A Conceptual Alternative to Spacetime

[jedaisoul]

Note: For reasons that will become self–evident, I have split this post into three parts.

A Conceptual Alternative to Spacetime – Part 1


Introduction

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.

I would direct anyone who is not familiar with this form of relativity to Wikipedia, which contains an article entitled “Galilean Invariance”.

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 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. 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…

[jedaisoul]

A Conceptual Alternative to Spacetime – Part 2


A Thought Experiment on Newtonian Relativity (continued...)

Let’s 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.

Note: You may have noticed that the Doppler effect has not been mentioned. It is true that 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.

[jedaisoul]

A Conceptual Alternative to Spacetime – Part 3


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 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 generally 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 add as an axiom that time is not a dimension, at least, not in the same sense that the spatial ones are.

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. Let’s take this idea, but instead of attributing the effect to the relative motions of the frames of reference, let us assume that it is an inherent property of macro objects. The significance of this may not be immediately apparent, so let’s put it 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? It is undefined. 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 its 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.

For convenience we may refer to this concept of the universe as simultaneity-time, but that is not intended to be interpreted as an actual physical entity. It is merely a metaphor. The “spatial” dimensions of the continuum are properties of the macro objects which are not in space but rather define it. So space is a property of the macro objects and has no objective existence. Similarly, time, if it exists as an objective reality, exists only as the present. The past and the future are purely abstract concepts.

It follows 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. This might explain why the velocity of light and the velocities of the source and receiver do not add; they are conceptually different entities.


Conclusion

I hope I have shown that it is theoretically possible to incorporate the known behaviour of light in an otherwise Newtonian environment. This leads to the question of how could we tell whether the universe is actually a simultaneity-time or a spacetime continuum? Well, in principle, using the Lorentz transformation, the time dilation and spatial contraction effects are real, i.e. they affect the actual passage of time and spatial distances. Whereas the effects of this scenario are apparent, i.e.as they only affecting the view of distant objects. So in theory it should be possible to distinguish them. However, the practicality of performing an experiment with macro objects to determine which scenario corresponds more closely to reality is another matter...

[Rade]

Suppose two moments, A and B. That which is intermediate between two moments is time, thus A-------------B and the (...---...) = time. Now suppose a third moment C such that A--------------B------C. So we see how time now has three realities (1) that which is intermediate between A & B, (2) that which is intermediate between B & C, and (3) that which is intermediate between A & C. Moment B is within the real past of moment C and in the real future of moment A, so I think I do not agree with your comment above that ..."the past and future are purely abstract concepts"...

[jedaisoul]

Originally Posted by Rade

Suppose two moments, A and B. That which is intermediate between two moments is time, thus A-------------B and the (...---...) = time. Now suppose a third moment C such that A--------------B------C. So we see how time now has three realities (1) that which is intermediate between A & B, (2) that which is intermediate between B & C, and (3) that which is intermediate between A & C. Moment B is within the real past of moment C and in the real future of moment A, so I think I do not agree with your comment above that ..."the past and future are purely abstract concepts"...

Firstly, thanks for your comment. I was worried that no one was going to bother to address the issue!

I think that it is important to distinguish between time itself and our scientific models of it. As far as I'm aware, all scientific models that deal with time treat it as a dimension. To me this seems unavoidable. Even Newtonian mechanics does so. In a given scenario, you can run time forwards and predict the results of an action. You can also take the results and run time backwards to determine the cause. We are so used to this that it is very easy to mistake the model for the reality it describes.

I would suggest that there are three spatial dimensions in which objects freely interact. So the gravitational forces acting on any body is the sum total of the gravitational attraction of every other object in the universe. That is an awesome concept, but I think it is true. However, the gravitational forces that affect a body at one instant are the gravitational forces acting at that time. Not the forces acting throughout time. This is a vital difference. If the past and furture materially existed, then the gravitational forces acting at a time in the past (or future) would affect an object now. That is blatantly not the case, otherwise Newtonian mechanics would have to take it into account. It doesn't and they don't.

So, returning to your comments, I would suggest that time is a sequence of instants "now". The time A is one instant. The time B is another, as are all the instants between. But they do not coexist. They are a sequence of discrete instants, only one of which exists at any time. That is why I suggest that time is not a dimension, at least, not in the same sense as the spatial ones.

So although Special and General Relativity, and Newtonian mechanics, unavoidably treat time as a dimension, it is important to distinguish these abstract models of the universe from the reality they describe. As they say "the map is not the territory".

[Rade]

Originally Posted by jedaisoul

Firstly, thanks for your comment. I was worried that no one was going to bother to address the issue!

Your welcome.

Originally Posted by jedaisoul

I would suggest that time is a sequence of instants "now". The time A is one instant. The time B is another, as are all the instants between. But they do not coexist. They are a sequence of discrete instants, only one of which exists at any time.

First, I agree with you that time is not a dimension like space, for me, time is a “type of number”. Time = the measure of the number of movement in respect of the before and after, and it is continuous since it is an attribute of what is continuous. But I do not agree with you that time is a sequence of discrete instants (of "nows"). What I present is from my understanding of Aristotle who had lots to say about time and space and motion.

Some definitions:

(1) continuous = things having extremities as one, so if a = extremity of A and b = extremity of B then a picture of continuous is: { (A…..(ab)…..B)}; continuous things can be divided, but are not formed by things that can be divided.
(2) in contact = things having extremities that are together: {(A…..a)|(b…..B)} and allow something (|) of their own kind to be intermediate between them, such as another A or B; where | = <A or B>.
(3) in succession = things having extremities where there is nothing of their own kind intermediate between them { (A…..a)|(b…..B), but some other thing C may be between them, where | = <not A or B>.

So, given that time is a number that is continuous, it cannot be formed by a sequence of “nows” that are discrete and in contact or in succession, for that which is continuous cannot be formed by units that can be divided. What you call "the one instant" or "the now" is not within "time". Each “now” is the limit of some time (t1) as it ends (A…..a-- forming one (ab) as the limit of some time (t2) as it begins--b…..B)

Next, as to gravitation force between two bodies, say X and Y, this is how I view their relation to "time" and the "now". The measure of the "number of the movement" caused by the gravitational force between X and Y is = "time", while the "now" corresponds to the moving masses of X and Y.

Suppose we have an interacting gravitational system {X <---gravitation force --->Y} at some moment M1. Then, at that instant (M1), our concept of the "now" = measure of masses of X and Y, while our concept of time = the measure of the "number of gravitational movement" of X relative to Y. Thus, to say that {X<---gravitation force --->Y} is "to be in time", what this means (to me), is to say that the identity of X and Y at M1, as things that exist and feel the force of gravity, is confirmed because their movement at M1, relative to each other, is being measured by time. Thus, I would say that time gives identity to existence . That is, while it is true that the map is not the territory, the territory (the metaphysical given) is mapped (given identity in human mind) by time.

Finally, as to "space-time", I view time to be that which is intermediate between moments, and space to be that which is intermediate between existents, thus "space-time" = that which is intermediate between moments of existents. So, from your discussion above, photons (imo, this is how I see it), because they have no mass and are not existents, are within "space-time", and all things with mass, are within "moments". If nothing else, you have to at least agree I have an active imagination, and I am interested to read where you (or anyone on the forum) disagree with what I say, and why.

[jedaisoul]

Originally Posted by Rade

First, I agree with you that time is not a dimension like space

Good.

Originally Posted by Rade

for me, time is a “type of number”.

Numbers are abstract, they do not materially exist. If you accept that the universe materially exists, how could time be an abstract concept?

Originally Posted by Rade

Time = the measure of the number of movement in respect of the before and after, and it is continuous since it is an attribute of what is continuous.

I would suggest that it is important to distinguish between time itself and the measurement of the passage of time. The measurement of the passage of time requires motion (or at least change). But the universe (and hence time) exists whether or not there is any motion against which the passage of time can be measured.

Originally Posted by Rade

But I do not agree with you that time is a sequence of discrete instants (of "nows"). What I present is from my understanding of Aristotle who had lots to say about time and space and motion...

The scientific view of time and space has moved on since Aristotle. There is a unit of time, the Planck time, which is the time taken for a ray of light in vacuo to move a Planck length. The Plank time is indivisible. It is the shortest length of time that can exist. Similarly the Planck length is the shortest distance that can exist. Those are not my opinions, thats mainstream science. Putting it another way, if "now" was an infinitely short period of time in a continuous stream, how could change happen? Surely it takes time for the minuest possible change to happen? That time is the Planck time.

Originally Posted by Rade

Next, as to gravitation force between two bodies, say X and Y, this is how I view their relation to "time" and the "now". The measure of the "number of the movement" caused by the gravitational force between X and Y is = "time", while the "now" corresponds to the moving masses of X and Y.

Again, you seem to be talking about the measurement of change, not time itself.

Originally Posted by Rade

Finally, as to "space-time", I view time to be that which is intermediate between moments, and space to be that which is intermediate between existents, thus "space-time" = that which is intermediate between moments of existents. So, from your discussion above, photons (imo, this is how I see it), because they have no mass and are not existents, are within "space-time", and all things with mass, are within "moments".

I can't really comment on this as I'm not sure of the meaning you are using for the word "existents". Photons most definitely exist physically. So I'd just ask: How does your scenario account for the fact that the velocity of light in a vacuum is fixed and finite irrespective of the velocity of the source and the observer? You can't just ignore it, it has been scientifically verified many times. The Lorentz transformation and the ideas put forwards in the OP are two ways of interpreting it, do you have a viable alternative?

Originally Posted by Rade

If nothing else, you have to at least agree I have an active imagination, and I am interested to read where you (or anyone on the forum) disagree with what I say, and why.

You certainly have a fertile imagination, but I would suggest that you need to read up about mainstream cosmology. There is a lot of useful stuff on Wikipedia.

[bobo69x11]

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