universe which macro objects experience in a Newtonian manner, but photons experience in a quite different way.
Furthermore, this suggests that, rather than being a velocity, c is an universal constant that links a difference in simultaneity between two macro objects to the physical distance between them. Which might explain why the velocity of light and the velocities of the source and receiver do not add.
Thus we can reconcile the invariance of the velocity of light with Newtonian Relativity by adopting a simultaneity-time framework for cosmology.
This leads to the question of whether the universe might actually be a simultaneity-time continuum? How could we tell? Well, in principle, the time dilation and spatial contraction effects of Special Relativity are real (affecting the actual passage of time and spatial distances), whereas the effects of this scenario are apparent (only affecting the view of distant objects). However, the practicality of performing an experiment with macro objects to determine which scenario corresponds more closely to reality is another matter. Which is why at the moment, this is just an interesting idea. At least, I hope that, if you have read this far, you found it interesting.