Thinking Straight About Curved Space

[Scott Mayers]

In reality the best map coincides with the reality itself.

To say the curvature of spacetime is just a perspective which could be removed by adding a dimension, is to ignore the fact that we are physical beings 'embedded' in three space and one time dimensions. What we measure with our meter sticks and clocks is the 4-D spacetime. The curvature or otherwise of this spacetime is then a question which can be determined empirically and has been by experiments such as gravitational redshifts, gravitational lensing, and the direct determinations of the rates of atomic clocks in different gravitational fields (differential aging of twins in different gravity). In the latter experiments the clocks start off together and are identical, they are then moved to locations with different gravitational fields and later are brought back together. The clock in the higher gravitational field actually ages less than the other in accordance with the general theory of relativity.

I'm not sure what you're interpreting upon me here. I already interpret the spacetime in a similar way as Einstein with regards to the geometric descriptions. It is the particular relationship to reality that I question. It is the interpretations of the maps, not the maps themselves.

I can prove the trouble with these interpretations easily. They do NOT dismiss the results of the findings of the experiments. The experiments err in their presumption that they uniquely support certain past scientists' views. I'm aware of the experiments you mentioned. But these still follow on a different interpretation of my own. I gave one such example to Obvious Leo in "Does Science have limitations?". There, for example, I showed how the it is an error to assume that you really CAN determine whether you are in an elevator or not. One such means is to measure the damage done to the device, like a clock, or a person who has traveled in these different realms. The one traveling in a vector direction moves through an real absolute space and is subject to more radiation than one merely accelerating as they move through the background only at the speed of Earth rotation, the speed of the Earth going around the sun, etc. One accelerating away from Earth is thrust through this. The age factor still appears true of a clock or person, but this slow down of apparent time is actually due to the very fact that all atom of each thing measuring something in acceleration or fixed velocity through space moves through this background limiting the actual potential of these things to function in the same way as the Earth. That is, time itself does not slow down, only the perception of it. This mistake interprets space itself as unfixed or relative. My example demonstrates the error.

[Obvious Leo]

My example demonstrates the error.

No it doesn't. You merely substitute the geometric aether with the Lorentz aether which spacetime was intended to supersede. Both leave physics with a non-mechanical explanation for gravity.

[nix]

The age factor still appears true of a clock or person... (but), time itself does not slow down, only the perception of it.

You admit that the twins age at different rates, (that is the proper time for each twin differs between the moment when they are initially together until they are finally together), but you then maintain there is some sort of absolute time applicable to both twins, even though all physical indicators of time's passage are different for the two twins.

By the term 'my perception of time' I take it you mean 'the time measured on my clock'. So perceived time is time measured on a clock at rest with respect to the perceiver. Where is the absolute 'time itself ' measured? In an frame of reference at absolute rest? But the whole point of relativity was to show that such absolute frames of reference were redundant and in fact physically meaningless.

You suggest that you really can determine motion through absolute space by monitoring damage caused by cosmic radiation or some such. This is not so, all differential damage will tell you is the motion relative to the cosmic particles reference frame. You can imagine situations in which observer A on earth and B in the lift have exactly the same damage , or damage A<B , or A>B.

If by this example you meant that the equivalence principle is undermined by being able to say you are in a lift rather than stationary on earth by detecting differential damage well that is the same as say putting a window in the side of the lift and looking out at the fixed stars to tell you are moving. But that is to misunderstand the equivalence principle which says that the physics within a uniformly accelerated closed lift with no physical influences from outside are the same as the physics in a gravitational field.

[nix]

The one traveling in a vector direction moves through an real absolute space ...

The nearest thing to this "real absolute space" would be an inertial frame based on the fixed stars. But this whole space could be in uniform motion and we would not be able to detect it by any means, so the notion of absolute rest becomes redundant and with it the notion of absolute space. If we take the fixed star space as our 'absolute frame of reference' then there will be clocks and meter rulers in this frame which we might define as keeping the 'real absolute time' etc but it is no more 'absolute' than the proper times measured in any other frame in uniform motion with respect to the fixed stars.

[Scott Mayers]

nix,

If one does not 'age' this is only a misinterpretation of how one's chemistry has slowed down due to motion. This is no different than considering one who is cryogenically ''frozen". It may not be possible for us as humans but this can be done by certain other living things where they can go into hibernation, for instance. But just because the entity was frozen doesn't imply that time itself is a substantial thing that caused these things to preserve their youthfulness upon being unfrozen. Time still flowed in an objective sense (the background environment). Their age HAS increased with respect to that environment and "age" is defined only first from that environment, not its solipsistic interpretation of existing.

Einstein's explanation was intended to cooperate with the present understanding of the day regarding the aether. But while useful for most practical purposes, by abandoning a 'fixed' background, it contributes to how QM and Relativity conflict. It also begs that there is NO such background in reality. This raises a lot of problems when considering the 'age' of the universe. Taking Einstein's view, we should have then recognized that the determined 'age' of our universe is only an illusion of the observer. For instance, given the Big Bang as a 'fixed' point in time of the past should actually be reinterpreted as being infinite. This is because most supporting BB believe that nearer to the singularity, extreme quick inflation occurred. But this is true, then this period is akin to frames of acceleration that are faster than what we see now. Then why not recognize Einstein's Relativity as functioning there too? That is, if things moved absurdly quick back then, why has it not been interpreted as 'time' itself slowing down (from our perspective) the further back we go? So you can imagine an infinite regress such that time itself is always relative and thus, no big bang! This is an example of my concern here.

As an extended example, when we observe a quasar from great distances as appearing uniquely too intensely bright, why not interpret this as the effect of our perceiving a second's worth of our time in exposing a photo of these as actually being a much longer duration of time from the quasar's perspective that could have been say, a year's worth of light radiation, being compressed into our perception of it occurring in only a second? This would suggest that quasars are actually normal galaxies if we saw them up closer but only 'appear' different from our perspective!!

I believe that the errors in interpretation are due to scientists not remaining consistent with definitions. I propose redressing our past interpretations of observations and theories based on them to find better consistency across all sciences. Curved or warped spaces may seem 'simple' and accord with Occam's Razor but this is no different that how many have defaulted to using "God" as a simpler word to stand for "the unknown cause origin of the universe". It is how we use the same term to transfer across other meanings which presents confusion between ideas. If we don't redress these problems, we'll remain unable to solve the actual questions of our reality.

[Obvious Leo]

This is because most supporting BB believe that nearer to the singularity, extreme quick inflation occurred.

Try and keep up Scott. The singularity is so.. yesterday. Every theorist in the game knows that the GR field equations lose their applicability in proportion to gravitational field strength and thus the singularity is an unrealisable mathematical abstraction with no analogue in the real universe. Time had no beginning because it never bloody well stopped. From this perspective inflation is an unnecessary hypothesis.

If one does not 'age' this is only a misinterpretation of how one's chemistry has slowed down due to motion.

That inertial motion is indistinguishable from the "at rest" state has been common knowledge since Galileo so this statement can be applied to accelerated motion only.

So you can imagine an infinite regress such that time itself is always relative and thus, no big bang!

This makes more sense but it doesn't negate the big bang. It merely negates the big bang as the beginning of the universe. I prefer to think of the big bang as the little whimper, where the new cycle of the universe simply emerges in its own good time out of a universe-sized black hole, somewhat analogously to Hawking radiation.

This would suggest that quasars are actually normal galaxies if we saw them up closer but only 'appear' different from our perspective!!

This is plain daft. Quasars no longer exist. All we're observing is what galaxies used to be like. They have long since evolved into the same sort of galaxies as those which we observe closer by.

Curved or warped spaces may seem 'simple' and accord with Occam's Razor

They accord with no such thing. They accord with the chilling doctrine of logical positivism and nothing else. Curved and warped spaces are mathematical objects and not physical ones and thus are purely metaphorical.

[nix]

Time still flowed in an objective sense (the background environment). Their age HAS increased with respect to that environment and "age" is defined only first from that environment.

No! The point is that there is no 'background environment' where time absolute and uniform is ticking away: twin A is moving with respect to twin B and the age difference caused by his journey only depends on this relative motion, i.e it doesn't depend on referring A and Bs motion to a third 'absolute' frame. Your 'Lorenzian' view that the aging is somehow caused by physical drag on everything moving through absolute space (aether) would mean that the 'actual age' of A and of B could never be measured, because they both could be moving with respect to this absolute frame (so both their clocks run slow compared to the absolute time but by an undeterminable factor. Undeterminable because we cannot physically define the absolutely stationary frame of reference.)

All processes, mechanical, chemical, physical, biological ...of everything co moving with A all experience the same rate of time passing -what a surprising coincidence if the slowing of this rate is somehow physically caused by an interaction with 'aether' through which it is passing (why does it interact with everything in exactly the same way? nothing else we have ever experienced does). Rather this coincidence is something to do with our concept of absolute time being faulty.
This is why the aether idea was abandoned and we rethought our ideas of space and time to remove hypothetical and in principle unmeasureable quantities.

The time passed for A is just what he sees on his own clock (A's proper time), the time passed for B similarly (B's proper time). that isn't solipsism by the way because A's clock is not just his own body/mind it is everything physical co-moving with him including his wristwatch!

[nix]

It also begs [the question] that there is NO such background in reality.

You wish to retain an absolute frame of reference which the relativists abandon. I guess your question is "does such a frame exist in reality?". If in principle there is no empirical way to define such a frame then physicists would claim that it does not exist in reality. That is not so much question begging as defining what we mean by 'reality'.

[nix]

This raises a lot of problems when considering the 'age' of the universe. Taking Einstein's view, we should have then recognized that the determined 'age' of our universe is only an illusion of the observer.

I.e. Would different observers dotted around the universe come up with different ages for the universe? Interesting question.

Some thoughts: If the universe is homogeneous, as it appears to be on large scales, and as it is expanding with an expansion which is everywhere the same, (general relativity predicts this and experiment agrees) then aliens no matter where they were, making the same sort of observations Hubble made, would come to the same conclusions, and hence deduce the same age for the universe as we do, if they were also viewing the universe 'now'. What does that 'now' mean?: that is to assume that those aliens are at the same spacetime interval (dS) from the big bang as we are i.e by definition their total elapsed proper time since the big bang is then the same as ours.

imagine an odd case: the universe dotted with intelligent aliens since its beginning and located on each object we can see, and able to send us radio signals. Have them use Hubble's method to measure the age of the universe and send the answer out into space as a spherical radio transmission. What would we see today? each star in the night sky would come with an age signal from the aliens telling us how old the universe was and all the ages would be different depending on how far away the objects are away from us.

From a relativistic viewpoint we need to use General relativity to describe the expanding universe (special relativity will not do). To ask what is the age of the universe in this framework then is to ask for very specific calculations (see Wienberg 'Cosmology' p59-65) The age we get is not an illusion of the observer, it is a well defined clock time, identified as the proper time since the big bang occured for that observer. i.e. the time which would be read on a clock carried by the observer from the big bang until the observers now.

This is only a conceptual problem if you think there should be a true and absolute time which is the same throughout the universe, then it would make sense to ask that all observers should measure the same age if they make the measurement at the same instant. But this 'same instant' makes no sense because of the relativity of simultanaity for space separated events.

The age of the universe will depend on where you measure it from i.e will depend on the spacetime location of the observer, that only seems to be a problem because of a persistent illusion that there is a universal 'now' time separable from space. There isn't.

[nix]

when we observe a quasar from great distances as appearing uniquely too intensely bright, why not interpret this as the effect of our perceiving a second's worth of our time in exposing a photo of these as actually being a much longer duration of time from the quasar's perspective

No!
A quasar is a much more massive object than the earth, it is moving away from us at high velocity if it is a long distance from us. Both these factors contribute to a slowing of the rate of the quasars clock compared to our own. So suppose 1 quasar second corresponds to 10 earth seconds If the quasar emits n photons per second in its own rest frame we see an intensity n/10 per second. We see a diminished intensity not an increased intensity due to this time dilation effect.

[nix]

Curved and warped spaces are mathematical objects and not physical ones and thus are purely metaphorical.

Not so! 3-D curved space is a physical possibility as Riemann showed in the 1850s and Gauss attempted to measure here on earth. If the planet had been thirty million times more massive than it is Gauss would have detected the curvature of space with his physical measurements.

[nix]

extreme quick inflation occurred. But if this is true, then this period is akin to frames of acceleration that are faster than what we see now. Then why not recognize Einstein's Relativity as functioning there too? That is, if things moved absurdly quick back then, why has it not been interpreted as 'time' itself slowing down (from our perspective) the further back we go?

We do recognize General relativity functioning there! As you say time itself does slow down there (compared to clocks on earth now) and that is recognized. Classically the answer to the "what happened before the big bang?" question was that there was no before because time slowed down as we got near the big bang and stopped at the big bang. (I am aware of all the recent multiverse speculations and bubble universes which begin to offer a different perspective on this , but none are giving testable predictions yet).

So why isn't the age of the universe infinite?

Well imagine you are an immortal indestructible observer at a point in space where you are now with a nice indestructable clock (i-clock) at that point. Now rollback the expansion of the universe all the way back to the big bang following the point through space and time. If you could stand outside this universe and watch the earth point and the readings on the i-clock from the perspective of an absolute time and space frame, then you would see the i-clock running at all sorts of crazy rates, perhaps speeding up and slowing down and eventually taking forever to come to a halt at the big bang. So from the perspective of absolute space and time the universe would have an infinite age. Now imagine you are inside the universe riding with the i-clock. To you now that i-clock rate is perfectly regular, those times when it seemed to be running fast seem to be exactly the same as those times when it was going slow because all physical,chemical,biological etc processes occurring in objects stationary in the frame run at the same rate as the clock. Eventually the i-clock registers 13.8 billion years when we get back to the big bang. This is the age experienced by our observer and all physical stuff at rest in the observers frame. This is the physical age of the universe measured from the big bang to here and now on earth.

This example shows how the absolute time you want to hold onto, doesn't relate to anything physically meaningful.

[nix]

by abandoning a 'fixed' background, it contributes to how QM and Relativity conflict.

Not quite true: special relativity, which has abandoned the fixed background, is fully compatible with quantum mechanics and is the basis of quantum field theory. It is more to do with the curvature of spacetime (hence the presence of gravity) rather than spacetime itself that is the problem.

[Scott Mayers]

This is because most supporting BB believe that nearer to the singularity, extreme quick inflation occurred.

Try and keep up Scott. The singularity is so.. yesterday.

I'm not sure how you figure this the case. If it was, what would it mean to maintain a definitive 'age' of the Universe by the proponents? Big Bang theory implies an origin and this origin is the point at which they labeled it as the "singularity".

If one does not 'age' this is only a misinterpretation of how one's chemistry has slowed down due to motion.

That inertial motion is indistinguishable from the "at rest" state has been common knowledge since Galileo so this statement can be applied to accelerated motion only.

I'm not referencing Galilean Relativity here. I'm discussing Relativity of Einstein which merely adds the known factor of the fixed speed of light in both SR and GR to Newtonian physics. What Einstein's explanations in his thought experiments missed is the fact that the physics of the atom also must not go faster than the speed of light with respect to how we measured it from Earth. As such, there is a difference if we discuss the source of light we are measuring.

If the source of light is created by a bulb in the same frame, then and only then will the measure of the speed of light will be measured to be 'c'. However, if one were to measure light that came from sources outside of the craft one is either in constant velocity OR in acceleration, the measure of those sources from outside in various directions actually represent different speeds via Doppler. Before you accuse me of misunderstanding Doppler, I assure you that I do. If we measure Doppler from light sources within the same inertial or accelerating frames, the speed of this light IS constant even though we see shifts. However, if we accelerate from Earth, shifts from Doppler from sources external to the craft also represent you accelerating with respect to the sources of those electromagnetic waves. There you'd have to interpret the the change of Doppler from the time you begin accelerating to the time you measure it accelerating away as the actual speed of those sources as accelerating too.

What I think is misunderstood moreover is that with respect to SR, the only way you can interpret anything fairly is if this inertial frame is your origin. If you require acceleration to get there as we have to realistically, even if you stop accelerating, measuring in this velocity has to ignore the memory of those observers that they accelerated in order to interpret external sources of electromagnetic Doppler shifts as representative of hitting you at the same speed. As such, you can't even be sure whether Doppler Shifts from sources external to one's frame represents changes in the relative differences in the speed of light due to acceleration OR due to a constant velocity. We default to assuming Doppler as being constant with respect to our original frame without justice no matter which source it comes from. This is a mistake.

I don't want to answer further responses here until I'm certain you and nix follow this thus far because this is relevant to understand some of the other responses. I may have to create some illustrations to help clarify. So be patient with me as I need time to create them for here. Do you understand what I'm saying so far without illustration?

[Obvious Leo]

Curved and warped spaces are mathematical objects and not physical ones and thus are purely metaphorical.

Not so! 3-D curved space is a physical possibility as Riemann showed in the 1850s and Gauss attempted to measure here on earth. If the planet had been thirty million times more massive than it is Gauss would have detected the curvature of space with his physical measurements.

Do you know what the term "physical" means? What physical properties does empty space have which allow it to perform these miraculous feats? The so-called "curvature" of space is merely a metaphorical expression for the inconstant speed at which time passes and this is what Gauss would have been measuring on his super-massive planet. You commit the logical fallacy of conflating the map with the territory and thereby defend an action-at-distance paradigm.

So why isn't the age of the universe infinite?

How could it be otherwise without the assumption of an external causal agent? Can you name a single physicist of the modern era who continues to insist that the big bang was the beginning of the universe. In the absence of a singularity it simply couldn't have been because in the absence of a singularity time cannot stand still.

Well imagine you are an immortal indestructible observer at a point in space where you are now with a nice indestructable clock (i-clock) at that point. Now rollback the expansion of the universe all the way back to the big bang following the point through space and time. If you could stand outside this universe and watch the earth point and the readings on the i-clock from the perspective of an absolute time and space frame, then you would see the i-clock running at all sorts of crazy rates, perhaps speeding up and slowing down and eventually taking forever to come to a halt at the big bang. So from the perspective of absolute space and time the universe would have an infinite age. Now imagine you are inside the universe riding with the i-clock. To you now that i-clock rate is perfectly regular, those times when it seemed to be running fast seem to be exactly the same as those times when it was going slow because all physical,chemical,biological etc processes occurring in objects stationary in the frame run at the same rate as the clock. Eventually the i-clock registers 13.8 billion years when we get back to the big bang. This is the age experienced by our observer and all physical stuff at rest in the observers frame. This is the physical age of the universe measured from the big bang to here and now on earth.

This example shows how the absolute time you want to hold onto, doesn't relate to anything physically meaningful.

This all makes sense but don't forget that if you had Superman's eyes and could see 380,000 years past the CMBR you would not be watching the universe exploding from a point. You would see it vanishing back into a point. The observer observes reality in temporal reverse.

Not quite true: special relativity, which has abandoned the fixed background, is fully compatible with quantum mechanics and is the basis of quantum field theory.

Quite true. However SR is NOT compatible with GR and thus neither is QFT. That's what all the fuss is about and that's the reason why theoretical physics has made no progress in a century.

I'm not sure how you figure this the case. If it was, what would it mean to maintain a definitive 'age' of the Universe by the proponents? Big Bang theory implies an origin and this origin is the point at which they labeled it as the "singularity".

A universe with a beginning is a statement of BELIEF and not a scientific statement. It was the a priori assumption on which Newton based his entire "science" of physics but it is a metaphysical absurdity.

I'm not referencing Galilean Relativity here. I'm discussing Relativity of Einstein which merely adds the known factor of the fixed speed of light in both SR and GR to Newtonian physics.

Einsteinian relativity is an attempt to put lipstick on a pig because the speed of light cannot possibly be a constant. The reason why it cannot possibly be a constant is because it is OBSERVED TO BE a constant is all referential frames.

Do you understand what I'm saying so far without illustration?

I understand perfectly what you're saying because I've seen it all before. You are assuming that which you seek to establish.