Well, the chapter from which this is quoted is entitled "The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity," and the thought experiment illustrates said inconsistency. What specifically do you find to be problematic?

The issue lies with the 'ray of light' term, that is, I can accept for the moment the assumption that light is measured at speed c by all observers.

In this instance

If a ray of light be sent along the embankment, we see from the above that the tip of the ray will be transmitted with the velocity c relative to the embankment

This is all well and good.

w is the required velocity of light with respect to the carriage, and we have
w = c-v.

There are no laws of nature broken here. All measurements are taking place in the embankment frame of reference. What Einstein is referring to is the 'closing speed' that is, the calculated difference between the speed of light of the carriage and that of the ray of light.

Then he goes on to say:

But this result comes into conflict with the principle of relativity set forth in Section V. For, like every other general law of nature, the law of the transmission of light in vacuo [in vacuum] must, according to the principle of relativity, be the same for the railway carriage as reference-body as when the rails are the body of reference

What exactly comes into conflict with the principle of relativity? Subtraction? Remember that the speed of light is never observed from the carriage as being less than c.

Whenever the example is given that two beams of light are travelling relative to each other at more than the speed of light, this is always explained away as being 'closing speed'.

What exactly comes into conflict with the principle of relativity? Subtraction? Remember that the speed of light is never observed from the carriage as being less than c. — FreeEmotion

Yes, subtraction formula is wrong. If light moves at c relative to the embankment and the train moves at half light speed, the intuitive subtraction yields measurements inside the train at half speed, which is not what is empirically observed as you point out. Subtraction does not describe reality. That's what Einstein is illustrating with that paragraph.

Whenever the example is given that two beams of light are travelling relative to each other at more than the speed of light, this is always explained away as being 'closing speed'.

Yes, closing speed works via subtraction, and can yield values > c. Closing speed is not a velocity. Notice they don't call it closing velocity.

So is it correct to say that an observer can see two objects approaching each other at a speed > c? For example if one object is travelling at 0.7c and the other one at 0.8 c?

Of course for the observers riding in those objects, the theory says that they will see the other object closing at them at c or less.

So is it correct to say that an observer can see two objects approaching each other at a speed > c? For example if one object is travelling at 0.7c and the other one at 0.8 c? — FreeEmotion

Yes, the closing speed would be 1.5c, assuming they're approaching from opposite directions.

Of course for the observers riding in those objects, the theory says that they will see the other object closing at them at c or less.

About .96c, yes. Observers aside, the wording of the situation is: In the frame of either object, the other object would actually be approaching at .96c. It takes light time to travel between the objects, so the observers never see where the other object is, but a picture of the past when the other object was further away.
Thus there might be a star a light year away, and I can watch a really fast ship appear to pass it and arrive here a month later. That's not twelve times faster than light, it is just the ship getting here almost as fast as the image being observed. The trip still took 13 months in my own frame.

Thank you. But this is interesting..

Thus there might be a star a light year away, and I can watch a really fast ship appear to pass it and arrive here a month later. That's not twelve times faster than light, it is just the ship getting here almost as fast as the image being observed. The trip still took 13 months in my own frame — noAxioms

You are saying that you may see a spaceship passing a star a light year away, the spaceship travelling directly towards you, and see the ship arrive at your location a month later.

So after the ship actually arrives, images of the ship will continue to arrive at your eyes? Will there be 13 months of images?

So after the ship actually arrives, images of the ship will continue to arrive at your eyes? Will there be 13 months of images? — FreeEmotion

One month of images. The ship leaves 13 months ago, but since it starts a light year away, we don't see that here on the arriving end for 12 months. Only one month between when we see the cannon poof that fires the thing at us until it arrives here at our orbital catcher's mitt. None of this is even an illustration of relativity. This all works under Newtonian mechanics. Relativity gets invoked only if the trip is described from the frame of the object making the trip.

The only way this can happen in real life is if the object is already travelling that fast and passes by checkpoints. Nothing can get an object up to a speed like that nor expect to stop it at the other end. OK, our particle accelerators do it. Maybe the distant star has a planet made of gold and somebody finds it economical to send the stuff here one atom at a time at .92c

This situation is equivalent to the spaceship sending out particles at the speed of light throughout its journey.

The ship takes 13 months to travel here. That is not in question. What of the particles emitted from the ship? The first one will take 12 months or one year to reach us. The last one will take zero time to reach us.

1 year of travel is compressed into 1 month of images?

This situation is equivalent to the spaceship sending out particles at the speed of light throughout its journey. — FreeEmotion

Photons, yes, and ships often show lights. It is actually sending them out, not just the equivalent.

The ship takes 13 months to travel here. That is not in question. What of the particles emitted from the ship? The first one will take 12 months or one year to reach us. The last one will take zero time to reach us.

Yes, the first one has 12 light-months distance to go, and the last one has zero distance to go. All this is in the frame of the planets.

1 year of travel is compressed into 1 month of images?

No, the image is as viewed by the observer on the destination side, who does not travel at all. He just observes the 13 month trip, and that observation takes only a month since he doesn't see the beginning until 12 months after the trip actually started and the ship is already almost at its destination.

Any time you see something, you are observing the past, not the present. The further away something is, the further back you are seeing. Things on Earth are so close that this effect doesn't matter, but even the sun actually sets 9 minutes before the image of it disappears.

Again, none of this is relativity or has relevance to Einstein's thought experiment. This stuff was known in the 18th century when they first started adjusting actual positions of planets due to measured light speed.

Let's move on to mutual time dilation. It is often said that moving clocks run slow. This may be a misleading statement, or at the least, incomplete. What I think it means is that when transforming measurements between moving frames, we can no longer use Galilean transformations when the relative velocity (speed?) of the frames is comparable to the speed of light. This is because of the constancy of the speed of light within each frame, no matter which frame the origin of the light.

Does it mean that in inertial frames moving relative to each other, that mutual time dilation occurs? Is it just an illusion?

Let's move on to mutual time dilation. It is often said that moving clocks run slow. This may be a misleading statement, or at the least, incomplete. — FreeEmotion

Incomplete I'd say. You can say that clocks run slow in frames in which they are not stationary. That's almost the same thing. Sans frame, a clock has no velocity.

What I think it means is that when transforming measurements between moving frames, we can no longer use Galilean transformations when the relative velocity (speed?) of the frames is comparable to the speed of light. This is because of the constancy of the speed of light within each frame, no matter which frame the origin of the light.

Sounds good. Frames don't move since they don't have a position, but they have velocity relative to each other and I think that's what you mean.

Does it mean that in inertial frames moving relative to each other, that mutual time dilation occurs? Is it just an illusion?

It's quite real. Not sure what you would consider an illusion, but none of it is fake and the clocks are not being inaccurate. It really is possible to get to a place 1000 light years away and not die of old age en-route or require cryonics. But alas, my car seems to be a bit underpowered for the task.

There are fast particles that get created in the upper atmosphere (60000 m up) that have a lifespan long enough for light to travel about 600 meters before decaying. Almost none should reach the ground, but a vast percentage of them do because their decay is delayed by the time dilation from moving at about 99.5% of light. They age slow enough to reach a destination well beyond their life expectancy of about 2 microseconds. They could not do this if the dilation was but an illusion.

I might also add that the Lorentz transformation is used to preserve the laws of physics when translating any event from a moving frame to a non moving or say local (your) frame. In effect, when we observe things happening in a fast - moving frame, it looks like the laws of physics are violated, but when the proper transformations are made, it all comes out right in the end. Is this more or less correct?

Take the statement

There are fast particles that get created in the upper atmosphere (60000 m up) that have a lifespan long enough for light to travel about 600 meters before decaying. Almost none should reach the ground, but a vast percentage of them do because their decay is delayed by the time dilation from moving at about 99.5% of light. They age slow enough to reach a destination well beyond their life expectancy of about 2 microseconds. They could not do this if the dilation was but an illusion. — noAxioms

"There are fast particles that get created in the upper atmosphere (60000 m up) "

Fast as measured in our frame

"that have a lifespan long enough"

A lifespan in our frame of reference

" for light to travel about 600 meters "

in which reference frame?

"before decaying. Almost none should reach the ground, but a vast percentage of them do because their decay is delayed"

When measured in our FoR

" by the time dilation from moving at about 99.5% of light."


" They age slow enough to reach a destination well beyond their life expectancy of about 2 microseconds. They could not do this if the dilation was but an illusion."

Could there be any other explanation for this? I accept it as is, but just wondering.

I might also add that the Lorentz transformation is used to preserve the laws of physics when translating any event from a moving frame to a non moving or say local (your) frame. — FreeEmotion

Frames don't move, and there are not fast and slow ones. They all are references defining zero velocity, so we might for instance consider the frames in which the Earth, the moon, the ship, or the muon is stationary. None of these different frames is 'faster' than another. Yes, the Lorentz transformation is used to translate time and distance between various frames.

In effect, when we observe things happening in a fast - moving frame, it looks like the laws of physics are violated, but when the proper transformations are made, it all comes out right in the end. Is this more or less correct?

Well, at no point does it look like any laws are being violated. The laws would be wrong if that was observed. That's how ToR came about: The laws appeared to be violated, so they knew they needed better ones. I think I see what you mean though. The muons in the atmosphere appear to violate half-life laws (under Newtonian physics) until the transformation is used to yield the actual age of the typical particle measured here near sea level.

Take the statement

There are fast particles that get created in the upper atmosphere (60000 m up) that have a lifespan long enough for light to travel about 600 meters before decaying. Almost none should reach the ground, but a vast percentage of them do because their decay is delayed by the time dilation from moving at about 99.5% of light. They age slow enough to reach a destination well beyond their life expectancy of about 2 microseconds. They could not do this if the dilation was but an illusion.
— noAxioms

"There are fast particles that get created in the upper atmosphere (60000 m up) "

Fast as measured in our frame

Yes. Those particlues (muons I think) are stationary in their own frame, and Earth is what moves fast.

"that have a lifespan long enough"

A lifespan in our frame of reference

No, in its own. I have a halflife of 72 years in my own frame, and an arbitrarily large one in other frames, which is why I can get to places more distant than 72 light years away.

" for light to travel about 600 meters "

in which reference frame?

2.2μs half life multiplied by c. In its own frame I guess, since duration is otherwise ambiguous.

"before decaying. Almost none should reach the ground, but a vast percentage of them do because their decay is delayed"

When measured in our FoR

Yes, only in our frame. In its own frame, it doesn't travel at all, but Earth moves and hits the particle before it dies.

Could there be any other explanation for this? I accept it as is, but just wondering.

No other theory competes at this time. If you want, you can interpret the data as one 'correct' inertial frame, and none of the clocks or tape measures are accurate unless stationary in that frame. In that sense, time and space dilation would be an illusion born of not having accurate measuring tools, but then we would have no tools to measure actual time and space at all, so we're not really measuring anything accurately. That's a pretty useless interpretation.

Thank you for the corrections. First this, though:

No other theory competes at this time. If you want, you can interpret the data as one 'correct' inertial frame, and none of the clocks or tape measures are accurate unless stationary in that frame. In that sense, time and space dilation would be an illusion born of not having accurate measuring tools, but then we would have no tools to measure actual time and space at all, so we're not really measuring anything accurately. That's a pretty useless interpretation. — noAxioms

Imagine, if there was a God, or an "Intelligence" that knew everything, and whose knowledge is not limited by the speed of light. Would this allow the possibility of an absolute centre of the universe, or an absolute frame of reference? Could God know if one 'correct' inertial frame exists, or not?

Imagine, if there was a God, or an "Intelligence" that knew everything, and whose knowledge is not limited by the speed of light. Would this allow the possibility of an absolute centre of the universe, or an absolute frame of reference? Could God know if one 'correct' inertial frame exists, or not? — FreeEmotion

It's not that we don't know the absolute frame. Any designation of one would render over 99% of the universe nonexistent since only a tiny percentage of matter exists in any particular frame. Most of it is increasing its distance from that frame at a pace considerably faster than light and thus can never ever interact with the matter reasonably stationary in the frame. The bulk of all matter is nonexistent in any given frame. So it is not a matter of us simply not knowing. There cannot be one correct answer.

There is a center of the universe, but it doesn't suggest a frame. Most people deny it for the same reason the center of the Earth appears on no map. If it did (Paris??), it would define the correct time zone, no? Look at the entire Earth and the center is obvious. Look at the entire universe, not just one surface of it, and the center becomes obvious.

Any designation of one would render over 99% of the universe nonexistent since only a tiny percentage of matter exists in any particular frame. Most of it is increasing its distance from that frame at a pace considerably faster than light and thus can never ever interact with the matter reasonably stationary in the frame.The bulk of all matter is nonexistent in any given frame. — noAxioms

Not sure I am getting the connection between things that expand from us at a speed faster than light and them not existing. Sure they won't ever interact with us given the light speed limit and all, but that does not imply that they would cease to exist for us.

Not sure I am getting the connection between things that expand from us at a speed faster than light and them not existing. Sure they won't ever interact with us given the light speed limit and all, but that does not imply that they would cease to exist for us. — Mr Bee

I'm going to have to eat my words then.
I am on record for saying that the distance between any two events (points in spacetime) can be expressed by pure spatial separation or by pure temporal separation, or if right on the edge between the two, then undefined singularity. That assertion contradicts my denial of existence of things not in our reference frame.

So consider the event of you making that post, and Mr Cee on some other forum on some seriously distant planet making a similar post. Mr Cee does not exist in the frame in which Mr Bee is at rest, but that just means the wrong frame was chosen. Consider the frame where some spot about halfway is at rest. In that frame, the universe is now about a trillion years old and Mr Bee and Mr Cee are very near opposite edges of the expanding universe where time is dilated about 70x. Mr Cee is moving at about .9999c one way and Mr Bee the same speed in the opposite direction. Nobody is going faster than light. The separation is about 2 trillion light years and they both exist in that frame.
Words eaten. Thank you for the correction.

I am on record for saying that the distance between any two events (points in spacetime) can be expressed by pure spatial separation or by pure temporal separation, or if right on the edge between the two, then undefined singularity. That assertion contradicts my denial of existence of things not in our reference frame. — noAxioms

So which one are you rejecting here? Seems like the former, but if that is the case, then I still don't understand where the assertion that some things don't exist in some reference frames if they are moving away faster than light. Your response still amounts to this assumption that they do, but I am afraid I don't see how or why.

Also, since we are on the topic of absolute frames, I don't think that GR allows for the notion of a reference frame, due to the curvature of space-time. Instead the idea of an absolute frame is replaced with a preferred global foliation, which though technically not a frame of reference, defines a global time like the correct inertial frame should under SR. I am not sure if your statements above apply there, but I think I should throw that out since GR is the theory we are currently using.

So which one are you rejecting here? — Mr Bee

I'm rejecting the prior post saying that sufficiently distant places don't exist. I gave an example of an event 2 trillion light years away that exists now, and where nothing is moving faster than light, thus refuting my assertion of the nonexistence of the event.

Seems like the former, but if that is the case, then I still don't understand where the assertion that some things don't exist in some reference frames if they are moving away faster than light. Your response still amounts to this assumption that they do, but I am afraid I don't see how or why.

Well, in our frame, Mr Cee is in the future and does not currently exist, so is not moving faster than light. Similarly, we don't exist in Mr Cee's frame. The frame is not a valid one for us since it would have us moving at about 140c, far beyond light speed.

Also, since we are on the topic of absolute frames, I don't think that GR allows for the notion of a reference frame, due to the curvature of space-time.

Yes, it says that SR laws only work locally. They break down over any significant distance, and my example far exceeded that. Does it make it invalid? I was just trying to counter my prior assertion.
Messages could in principle reach distant places if the expansion of the universe was constant, but it isn't. Hence the event horizon, which delimits events that can never have a causal effect here on Earth.
But coordinate systems exist that map really distant events like Mr Cee's post. Mr Cee has a proper-distance from us (length of a tape measure that curves with space), and a proper velocity (how much that measurement grows per second) and that value can be greater than light speed without violation of GR.

Instead the idea of an absolute frame is replaced with a preferred global foliation, which though technically not a frame of reference, defines a global time like the correct inertial frame should under SR. I am not sure if your statements above apply there, but I think I should throw that out since GR is the theory we are currently using.

Yes, there is an obvious global foliation (comoving coordinates), and I was unaware that GR rules (with space and velocity expressed in actual distance, not proper distance) would be valid at all in that coordinate system. Yes, that's where 'proper-distance' comes from. It essentially paints 4D spacetime in polar coordinates instead of the rectangular coordinates that yield inertial frames. The math to do Lorentz calculations in polar coordinates would be an interesting exercise, perhaps beyond my capabilities.

Mr Cee is moving at about .9999c one way and Mr Bee the same speed in the opposite direction. Nobody is going faster than light. The separation is about 2 trillion light years and they both exist in that frame. — noAxioms

The above assumes a constant expansion rate to the universe, not a true thing. Given that it is accelerating, neither Mr Bee nor Mr Cee are in that frame of reference....
The trick works for fairly distant places, but my example put these events a couple trillion light years apart, too far.
So that brings us down to one's definition of existence to ask if Mr Cee exists.

As purely philosophical question, would God be able to define an absolute frame of reference, say the centre of the known (to Him) universe, and all that there is beyond the reach of light and time?

Once we say God knows something, then it forces it into the realm of existence since God cannot know something that does not exist?

As purely philosophical question, would God be able to define an absolute frame of reference, — FreeEmotion

God is free to define a sorting of all the events into time order. No inertial frame of reference does that, so it would not be an inertial frame if it was done.
It would have no effect on us if such an arbitrary definition was made.

say the centre of the known (to Him) universe,

It is known to me even, so I hope God is aware of it. Didn't you see my post about that? The centre of the universe does not define a frame, even if it does suggest an origin for a non-orthogonal coordinate system.

and all that there is beyond the reach of light and time?

Don't know what you mean by that. All parts of the universe of which I am aware (including the ones undetectable from here) are temporal and lit up, even if only dimly. Perhaps you define the universe as more than just what came from the big bang.

Once we say God knows something, then it forces it into the realm of existence since God cannot know something that does not exist?

Not sure if that qualifies as a circular definition. What if God knows that something doesn't exist? Probably not a valid example since I seem to be playing epistemological meta-language games in making that statement. The nonexistent thing doesn't exist, but the fact that God is aware of its nonexistence does exist. But it must exist, having been referenced...

I'm not sure of your definition of 'exists' either. Does 2+2=4 exist? Surely God knows it, so it must exist.
I find existence to be a relation, not a property, so there is no 'exists', there is only 'exists in'. Your definition may vary, but I cannot comment clearly without knowing it.

Have there been any philosophical criticisms of this thought experiment and its conclusions? (The train experiment) At times it appears to follow inconsistent reasoning. — FreeEmotion

Probably the most demonstrative and damaging philosophical critiques of Relativity derive from Bergson's approach to the issues raised.

http://m.nautil.us/issue/35/boundaries/this-philosopher-helped-ensure-there-was-no-nobel-for-relativity

Bergson had no problem with the scientific issue of determining simultaneity via use of clocks. His objections were giving Relativity and Relativity's definition of time, ontological status, which he thought was absurd (I agree). The time (duration) is the one that we experience, clocks and simultaneity are only products of this duration and the mind that is experiencing it.

Stephen Robbins provides his own Bergsonian critique of Relativity here:


https://www.amazon.com/review/R17WTYWUM6881A

I think what I am really getting at is: is a purely Newtonian universe possible, with all relativity being Galilean Relativity. Could God create such an universe which neither violated Newtonian physics nor Relativity as an illusion due to the limits of the speed of light, meaning limiting the speed of information transfer?

One can imagine that information transfer is limited by the speed of light, reality is not. For example, is God's knowledge of an event is delayed by the time it takes light from the event to reach Him? Surely this is an absurd statement? (Asimov hinted at this, that the speed of light was slowing the second coming of Christ).

Thank you. What about Herbert Dingle's critiques?
Despite criticisms, the theory, or at least the popular thought experiments and popular conception of the theory is still widely accepted. Is this changing? And how can an inconsistent theory be confirmed by experiments?

Bergson's critiques were philosophical in nature. He didn't question the scientific aspect, i.e. simultaneity of measurements.

You will find this article of interest - a reflection on the debate between Einstein and Bergson, by Adam Frank, a science writer whom I respect.

Thanks. The article points out the issue of elevating scientific mathematical equations to an ontology.

Probably the best discussion of the philosophical issues appear in these two videos by Stephen Robbins:

https://youtu.be/mcMnn5TpqT0

https://youtu.be/RjQg8on4yS0

Ontologically, Relativity is quite a mess especially if one tries to bounce between time as used in Special vs. General and then attempting to use both interchangeably. For those who are interested in the"experience" of life, this subject is well worth studying.

Bergson's critiques were philosophical in nature. He didn't question the scientific aspect, i.e. simultaneity of measurements. — Rich

This is correct. ToR suggests but does not assert an ontological status to time. To date I've seem many claims of empirical evidence supporting both sides, but I've never found any of them to be valid.
Bergson's claim was religious based, claiming that the immaterial mind somehow can detect what no clock or other physical device can: The rate of advancement of the present.
There is an empirical test against that claim (do the twin experiment with a human instead of a clock), but such an expenditure of resources would only prove that people detect time, not the advancement of the present. It would not conclusively be evidence of the ontological status of time.
Wayfarer, I've yet to read your article on the subject

Bergson's claim was religious based, claiming that the immaterial mind somehow can detect what no clock or other physical device can — noAxioms

Not a religious argument, but more an experiential and intuitive one based upon Bergson's studies of biology, mathematics, and education. Time (durée), as it is experienced, is heterogeneous and continuous. This is the opposite of scientific time which is homogenous and discontinuous. These differences provide a completely different view if the nature of experience and the mind that is experiencing. Bergson's series of books and papers on this subject provide a steady development of this point of view and metaphysics. The key components of the metaphysics are Durée, Memory (the experience of mind), and Elan vital (the creative impetus).