[fisherman]

Ever since finding this site, I have had this nagging thought that there was something fundamentally wrong with the logic behind relying on the equivalence principle to justify UA, but couldn’t  quite put my finger on it.

I wasn’t thinking about people falling off a roof, but it finally dawned on me.  Special Relativity tells us that accelerated motion warps spacetime. The faster you go, the slower time moves and objects will contract.  The equivalence principle tells us that accelerated motion and gravity are indistinguishable.  The logical conclusion then is that gravity is the warping of spacetime.

Instead, the UA crowd concludes that the EP means there is some mysterious force that is accelerating the earth (and maybe, but maybe not, everything else.) upwards. 

I couldn’t find anything in the wiki that justifies this leap (no pun intended) in logic. Maybe if you took SR out of the equation, it would make some sense but that creates even more problems for UA.  Not to mention the fact that part of what makes the EP so important is that it serves a bridge between SR and GR so that SR is consistent with gravity.

Why should UA be considered a better theory for gravity when it doesn’t even logically follow from the very premise it is based on?  Not to mention the fact that it leaves so many questions unanswered that GR very elegantly solves.

[Tom Bishop]

Your statement "accelerated motion warps spacetime" doesn't make much sense on its own. How is spacetime warped exactly? Can you describe it in a step-by-step physical manner instead of using it as a magic wand?

The effect of Time Dilation makes far more sense if you imagine a rocket accelerating:

https://books.google.com/books?id=t8O-yylU0j0C&lpg=PA7&ots=zD8YCKNu7M&pg=PA7#v=onepage&q&f=false

GRAVITATIONAL TIME DILATION

  “ Many of the important features of general relativity can be obtained via rather simple arguments that use the equivalence principle. The most famous of these is the thought experiment that leads to gravitational time dilation, illustrated in figure 1.1. Consider an accelerating frame. which is conventionally a rocket of height h, with a clock mounted on the roof that regularly disgorges photons towards the floor. If the rocket accelerates upwards at g, the floor acquires a speed v = gh / c in the time taken for a photon to travel from roof to floor. There will thus be a blueshift in the frequency of received photons, given by Δv / v = gh / c^2, and it is easy to see that the rate of reception of photons will increase by the same factor.

Now, since the rocket can be kept accelerating for as long as we like, and since photons cannot be stockpiled anywhere, the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor. Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect. Noting that ΔΦ = gh is the difference in potential between roof and floor, it is simple to generalize this to Δt / t = ΔΦ / c^2 ”



“ Figure 1.1. Imagine you are in a box in free space far from any source of gravitation. If the box is made to accelerate ‘upwards’ and has a clock that emits a photon every second mounted on its roof, it is easy to see that you will receive photons more rapidly once the box accelerates (imagine yourself running into the line of oncoming photons). Now, according to the equivalence principle, the situation is exactly equivalent to the second picture in which the box sits at rest on the surface of the Earth. Since there is nowhere for the excess photons to accumulate, the conclusion has to be that clocks above us in a gravitational field run fast. ”

--

See the bolded above. If you imagine yourself accelerating into the line of oncoming photons it is apparent that physical acceleration would cause the time from the clock to appear to dilate. This is a physical explanation for why acceleration would cause time dilation, and also for why photons are blueshifted or redshifted when traveling horizontally upwards or downwards (Pound Rebka Experiment).

Can you give us a step-by-step physical explanation for how space-time is warped to do this?

[fisherman]

Your statement "accelerated motion warps spacetime" doesn't make much sense on its own. How is spacetime warped exactly? Can you describe it in a step-by-step physical manner instead of using it as a magic wand?

For someone who purports to have better insight into physics than every other actual physicist in the world, it seems like special relativity shouldn’t be something you would need explained to you.  But here goes anyway...highly simplified of course.

The essence of SR is that observers in relative motion to one another will have different perceptions of distance and time. Wristwatches worn by two different people in relative motion will move at different rates. Two people in motion relative to one another will not measure the same lengths using the same tape measure.  This is because if two people are moving relative to another, light takes longer to reach one person than the other.  Speed of light is constant, but it must travel different distances to reach each person.  The constant speed of light also effects the relativity of space because speed is distance divided by time.  If two observers don’t agree on speed or time, they aren’t going to agree on distance. Another related concept is that everything is always moving through time.  You can’t separate the two.  A parked car is moving through time only, but when it starts up and drives away, it also begins moving through space, so some of the energy directed to moving through time is diverted to moving it through space.  The faster it goes, more energy is diverted moving through space than time, so time begins to slow for the car.  It isn’t moving through time as fast as when it was parked.

This is essentially how acceleration “warps” spacetime.  The greater the relative velocity of the two observers, the more their observations of space and time will differ.  If the same spacetime is different for two different observers, it can be described as “warped” much the same way a piece of lumber is considered warped. If it doesn’t look straight and flat from every angle, it is warped.  If spacetime is experienced differently from different "angles" or frames of reference, it is warped.

That’s about as simple as I can make it.

Gravitational time dilation, in GR and time dilation in SR are two completely different concepts with different causes.(although they can occur at the same time, like with GPS satellites)  So as pretty as your illustrations are, they have nothing to do with how accelerated motion in SR warps space time.

[Tom Bishop]

The faster it goes, more energy is diverted moving through space than time, so time begins to slow for the car.  It isn’t moving through time as fast as when it was parked.

This is essentially how acceleration “warps” spacetime.

That is not a step-by-step physical explanation. You are just saying that it happens. You can't explain how it happens, or show direct evidence that it happens. You can only say that it happens. Your description involves the assumption of "space-time", where acceleration "diverts energy to space", "causing time to slow down," in an ad-hoc untestable explanation which does not have fundamental experimentation behind it.

How does acceleration "divert more energy to space than time" exactly? Why should that cause time to slow down? How does space "warp" and cause time to slow down when more acceleration energy is present exactly? You are introducing a lot of mechanistic questions there.

Is there a device we can buy to manipulate or see into spacetime to measure this energy, or is there a device which can manipulate and see into the fabric of space and how much it is bending? Or do we just have to take your word for it?

You can't show how we know that space is manipulated in this way. You can only claim this fanciful mechanism which has nearly zero direct supporting evidence. If you can't verify this spacetime mechanism by experiment, and can only claim it, then you may as well be invoking magic and mysticism to do this. Not to rain on your parade, but this mechanism is not as proven and demonstrated as other theories in science. We know how chemicals react because we can test them and manipulate them. The same can't be said about the manipulation of spacetime.

The scenario of being in an accelerating rocket and hitting a line of photons at an accelerating pace is a physical mechanism that we can understand from A to Z. What you proposed is no such explanation that we can understand with any clarity. It is not a physical mechanism because you can't test it or manipulate it by physical means. You can only say it. You can only invoke an allegedly hidden layer of reality that we can't touch or experiment with.

There is, indeed, basic fundamental experimentation showing that when you accelerate into objects they approach you at an accelerating pace. There is no basic fundamental experimentation which manipulates "space-time" to demonstrate the basis of your scenario, however.

[Bikini Polaris]

It is my understanding that UA plays along with SR. Gravity is a force in UA, like gravity from stars and planets, but that's very faint. UA states the surface we are on has a negligible gravity due to mass and the rest is just acceleration from an undefined force, which keeps pushing this "special" plane since the dawn of time. But on other planets, like Mars, gravity works as Einstein says.

[fisherman]

That is not a step-by-step physical explanation. You are just saying that it happens. You can't explain how it happens, or show direct evidence that it happens. You can only say that it happens. Your description involves the assumption of "space-time", where acceleration "diverts energy to space", "causing time to slow down," in an ad-hoc untestable explanation which does not have fundamental experimentation behind it.

I explained exactly how it works.  As the relative velocity between two observers increase, how each perceives time and space becomes increasingly different and more distorted.  Perhaps this analogy will help.

Imagine a cylindrical carnival ride that is rotating faster and faster and you are pinned to the perimeter.

Now imagine there is another passenger in the center of the cylinder.  Every time the ride rotates, you will travel the full circumference of the cylinder, but the person in the middle hardly moves.   If the ride is rotating fast enough, the person in the middle will observe  you contract in length and your wristwatch running slower because your velocities are different. The faster the ride goes, the the person in the middle will watch you get shorter and shorter and your watch get slower and slower.  With the increased acceleration, the “spacetime” inside of the ride becomes more and more distorted.

How does acceleration "divert more energy to space than time" exactly? Why should that cause time to slow down? How does space "warp" and cause time to slow down when more acceleration energy is present exactly? You are introducing a lot of mechanistic questions there.

 It works the same way that the relative speed between directions changes when you change directions. (IOW, when your velocity changes and you are, by definition, accelerating)  I know that’s not very well put, so here’s another analogy.

 If you’re speeding along going directly north at 65 mph and then merge onto the highway going northeast,(you've changed direction so you are accelerating) the speed that is moving you north will decrease as some of it is diverted to move you east.  You are going slower in the north direction and covering less ground "northward" than you were before you merged.

Now think of “speed” as the energy available to move a car through spacetime, let’s call it 65 newtons just to keep things consistent. “Time” is the north direction and space is the “east” direction.  If it’s sitting still, according to my analogy, it would be the same as a car moving a steady 65 mph directly north.  65 newtons of energy are being expended to move the car through time (north). When it starts up and begins moving, some of those newtons will have to be diverted to move it through space (east). Let’s say 50 newtons of the energy will move it through time and 15 newtons of energy would be moving it through space.  As the car begins to move faster and faster through space, more newtons will be expended moving it through space and less dedicated to time.   Just like our car, the more it turns in an easterly direction , more of its speed is dedicated to moving east and less to north .  The more of its speed  that is dedicated to moving it east (space), the more ground it covers in the east direction  and the less “ground” it covers in the north direction (time).  Covering less “ground” in time means time is moving slower.

If the car’s speed keeps increasing, then eventually all of the energy will be dedicated to moving through space and time will stop.  Just like if a car keeps increasing its easterly direction, eventually all of its speed is moving it in an east direction and it is no longer going north.

Slowing of time due to acceleration has been experimentally proven plenty of times, but if you want to deny the validity of SR, that’s fine by me.  You might want to update your wiki, though and find another explanation as to why an earth constantly accelerating at 1g doesn’t exceed the speed of light. Or maybe we are moving faster than c.  After all, UA isn’t based on any known or accepted laws of physics.  I believe you said so yourself.

https://www.scientificamerican.com/article/einsteins-time-dilation-prediction-verified/


https://www.atmosp.physics.utoronto.ca/people/strong/phy140/lecture32_01.pdf

https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation

[fisherman]

It is my understanding that UA plays along with SR. Gravity is a force in UA, like gravity from stars and planets, but that's very faint. UA states the surface we are on has a negligible gravity due to mass and the rest is just acceleration from an undefined force, which keeps pushing this "special" plane since the dawn of time. But on other planets, like Mars, gravity works as Einstein says.

Gravity and special relativity didn't play well together when Einstein first introduced it. SR directly contradicted Newtonian gravity as an "instantaneous" force That's the reason Einstein worked so hard to come up with general relativity and it is the EP that allowed him to make gravity compatible with SR.

I'd have to think about it, but off the top of my head I can't think of any reason why UA would contradict SR.  In fact, it needs it to explain why the earth isn't accelerating at greater than c.  It's only when you start getting into the nature of gravity (general relativity)that the problems start.  SR doesn't really address that, not directly anyway.

[jack44556677]

@fisherman

"The equivalence principle tells us that accelerated motion and gravity are indistinguishable."

Not really, but this is a common misconception.

They are, in fact, easily distinguishable :  tom has an excellent diagram showing this in a hanging, falling, and resting water balloon that, despite my best efforts, I couldn't find

Gravity does not equal acceleration.

Please do not let this diminish your happiness!

[fisherman]

@fisherman

"The equivalence principle tells us that accelerated motion and gravity are indistinguishable."

Not really, but this is a common misconception.

They are, in fact, easily distinguishable :  tom has an excellent diagram showing this in a hanging, falling, and resting water balloon that, despite my best efforts, I couldn't find

Gravity does not equal acceleration.

Please do not let this diminish your happiness!

Jack, you don't believe that gravity and acceleration and gravity are indistinguishable and that's fine.  My question was directed to those that do believe it.  And whether or not it is actually true really isn't the point anyway.

The question is essentially, if you believe that gravity and acceleration are equivalent, why does it make sense, logically, to reject GR in favor of UA?

[scomato]

I believe that gravity is actually the warping of spacetime by large masses such as the Earth and the Sun. As John Wheeler puts it, "Space-time tells matter how to move; matter tells space-time how to curve." Using the example below, an inertial observer passing through the object warping spacetime experiences a straight-line path (straight at first, but then straight down towards the center of the mass) it's just that spacetime itself is warped.



This video explains everything much better than I can, it is fantastic and explains things in a way that can be understood by even children. It goes into a lot of stuff that Flat Earthers might find intriguing to learn about, and he uses the exact same analogy of an accelerating rocketship example that is thrown around in this thread. It is only 17 minutes long, trust me it's worth the time.

[Tom Bishop]

Accelerating Rocket vs. SR

What would be the point of explaining the time dilation that would occur in an accelerating rocket, where a clock on the ceiling runs fast, with SR's spacetime warping when time dilation is also explained through the non-SR example of the rocket accelerating into the photons?

Experiments involving photon-emitting particles in a particle accelerator which accelerate towards the detector are approaching the detector at an accelerating rate, and any time dilation seen from the photons is no different than the accelerating rocket example. There are likely other explanations for those experiments than jumping to the conclusion that 'spacetime warped and caused time dilation'.

Accelerating Rocket vs. GR

If GR and the Equivalence Principle is explained as being physically identical in every way to the effects in an upwardly accelerating rocket, it is clear that it makes more sense that the Earth is accelerating upwards than the explanation that 'space is bending' in a hidden untestable layer of reality. GR only exists because the physical conclusion of an upwardly accelerating earth can't be explained with RE Theory.

Non-local effects are of questionable veracity.

UA and the Speed of Light Limit

The speed of light limit is a concept from SR. If we discard SR then there is no speed limit. Why should the universe have a "speed limit"? Is there any experimental evidence for that?

A look at the Sagnac Experiments shows that the speed of light is actually c +/- v, where v is the velocity of the moving emitter. The speed of light as a maximum velocity of c is the Special Relativity theoretical interpretation of the Michelson Morley Experiment which saw that Earth was motionless on a horizontal plane.

These theories were created to explain why the Earth seems to be horizontally motionless and accelerating upwards.

"The equivalence principle tells us that accelerated motion and gravity are indistinguishable."

Not really, but this is a common misconception.

They are, in fact, easily distinguishable :  tom has an excellent diagram showing this in a hanging, falling, and resting water balloon that, despite my best efforts, I couldn't find

You appear to be referring to this:

http://gravityprobe.org/GravityProbe%20Links/Galileo-Undone-Mar-10-2020.pdf

[jack44556677]

You appear to be referring to this:

http://gravityprobe.org/GravityProbe%20Links/Galileo-Undone-Mar-10-2020.pdf

That's the one. I spent an embarrassingly long time searching through old posts for it (I thought it was black and white too, memory can leave things to be desired...)

Thanks a lot!

[fisherman]

What would be the point of explaining the time dilation that would occur in an accelerating rocket, where a clock on the ceiling runs fast, with SR's spacetime warping when time dilation is also explained through the non-SR example of the rocket accelerating into the photons?

The “accelerating rocket” excerpt you posted is special relativity.  The whole excerpt is essentially my argument.

Everything the author describes prior to “Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect” is describing the warping of spacetime due to SR.  If the clock on the roof has a different time than the clock on the floor, the spacetime inside the rocket has been warped due to the acceleration of the rocket.

Then the author gets into his explanation of GTD by introducing the EP.

“Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect”.  IOW, prior to this, the EP has not been taken into account, but once it is, the logical conclusion is that gravity causes the same effect as what was previously described (spacetime warp). 

Its exactly my argument.  The EP is what bridges SR and GR.  If you accept the EP, you can’t logically reject either one of them. Its like saying there’s a bridge between points a and b but points a and b don’t exist. If gravity is the equivalent of acceleration and acceleration induces warp of spacetime, then gravity induces the warp of spacetime.  Once the relationship between gravity and spacetime warp is established, its easy to explain why it appears that massive objects appear to attract one another.

The speed of light limit is a concept from SR. If we discard SR then there is no speed limit. Why should the universe have a "speed limit"? Is there any experimental evidence for that?

If you want to suggest that exceeding c is possible, go for it.  Keep in mind you would be explicitly acknowledging UA violates the most basic principle of known physics and it would be intellectually dishonest to try and defend it with known physics.  You’d need to change your wiki and admit UA results in the earth exceeding c and explain why we don’t observe effects prior to their cause occurring.  That’s the paradox that exceeding c would cause.

You appear to be referring to this:

http://gravityprobe.org/GravityProbe%20Links/Galileo-Undone-Mar-10-2020.pdf

Now I’m really confused.  Do you or don’t you agree that gravity and acceleration are indistinguishable?  Jack seems to think you don’t.

[Bikini Polaris]

These theories were created to explain why the Earth seems to be horizontally motionless and accelerating upwards.

If this plane is going upwards at a speed which is, hands waving, ginormous, how's that we are not hit by debris from space at an equally ginormous speed? Or how's that we aren't leaving behind nearby planets?

[Pete Svarrior]

If this plane is going upwards at a speed which is, hands waving, ginormous, how's that we are not hit by debris from space at an equally ginormous speed?

Universal Acceleration is (mostly) universal. Velocity is relative.

[Tom Bishop]

Accelerating Rocket vs. SR

The quote and illustration I provided in the second post of this thread with the rocket accelerating into the line of photons of the clock shows how the effect of time dilation can be explained to occur from the act of acceleration of the rocket into the photons, without using any spacetime-bending explanations. Once again, if time dilation can be explained without the spacetime-bending, why do we need the spacetime-bending?

Equivalence Principle

The Equivalence Principle which postulates the equivalence of inertial and gravitational mass is not specifically tied to General Relativity. In fact, Einstein came up with the Equivalence Principle 8 years before he came up with GR (as mentioned in the PBS EP video). GR incorporates it. Newton and Galileo also had their own theories of equivalence to explain why bodies of different masses and substances fell at the same rate, long before Einstein was born.

Speed of Light Limit

There is a physicist cited on the Signac Experiment page who states that light can be faster than c in the Sagnac and Wang Experiments. I don't see how it is clear that there is a universal speed limit of c when there are experiments which contradict that idea.

https://wiki.tfes.org/Sagnac_Experiment

José Croca
On p.306 of the book Unified Field Mechanics II we find a paper (Archive) by Physicist José R. Croca, Ph.D. (bio), where we see:

  “  Since the realization of this [Sagnac] experiment, which has been done with photons [25], electrons [26] and neutrons [27], many trials have been made to interpret the observed results seen, for instance, Selleri [28]. Indeed, Sagnac utilized the habitual linear additive rule and with that he was able to correctly predict the observed results. Still, since his prediction lead to velocities greater than c and consequently are against relativity which claims that the maximal possible velocity is c this raised a large amount of arguing. In fact, many authors tried to explain the results of the experiment in the framework of relativity which assumed that the maximal possible velocity is c. As can be seen in the literature, there are almost as many explanations as the authors that have tried to explain the results in the framework of relativity. In some cases the same author [29] presents even more than one possible explanation. The complexity of the problem stems mainly from the fact that the experiment is done in a rotating platform. In such case, there may occur a possible accelerating effect leading the explanation of the experiment to fall in the framework of general relativity.

This controversy, whether Sagnac experiment is against or in accordance with relativity, was settled recently by R. Wang et al. [30] with a very interesting experimental setup they called linear Sagac interferometer. In this case the platform is still, what moves is a single mode optical fiber coil, Fig. 12.



They did the experiment with a 50 meter length linear interferometer with wheels of 30 cm. The observed relative phase shift difference for the two beams of light following in opposite directions along the optical fiber was indeed dependent only on the length of the interferometer and consequently independent of the angular velocity of the wheels. From the experimental results obtained with the linear Sagnac interferometer one is lead to conclude that in this particular case the linear additive rule applies. Consequently we may have velocities greater than c, which clearly shows that relativity is not adequate to describe this specific physical process. ”

[fisherman]

The quote and illustration I provided in the second post of this thread with the rocket accelerating into the line of photons of the clock shows how the effect of time dilation can be explained to occur from the act of acceleration of the rocket into the photons, without using any spacetime-bending explanations. Once again, if time dilation can be explained without the spacetime-bending, why do we need the spacetime-bending?

No it doesn’t and I explained why.  It plainly describes the bending of spacetime.

the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor.

That is a description of the warping of spacetime.  Time is moving at a different rate at the roof than on the floor.  That means spacetime is warped.  If the front of your car is moving at a faster rate than the tail end, your frame is bent.

The Equivalence Principle which postulates the equivalence of inertial and gravitational mass is not specifically tied to General Relativity. In fact, Einstein came up with the Equivalence Principle 8 years before he came up with GR (as mentioned in the PBS EP video). GR incorporates it. Newton and Galileo also had their own theories of equivalence to explain why bodies of different masses and substances fell at the same rate, long before Einstein was born.

No, we’ve been down this road before.  Einstein’s EP asserts that gravitational mass and inertial mass are the same thing.  I quoted him saying that.  You didn’t address that.  I also suggested that if you accept the fact that gravity is not a force, then logically there can be no distinction gravitational mass and inertial mass.  If gravity is not a force it can’t effect the motion of mass.  Mass can’t respond to or resist a non-force. You never addressed that either.

So I’ll try another way.  If the guy in the spaceship who doesn’t know if he is accelerating or in gravitational field steps on a scale...how does he know if he is measuring his gravitational mass or inertial mass?

Of course Einstein was aware of the Newtonian and Galilean observations that all objects fall at the same rate.  What he came up with is a better explanation...or really just an explanation for it at all.  Prior it had just been regarded as a coincidence.  Which theory is better do you think? One that just chalks something up to being a coincidence or one that explains the coincidence?  Note in my OP I didn’t ask why GR is right or UA is wrong.  I asked why UA should be considered a better theory when UA leaves so many things unexplained or just a coincidence.

In such a theory, inertial mass and gravitational mass are not just accidentally numerically equal, they are ontologically identical. As a result, general relativity is far more exposed to falsification than Newtonian theory, which is to say, general relativity is a much stronger theory.

https://www.mathpages.com/home/kmath582/kmath582.htm

There is a physicist cited on the Signac Experiment page who states that light can be faster than c in the Sagnac and Wang Experiments. I don't see how it is clear that there is a universal speed limit of c when there are experiments which contradict that idea.

Saying that the speed of light can be increased or could be higher than c isn’t the same thing as saying it isn’t constant or more importantly, that matter can exceed the speed of light, whatever it is.  Can we add that to the list of unknowns?

[Action80]

Your statement "accelerated motion warps spacetime" doesn't make much sense on its own. How is spacetime warped exactly? Can you describe it in a step-by-step physical manner instead of using it as a magic wand?

For someone who purports to have better insight into physics than every other actual physicist in the world, it seems like special relativity shouldn’t be something you would need explained to you.  But here goes anyway...highly simplified of course.

The essence of SR is that observers in relative motion to one another will have different perceptions of distance and time. Wristwatches worn by two different people in relative motion will move at different rates. Two people in motion relative to one another will not measure the same lengths using the same tape measure.  This is because if two people are moving relative to another, light takes longer to reach one person than the other.  Speed of light is constant, but it must travel different distances to reach each person.  The constant speed of light also effects the relativity of space because speed is distance divided by time.  If two observers don’t agree on speed or time, they aren’t going to agree on distance. Another related concept is that everything is always moving through time.  You can’t separate the two.  A parked car is moving through time only, but when it starts up and drives away, it also begins moving through space, so some of the energy directed to moving through time is diverted to moving it through space.  The faster it goes, more energy is diverted moving through space than time, so time begins to slow for the car.  It isn’t moving through time as fast as when it was parked.

This is essentially how acceleration “warps” spacetime.  The greater the relative velocity of the two observers, the more their observations of space and time will differ.  If the same spacetime is different for two different observers, it can be described as “warped” much the same way a piece of lumber is considered warped. If it doesn’t look straight and flat from every angle, it is warped.  If spacetime is experienced differently from different "angles" or frames of reference, it is warped.

That’s about as simple as I can make it.

Gravitational time dilation, in GR and time dilation in SR are two completely different concepts with different causes.(although they can occur at the same time, like with GPS satellites)  So as pretty as your illustrations are, they have nothing to do with how accelerated motion in SR warps space time.

I have a question concerning your explanation.

Specifically, the issue of acceleration and relative velocity of two observers.

Are you supposing 1)the acceleration; and, 2) relative velocity: of the two observers is the same in this scenario?

[Tom Bishop]

The quote and illustration I provided in the second post of this thread with the rocket accelerating into the line of photons of the clock shows how the effect of time dilation can be explained to occur from the act of acceleration of the rocket into the photons, without using any spacetime-bending explanations. Once again, if time dilation can be explained without the spacetime-bending, why do we need the spacetime-bending?

No it doesn’t and I explained why.  It plainly describes the bending of spacetime.

the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor.

That is a description of the warping of spacetime.  Time is moving at a different rate at the roof than on the floor.  That means spacetime is warped.  If the front of your car is moving at a faster rate than the tail end, your frame is bent.

Incorrect. It doesn't say that the scenario on the left hand side of the image is caused by Special Relativity or "spacetime bending". It clearly says that it occurs simply because the rocket is accelerating into the photons, causing time of the clock to appear to speed up.

https://books.google.com/books?id=t8O-yylU0j0C&lpg=PA7&ots=zD8YCKNu7M&pg=PA7#v=onepage&q&f=false

GRAVITATIONAL TIME DILATION

  “ Many of the important features of general relativity can be obtained via rather simple arguments that use the equivalence principle. The most famous of these is the thought experiment that leads to gravitational time dilation, illustrated in figure 1.1. Consider an accelerating frame. which is conventionally a rocket of height h, with a clock mounted on the roof that regularly disgorges photons towards the floor. If the rocket accelerates upwards at g, the floor acquires a speed v = gh / c in the time taken for a photon to travel from roof to floor. There will thus be a blueshift in the frequency of received photons, given by Δv / v = gh / c^2, and it is easy to see that the rate of reception of photons will increase by the same factor.

Now, since the rocket can be kept accelerating for as long as we like, and since photons cannot be stockpiled anywhere, the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor. Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect. Noting that ΔΦ = gh is the difference in potential between roof and floor, it is simple to generalize this to Δt / t = ΔΦ / c^2 ”



“ Figure 1.1. Imagine you are in a box in free space far from any source of gravitation. If the box is made to accelerate ‘upwards’ and has a clock that emits a photon every second mounted on its roof, it is easy to see that you will receive photons more rapidly once the box accelerates (imagine yourself running into the line of oncoming photons). Now, according to the equivalence principle, the situation is exactly equivalent to the second picture in which the box sits at rest on the surface of the Earth. Since there is nowhere for the excess photons to accumulate, the conclusion has to be that clocks above us in a gravitational field run fast. ”

While this example is using an Accelerating Rocket in corporeal space versus General Relativity, it is easy to see that it also applies to a comparison with the spacetime warping of Special Relativity which also purports to explain this effect. This effect simply doesn't need Special Relativity or space-time bending because we can explain it as the rocket accelerating into the photons and observing that they approach at an increasing rate, and that time from the clock seems to quicken.

Here is another quote:

The Five Ages of the Universe: Inside the Physics of Eternity

https://books.google.com/books?id=VY5yDQAAQBAJ&lpg=PA116&pg=PA116#v=onepage&q&f=false

In this book its authors describe gravitational time dilation by giving an analogy of an accelerating rocket in space which contains a clock attached to the ceiling and an astronaut sitting on the floor of the rocket with another clock. The astronaut on the floor first observes his own clock, and then observes the ceiling clock:

however, he observes that the ceiling clock is running faster. The ceiling clock sends a tone (in the form of a radio wave) down to the floor. Because the floor is accelerating upwards, it intercepts the radio wave sooner than if the rocket were merely coasting along. If the acceleration continues, subsequent tones also arrive earlier than expected. In the viewpoint of the astronaut on the floor, the ceiling clock is broadcasting its time intervals at an increased rate, and is running fast compared to the floor clock.

According to the equivalence principle, the phenomenon of mismatched clock rates, which occurs in response to the acceleration of a rocket, also occurs in a uniform gravitational field. The equivalence principle therefore insists on a seemingly bizarre conclusion. Two clocks at different heights above Earth's surface must measure the flow of time at different rates. This strange behavior is an intrinsic feature of gravity. The variation of the flow of time within a gravitational field is entirely independent of the mechanism used to measure time. Atomic clocks, quartz watches, and biological rhythms all experience the passage of time to be dilated or compressed in the same manner.

See the bolded above. It is not describing space-time warping to create this time dilating effect. It is describing a rocket accelerating into photons, exactly like the previous example. Spacetime manipulation is not needed for time dilation.

[fisherman]

Incorrect. It doesn't say that the scenario on the left hand side of the image is caused by Special Relativity or "spacetime bending". It clearly says that it occurs simply because the rocket is accelerating into the photons, causing time of the clock to appear to speed up.

IOW, it describes exactly what we’d expect to see if spacetime was warped by acceleration. Accelerating objects and differences in time.

You can’t always expect things to be explicitly stated and handed to you on a silver platter.  Sometimes you have to draw logical conclusions from the evidence.  If you came home with trash strewn about and last night’s leftovers all over the dog’s face, what conclusion would you draw? 

The fact that the clocks show two different times while accelerating is evidence that spacetime is warped...because that is exactly what we expect to happen if spacetime is warped...accelerating objects showing different times.

If you don’t think that is the logical conclusion, why not?

@action80...I’ll have to get back to you later.  Tom’s comment was easier to respond to and I want to think about how I respond to you so I don’t cause any confusion. Maybe later this evening.