In one person’s reference frame the event is in the present (or past), and in the other person’s reference frame the event is in the future. I find this peculiar. — Michael

Think of what this means as that "the present", or "now" is defined by the frame of reference. This is a type of subjectivity. The present, and therefore future and past, are defined by the frame of reference. So if we want an "objective" present, or now, or an objective divisor between events of one period of time and those of another another, we have to realize that this is impossible under the precept of special relativity. Such divisions of before and after are arbitrary, as is the frame of reference which defines the divisor.

This becomes problematic when you try to relate the before and after of one frame of reference to that of another. This give the problem you describe. Physics resolve this problem with the creation of a "world line" for the object at question, in this case Andromeda. The world line allows for a "proper time" relative to that object. So once a world line is created for Andromeda we could use that to say which events are before others, for Andromeda itself, despite the differences between different frames of reference. The problem with this is that the world line is somewhat arbitrary.

Maybe this helps: https://en.wikipedia.org/wiki/Light_cone

I don't see what that has to do with the Rietdijk–Putnam argument and/or Andromeda Paradox.

If that's not immediately apparent, I think you have to read up a bit more on GR in general. You can in any case Google it by combining search terms.

It's the notion that a few seconds on Earth could mean fifteen minutes in distant galaxies. :chin:

If we send two signals to the Mars Rover, spaced at exactly 10 seconds apart, does the Rover receive them in that same time spread? Assume the relative positions don't change.

I'm not seeing it. Light cones concern causal past and causal future. The Rietdijk–Putnam argument and Andromeda Paradox concern events outside the light cone.

If you want to be very precise with the terminology, the Andromeda Paradox shows that some spacelike separated event in my present is some spacelike separated event in some other person's causal future even though that person is also a spacelike separated event in my present. I find that peculiar.

And let's take it further and consider this:



Some event (A₁) in my (A₀) future is spacelike separated from some event (B₀) in someone else's (B₁) past, even though this person is spacelike separated from my present. It might be impossible for me to interact with B₁ (or for B₁ to interact with A₁), but Special Relativity suggests that A₁ is inevitable, hence why this is an argument for a four-dimensional block universe, which may have implications for free will and truth.

The galaxies you are moving towards would have come into view regardless of your motion, only at a later time as measured by your clock. Similarly, the galaxies you are moving away from will also come into view, but at a later time — Pierre-Normand

the edge of the visible universe is receding from us faster than the speed of light. Although individual galaxies are much slower than light their apparent movement adds up radially away from us. Over billions of years we would see fewer galaxies spread further apart in ever darkening space.

The moving observer effect is special because it is in the observer's present, here and now. But that present, that 'origin' is not fixed in space-time. I'll throw another log in the fire.

The Hubble space telescope orbits Earth. Let's suppose that when flying at maximum approach speed in the direction of Andromeda it sees a quickly brightening supernova star. Mission control decides to keep the telescope pointed there to record continuously for 10 days. From Earth we will not discover that supernova for another 3 days, and on the other side of the orbit, now moving away from Andromeda, Hubble will not see it for another 3 days. This is not an illusion. NASA could set this up just to make Penrose's point, showing that the universe is a weird place.

I only talked about the Rietdijk–Putnam argument itself and how it didn't make much sense to me. — Alkis Piskas

The Rietdijk–Putnam preceded Penrose and is seen more as a philosophical argument in the literature. Frankly, reading wiki and the SEP articles on Time and Becoming and Temporal Parts very little of it makes sense to me either.

That's probably because I am more hung up on Plato's various suggestions of space, time and change.

The Ship of Theseus makes more sense to me in terms of temporal parts, identity and change. but the notion of same time or gaps in time between events still throws me for a loop..

the edge of the visible universe is receding from us faster than the speed of light. Although individual galaxies are much slower than light their apparent movement adds up radially away from us. Over billions of years we would see fewer galaxies spread further apart in ever darkening space. — magritte

This is due to the expansion of the universe, which is a general relativistic effect. It is unrelated to the shifting of the simultaneity plane due to the substitution of inertial reference frames is special relativity.

If you want to be very precise with the terminology, the Andromeda Paradox shows that some spacelike separated event in my present is some spacelike separated event in some other person's causal future even though that person is also a spacelike separated event in my present. I find that peculiar. — Michael

In essence, you're saying that even though a distant event currently lies beyond your ability to influence it (due to the fact that any influence you exert cannot travel faster than light), someone else, presently positioned closer to the event, can influence it.

Some event (A1) in my (A0) future is spacelike separated from some event (B0) in someone else's (B1) past, even though this person is spacelike separated from my present. It might be impossible for me to interact with B1 (or for B1 to interact with A1), but Special Relativity suggests that A1 is inevitable, hence why this is an argument for a four-dimensional block universe, which may have implications for free will and truth. — Michael

If we let c approach infinity, Galilean spacetime converges with Lorentzian spacetime. In this case, the "absolute elsewhere" of an event (the region outside of the light cone) shrinks into a unique simultaneity hyperplane. In Galilean spacetime, an observer at a given time views any event in its (absolute) past as "inevitable." In Lorentzian spacetime, an observer deems "inevitable" any event that resides either in its (absolute) past light cone or in its (also absolute) elsewhere region. The "inevitability" relation between observers-at-a-time (events) and other observers-at-a-time becomes intransitive.

This intransitivity means that even if

1. A1 is inevitable by B1, and
2. B1 is inevitable by A0,
it does not follow that (3) A1 is inevitable by A0.

This inference is invalid because the inability of A0 to affect A1 indirectly by influencing B1 does not mean that A0 can't influence A1 directly.

no. https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

(1) Relativity of simultaneity + all observers’ 3D worlds are real at every event = block universe

The argument on that page accepts that relativity of simultaneity is true but claims that "all observers’ 3D worlds are real at every event" is false because "Our intuitions don’t really know how to deal with “elsewhere”; it’s neither fixed and certain, since we can’t predict what happens there with certainty based only on the data in our past light cone, nor changeable since we can’t causally affect what happens there; we can only causally affect events in our future light cone."

This is a non sequitur. That an event cannot be predicted with certainty isn't that the event isn't certain. Or to phrase it another way, even if we cannot know (with certainty) whether or not "there is intelligent alien life in the Andromeda Galaxy" is true, it doesn't follow that it isn't true (or false).

And nobody is suggesting that it's changeable. In fact if the block universe is true then nothing is changeable; it just is what it is.

So the Andromeda Paradox is the claim that if "aliens are leaving Andromeda en route to Earth" is (unknowably) true in some reference frame then "aliens will leave Andromeda en route to Earth" is (unknowably) true in my reference frame.

And furthermore, that for every proposition "X will happen" either there is some reference frame A in my present elsewhere such that "X is happening" is (unknowably) true, and so "X will happen" is (unknowably) true in my reference frame, or there is no reference frame A in my present elsewhere such that "X is happening" is (unknowably) true, and so "X will happen" is (unknowably) false in my reference frame.

This is a non sequitur. That an event cannot be predicted with certainty isn't that the event isn't certain. Or to phrase it another way, even if we cannot know (with certainty) whether or not "there is intelligent alien life in the Andromeda Galaxy" is true, it doesn't follow that it isn't true (or false). — Michael

That the event is certain to you in your frame of reference is irrelevant to my frame of reference. For us to exchange that information at (sub-)light speeds, brings your event within my frame of reference. The "elsewhere", e.g. anything outside my frame of reference, is incoherent to be talking about as it doesn't exist for me. When the information is exchanged, it's already in my frame of reference.

EDIT: this is why it's useful to realise that when you actually observe the event happening in your frame of reference, you're 15 lightdays away from me, which will then be your present and I'll still not be aware of it. You notify me it's coming and by the time that information reaches me, the light of the event is there as well. Until that time there's no way for me to know what's coming.

The "elsewhere", e.g. anything outside my frame of reference, is incoherent to be talking about as it doesn't exist for me. — Benkei

This is where a realist would disagree. We can't know what's happening in the Andromeda Galaxy right now, but something is happening. Either "intelligent alien life exists in the Andromeda Galaxy" is (unknowably) true or "intelligent alien life doesn't exist in the Andromeda Galaxy" is (unknowably) true.

If we consider this in the context of presentism, the presentist would claim that only objects that exist in the present (including the present elsewhere) are real. But if B exists in A's present (elsewhere) and C exists in B's present (elsewhere) then C is real, even if C exists in A's future (elsewhere). And if special relativity is true then something like this is the case. Therefore presentism is false (as is the growing block universe theory). Or, given this fact, presentism and eternalism amount to the same theory.

Or are you an antirealist about events outside your (past?) light cone?

I'm merely stating what the epistemological claims can be. That has no bearing whatsoever as to philosophical realism or not.

Apologies for responding to stuff sometimes days old, but some of them needed comment. It turned into a long post.

About the Rietdijk–Putnam argument, to which the above link refers to, we read the following:
"In philosophy, the Rietdijk–Putnam argument, [...] uses [...] special relativity – to support the philosophical position known as four-dimensionalism." — Alkis Piskas

Also known as the block universe, or eternalism, a view that goes back to at least the 11th century.

"In contemporary metaphysics, temporal parts are the parts of an object that exist in time. A temporal part would be something like 'the first year of a person's life', etc." — wiki?

Would be more helpful to name a part that isn't a temporal part. If it doesn't exist in time, then it hasn't a location in spacetime, and it effectively doesn't exist.

But can a person's life be considered an "object"?

Yes, quite easily. It being an object only becomes problematic if its identity is challenged, but must such challenges don't apply to a human, at least not significantly beyond a few days from conception. A human life is bounded by a couple meters of space most of the time and several decades of time. That's what a worldline is.

And if we accept that to be true, should we also consider thoughts as objects too?

Why, because you don't consider thoughts to be a physical process, or because you don't consider a physical process to be an object. I would probably agree only with the latter. Given other parts of the post, I think you mean the former, in which case it is your choice or not to work with a model compatible with this 4 dimensionalism or not.

But both are concepts that cannot exist in space! How can we include them in 4 dimensions when they do not exist even in 3 dimensions? See the impasse one could get in? Well, this might be \a problem of mine only ...

We say that an object occupies space. I really cannot see how it can also "occupy time".

That's like saying you're ok with bread having width but you can't see how it can have length.

Your [Michae;'s] statement ["it's about that thing actually happening for one person before another person."] assumes a privileged frame of reference. It's not coherent within the context of relativity theory. — Benkei

For one thing, when you reference a statement like that, at least quote the statement. Anyway, I just don't see how the statement indicated seems to assume any privileged FoR.

Many of your posts (I lost count) seem to be about what somebody sees rather than which events one considers to be simultaneous with a given event. The scenario isn't empirical at all. It is meant to illustrate relativity of simultaneity, something new under SR. Even in Newtonian physcs, if somebody happens to be closer to the light coming from some distant event, they'll see it before somebody further away.

The scenario has nothing to do with light cones since none of the events in question are in anybody's light cones.

no. https://www.physicsforums.com/insights/block-universe-refuting-common-argument/ — Benkei

I agree, SR does not imply a block universe. The wording of it pretty much assumes it, but it is quite trivial to change that wording to more empirical wording. So for instance, instead of light moving at constant c relative to any frame, you say that light is measured to move at constant c relative to any frame. The later papers (and GR in particular) are worded more in this fashion.

I've never seen a good proof of either view, and I've put out a few myself, not all taking the same stance. For instance I found an empirical way to disprove presentism, but it works along the same lines as being able to prove the afterlife: You can only prove it to yourself, not to those you leave behind.

The "elsewhere", e.g. anything outside my frame of reference, is incoherent to be talking about as it doesn't exist for me. — Benkei

But the topic presumes a different view than the one you presume, so your personal beliefs are inapplicable. Your statement here seems outright solipsistic. What exists is determined by you and you alone.

According to special relativity some of these events happen in your future even though they are happening in my present. This is what I find peculiar. — Michael

The thing is, the way the story is worded seems to presume everybody uses the inertial frame in which they are stationary to consider what is going on. It simply isn't true. Almost everybody uses the same frame from day to day, which is the frame of the ground under you, which just happens to be an accelerating rotating frame, but pragmatically, it works for almost all uses. So the two people passing in the street don't have an opposing view of what time it is in Andromeda.

OK, all that changed a few centuries ago when they realized that such a frame doesn't work so well when looking at things further away than clouds, and in those cases, they probably use something more practical like the frame of the sun instead of the frame of the individual.
The point of the 'paradox' still stands. A small change in inertial coordinate system can translate to significant temporal differences at large distances, and this is what you find peculiar.

The rational part of me has been an eternalist for some time, and I find this intuitive, not peculiar at all. The pragmatic part of me doesn't care and always uses the rotating frame.

If you want to be very precise with the terminology, the Andromeda Paradox shows that some spacelike separated event in my present ... — Michael

Careful. The Andromeda scenario is supposed to assume 4 dimensional spacetime in which you don't have a present. So relative to a given event at which you are present, these different inertial frames with minor velocity differences translate to significant time differences at large distances.

You reference the present a lot in your posts. If there is a present, there is but the one, and what day it currently is in Andromeda has nothing to do with anybody's frame. Mixing the two views is what makes it seem paradoxical. So try not to mix.

even if we cannot know (with certainty) whether or not "there is intelligent alien life in the Andromeda Galaxy" is true, it doesn't follow that it isn't true (or false). — Michael

Under relativity, the point is irrelevant. Under QM, it is very relevant, and given a non-counterfactual interpretation of QM, the statement " there is life on <really distant planet X>" is not truth-apt any more than the statement "Schrodinger's cat is alive".

What the Andromeda Paradox implies is that the observed universe apparently shifts in its entirety towards a moving observer. — magritte

There's no such thing as a moving observer without establishing a frame. I suppose 'shifts' can describe the difference in the motion of things when the frame changes (the observer accelerates?). So in my frame, the tree gains velocity relative to me when I run towards it, but that's very different from the tree itself accelerating.

Which means that in the forward moving direction many more of the most distant galaxies come into possible view

Your velocity doesn't change what you see. OK, it can blueshift it a bit, but nothing comes into view that wasn't already there regardless of your velocity. Of course given enough time, you'll separate yourself from a observer left behind, and that separation (and not the velocity) will change which galaxies are in view.

It's the notion that a few seconds on Earth could mean fifteen minutes in distant galaxies. — jgill

That's just silly. It's not about the respective rate of time passage at all.

If we send two signals to the Mars Rover, spaced at exactly 10 seconds apart, does the Rover receive them in that same time spread?

Yes, and if the two observer walking past each other simultaneously send signals to Andromeda, and then another signal a minute later, they'd get to Andromeda at the same time, and the second signal a minute later, separated by the time it takes light to go however far apart the guys got in that minute.

the edge of the visible universe is receding from us faster than the speed of light. — magritte

Yes, and yet galaxies become visible over time as our expanding visible universe overtakes them. These newly visible galaxies are also receding faster than c (proper distance, constant cosmic time), but not as fast as the 'edge'.

Over billions of years we would see fewer galaxies spread further apart in ever darkening space.

More galaxies actually, but our capacity to see them diminishes as they indeed redshift into less detectable frequencies and lowed brightness due to increasing distances.

The Hubble space telescope orbits Earth. Let's suppose that when flying at maximum approach speed in the direction of Andromeda it sees a quickly brightening supernova star. Mission control decides to keep the telescope pointed there to record continuously for 10 days. From Earth we will not discover that supernova for another 3 days — "magritte

What? Hubble is in fairly low orbit, hardly 3 light days away. Light from the supernova reaches Earth in the same second as it reaches Hubble, presuming Hubble's view of it isn't blocked by Earth. It has nothing to do with the motion of Hubble, and nothing to do with this topic, which is about Relativity of Simultaneity, not about when things get measured. Hubble most certainly does not see a whole different view of distant things when it is approaching them vs 45 minutes later when its orbit takes it the other way.

If we send two signals to the Mars Rover, spaced at exactly 10 seconds apart, does the Rover receive them in that same time spread?

Yes, and if the two observer walking past each other simultaneously send signals to Andromeda, and then another signal a minute later, they'd get to Andromeda at the same time, and the second signal a minute later, separated by the time it takes light to go however far apart the guys got in that minute. — noAxioms

Of course.

By the time the light reaches her, she's simply closer to it. She's been walking millions of years towards it already. Once Bill sees the decision happening, for Ann at that point, having walked at 5 m/s for all that time, the light reaching her then is 15 days later and the armada is already on its way. — Benkei

:roll:

Apologies for responding to stuff sometimes days old, but some of them needed comment. It turned into a long post. — noAxioms

Why do you aplogize? I was not expecting a response from you but from the OP of this discussion, @Michael, who seems not to know what a discussion is and/or he lacks communication basics, esp. when he is the OP of a discussion.

Also known as the block universe, or eternalism, a view that goes back to at least the 11th century. — noAxioms

Thanks for letting me know.

Re "But can a person's life be considered an "object"?
Yes, quite easily. It being an object only becomes problematic if its identity is challenged ... — noAxioms

Then we are not speaking about the basic meaning of the term "object", which is anything that is visible or tangible and is relatively stable in form, but about is secondary and more general meaning, i.e. anything to which thought and action is directed, related or referred. The first is clearly physical. The second one not necessarily physical.

A human life is bounded by a couple meters of space — noAxioms

Most probably you mean a "human body". (A life occupying space is just absurd.)

Re "And if we accept that to be true, should we also consider thoughts as objects too?"
Why, because you don't consider thoughts to be a physical process, or because you don't consider a physical process to be an object. — noAxioms

I don't consider thoughts to be a physical process. There's nothing to prove this. The brain reactions that neurobiologitsts and other consider as thought are just that: reactions. The brain is a stimulous-response mechanism, And as such it reacts to thoughts, in various ways. That's all it does and can do. It cannot originate, create, imagine a thought from scratch.

Re "But both are concepts that cannot exist in space! How can we include them in 4 dimensions when they do not exist even in 3 dimensions?"
Re: "We say that an object occupies space. I really cannot see how it can also "occupy time""
That's like saying you're ok with bread having width but you can't see how it can have length. — noAxioms

"Width and length refer both to space. They have nothing to do with time.
Indeed, how do you imagine an object "occupying time"? I'm very curious ...

I was not expecting a response from you but from the OP of this discussion, Michael, who seems not to know what a discussion is and/or he lacks communication basics, esp. when he is the OP of a discussion. — Alkis Piskas

My wait was also in vain.

Then we are not speaking about the basic meaning of the term "object", which is anything that is visible or tangible and is relatively stable in form, but about is secondary and more general meaning, i.e. anything to which thought and action is directed, related or referred. The first is clearly physical. The second one not necessarily physical.

Most probably you mean a "human body". (A life occupying space is just absurd.) — Alkis Piskas

OK, we differ here. A body might continue after life, but I see no better way to interpret 'a life' than 'a body, while it is alive'. That makes it an object in any scientific sense. If you have a non-scientific definition of such things (and apparently you do), then yes, perhaps your definition isn't compatible with some of the concepts expressed in relativity theory as well as other theories.

The brain reactions that neurobiologitsts and other consider as thought are just that: reactions. The brain is a stimulous-response mechanism, And as such it reacts to thoughts, in various ways. That's all it does and can do. It cannot originate, create, imagine a thought from scratch. — Alkis Piskas

Do you have a reference for the consensus view of neurobiology that a brain cannot 'originate, create, imagine a thought from scratch'. I mean, there are probably some that hold such beliefs for supernatural reasons, but I'm speaking of the scientific consensus.

"Width and length refer both to space. They have nothing to do with time.
Indeed, how do you imagine an object "occupying time"? I'm very curious ... — Alkis Piskas

Under the spacetime view, they're just different dimensions of the same thing, so every 'object' has a series of 4D points (events) that it occupies and the rest of the events which it does not. This is the same as a 3D table in space occupying some points and not the rest.

So you're saying, like so many others, that you just cannot conceive of 4D spacetime, of a block universe, eternalsm, etc. The whole Andromeda scenario presumes it, so if you don't understand it, you're not particularly qualified to critique it.

I see no better way to interpret 'a life' than 'a body, while it is alive'. That makes it an object in any scientific sense. — noAxioms

Obviously.

If you have a non-scientific definition of such things ... — noAxioms

What things? And what do you mean by "non-scientific definition"?

Do you have a reference for the consensus view of neurobiology that a brain cannot 'originate, create, imagine a thought from scratch'. — noAxioms

How can I have such a ref? This is an impossible question for a philosophical discussion. It can be asked only and maybe among scientific communities. For out purposes, one can only know about the prevailing views of neuro(bio)logy on the subject. You can google if you like things like "Thoughts are created", "Thoughts are located", etc. You will see that almost all the results refer to the brain.

Under the spacetime view, they're just different dimensions of the same thing, so every 'object' has a ... — noAxioms

This isn't what I asked. I asked "how do you imagine an object 'occupying time'?" And I added that I'm very curious. Well, I'm not anymore! :smile: In fact, I wasn't curious at all. It was a manner of speaking. Because an object occupying time is a totally absurd idea.

so if you don't understand it, you're not particularly qualified to critique it. — noAxioms

This is called argumentum ad hominem, i.e. "argument against the person". And it's a bad thing.

How can I have such a ref? This is an impossible question for a philosophical discussion. It can be asked only and maybe among scientific communities. — Alkis Piskas

My mistake I think. I looked at your comment to which I was reacting and thought it said that the neurobiologists say that thoughts do not originate in the brain. It is only you that asserts this about where thoughts do or don't originate. My mistake.

This isn't what I asked. I asked "how do you imagine an object 'occupying time'?"

The same way it occupies space, since time and space are just different dimensions of the same thing under the spacetime view. Under the 3D view, objects and the entire universe are contained by time. I'm not sure if that would be considered 'occupying time' or not, since the term isn't typically used that way.

Because an object occupying time is a totally absurd idea.

so if you don't understand it, you're not particularly qualified to critique it.
— noAxioms
This is called argumentum ad hominem, i.e. "argument against the person". And it's a bad thing.

It's not against you personally. Anybody sufficiently unfamiliar with a given subject is unqualified to meaningfully critique the subject. You seem to attempt to demonstrate this unfamiliarity with statements like the above one where you consider it absurd. It happens to match empirical observations perfectly, so there's nothing absurd about it at all. That alternate views also match empirically indicates that there's no positive evidence one way or another. Somebody familiar with both views would realize that. Somebody positing the impossibility or absurdity of one view or the other only demonstrates ignorance of the subject. I'm ignorant of plenty of subjects, and it isn't anything against me to point out that I'm unqualified to critique them. But I'm quite familiar with this subject, which isn't very complicated at all. It gets more complicated when general relativity sets in and the 3D presentist view gets some real (but not insurmountable) challenges.

One solution is that there is but the one present (not even a frame really), and time doesn't exist at all, and the present doesn't move. It is the same moment forever. The last-Tuesdayism view illustrates this. If you can't defend or counter last-Tuesdayism, then you don't understand the subject very well. This is especially relevant when discussing Boltzmann brains, where last-Tuesdayism isn't just some reducto-absurdum, but is potentially the most probable thing.

This isn't what I asked. I asked "how do you imagine an object 'occupying time'?"
The same way it occupies space, since time and space are just different dimensions of the same thing under the spacetime view. Under the 3D view, objects and the entire universe are contained by time. I'm not sure if that would be considered 'occupying time' or not, since the term isn't typically used that way. — noAxioms

Saying "the same way it occupies space" is wrong because space and time are not "just different dimensions of the same thing"; they are two totally different things and concepts. Look them up! Besides, I already mentioned that we can undestand how an oblect occupies space, but we cannot say the same about time. So, you have avoided the question for the nth time.

After all these exchanges between us, you should have either given an exact and/or plausible answer, preferably with an example, or admitted you don't know or admitted that an object cannot actually occupy time.

So, I give up here.

My question concerns the gamma factor for s.r... I'm simply am posing a question as I am not a scientist.
Within a moving ship,relative to an outside observer, a light clock is introduced having a light signal going up horizontally and then being reflected downwards. The observer outside the spaceship will calculate light signal (up and down) having a greater distance to travel relative to the observer inside the ship, however still having a velocity of c; this will bring about an observed time dilation on the part of the moving ship....of course the same can be said for the observer within the spaceship, if the outside observer had a light clock as well, but we will only focus on the first example.

What would happen if the light clock was positioned horizontally instead?
I personally can't see how the horizontal clock would be synchronized with the vertical one.

Grampa Dee

Grampa Dee wrote:

"Within a moving ship,relative to an outside observer, a light clock is introduced having a light signal going up horizontally" ....sorry, I meant vertically...

I personally can't see how the horizontal clock would be synchronized with the vertical one — Gampa Dee

From the standpoint of the external observer ("stationary" reference frame) the emitted light has to catch up with the receding mirror. On the return path, the travel time is shorter due to the source rushing towards the light ray. It may therefore seem like the two effects cancel out. However, since the distance traveled forward is longer, more time is accrued for the light ray to catch up with the mirror than is saved on the shorter return path. Because of that, there still is time dilation, and calculation shows that the same gamma factor is in play.

Thank you Pierre-Normand for replying.

You wrote: "On the return path, the travel time is shorter due to the source rushing towards the light ray. It may therefore seem like the two effects cancel out. However, since the distance traveled forward is longer, more time is accrued for the light ray to catch up with the mirror than is saved on the shorter return path. Because of that, there still is time dilation, and calculation shows that the same gamma factor is in play."

Would it be possible for you to write down how this can be achieved, for I don't understand?

The way I see this is simply the length the path of light will have for the first leg would be increased
(L + vt) and the second leg would be foreshortened (L- vt) which, as you mentioned, seems to cancel the effect.
What happens during the first leg which gives the gamma factor is what I still don't understand.

However, this was only part of the problem as S.R. would identify the path itself as being contracted by a factor of gamma, giving (gamma L+vt) + (gamma L - vt) = 2 gamma L . With c being constant,...this seems to give us a time contraction cancelling the effect of the vertical clock..

I sure that I'm misunderstanding something, but don't know what exactly.

thank you for your time

Grampa Dee

The way I see this is simply the length the path of light will have for the first leg would be increased
(L + vt) and the second leg would be foreshortened (L- vt) which, as you mentioned, seems to cancel the effect.
What happens during the first leg which gives the gamma factor is what I still don't understand.

However, this was only part of the problem as S.R. would identify the path itself as being contracted by a factor of gamma, giving (gamma L+vt) + (gamma L - vt) = 2 gamma L. With c being constant,...this seems to give us a time contraction cancelling the effect of the vertical clock.. — Gampa Dee

Yes, you're right that the Lorentz contraction of the path must also be taken into account. The Lorentz factor, gamma, is always greater than 1, so the contracted length is L/gamma. The time required for the light ray to reach the receding mirror is therefore t1 = d/v1, where d is the distance between the source and the mirror (d = L/gamma) and v1 is the relative velocity between the source and the mirror (v1 = c - v). Similarly, the time required for the light ray to return to the source is therefore t2 = d/v2 where v2 = c + v.

The total time elapsed is therefore t1 + t2 = L/(gamma(c - v)) + L/(gamma(c+v)). To simplify, you can multiply the numerator and denominator of the first term by c + v and the numerator and denominator of the second term by c - v. You get

t = L(c + v)/(gamma(c^2-v^2))+L(c - v)/(gamma(c^2-v^2)) = 2Lc/(gamma(c^2-v^2))

Since gamma = 1/sqrt(1-v^2/c^2), 2Lc/(gamma(c^2-v^2)) simplifies to 2L*gamma/c which is the same time registered by the vertical light clock.

(Note that c/(gamma(c^2-v^2) = c*sqrt(1 - v^2/c^2)/c^2-v^2 = sqrt(c^2 - v^2)/(c^2-v^2) = 1/sqrt(c^2-v^2) = 1/(c*sqrt(1-v^2/c^2) = gamma/c.)

Intuitively, as v tends towards c and taking into account the Lorentz contraction of the clock, the duration of the return travel tends towards zero. Meanwhile, the duration of the forward travel tends towards infinity despite the shortened distance, as c - v approaches zero faster than sqrt(1-v^2/c^2) does.

Thank you for your time and patience, Pierre Normand

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Yes, you're right that the Lorentz contraction of the path must also be taken into account. The Lorentz factor, gamma, is always greater than 1, so the contracted length is L/gamma. — Pierre-Normand

Yes; thank you...I always think of gamma as being the SQRT 1 – v^2 / c^2, but it’s actually the inverse.

The time required for the light ray to reach the receding mirror is therefore t1 = d/v1 — Pierre-Normand

I have a problem understanding this though; I rather see the time light displaces any distances as being d / c; I would instead claim that v would be responsible for the length contraction instead, being d or L/ gamma + or - some other distance being vt .Also, isn’t the relative velocity between the source and the mirror 0? Therefore, I, for now, understand the 1st path as being
t1 = d / c or (L/gamma +vt) / c

Similarly, the time required for the light ray to return to the source is therefore t2 = d/v2 where v2 = c + v. — Pierre-Normand

Again, I would assume t2 = d / c, d being equal to L/gamma – vt.in this case.

The total time elapsed is therefore t1 + t2 = L/(gamma(c - v)) + L/(gamma(c+v)). To simplify, you can multiply the numerator and denominator of the first term by c + v and the numerator and denominator of the second term by c - v. — Pierre-Normand

I’ve got
(L / gamma + vt) / c + (L/gamma – vt) / c = 2L/gamma c

You get

t = L(c + v)/(gamma(c^2-v^2))+L(c - v)/(gamma(c^2-v^2)) = 2Lc/(gamma(c^2-v^2))

Since gamma = 1/sqrt(1-v^2/c^2), 2Lc/(gamma(c^2-v^2)) simplifies to 2L*gamma/c which is the same time registered by the vertical light clock. — Pierre-Normand

2L*gamma /c was what I had in my first response to you :); however you correctly pointed to me that gamma was a factor which increased the original value, where I needed one which would reduce the outcome ( length contraction).
Now, what I have is instead 2L/gamma c.
I will try to clarify a bit my point. Since the velocity remains c, I think that all we need is the distance for the light to travel in order to calculate the time.
In the first case, (the vertical light clock) the distances the outside observer calculates are the two hypothenuses SQRT L^2 + (vt)^2, the total being 2 * SQRT L^2 + (vt)^2
In the second case,for the horizontal clock, I have L/gamma. + vt one way, and the return path being L/gamma – vt.
If L/gamma +vt = L* [SQRT 1 –v^2/c^2] +vt ..and.the second path is even shorter.
Here’s my problem...as v tends to c, in the vertical clock the path tends towards L^2 +ct^2 ...a very long path,if not infinite, whereas for the horizontal path , it seems the path tends towards 0.
I seem to have two extreme opposite situations.

(Note that c/(gamma(c^2-v^2) = c*sqrt(1 - v^2/c^2)/c^2-v^2 = sqrt(c^2 - v^2)/(c^2-v^2) = 1/sqrt(c^2-v^2) = 1/(c*sqrt(1-v^2/c^2) = gamma/c.)

Intuitively, as v tends towards c and taking into account the Lorentz contraction of the clock, the duration of the return travel tends towards zero. Meanwhile, the duration of the forward travel tends towards infinity despite the shortened distance, as c - v approaches zero faster than sqrt(1-v^2/c^2) does. — Pierre-Normand

Interesting...it’s what I see in the two clocks...(vertical and horizontal). What I would disagree, for now, is that the duration of the clock for the forward travel (on the horizontal clock) would still tend to 0 due to the length contraction of the path between the source and the mirror

I thank you again for your time.
Grampa Dee.

I have a problem understanding this though; I rather see the time light displaces any distances as being d / c; I would instead claim that v would be responsible for the length contraction instead, being d or L/ gamma + or - some other distance being vt .Also, isn’t the relative velocity between the source and the mirror 0? Therefore, I, for now, understand the 1st path as being
t1 = d / c or (L/gamma +vt) / c — Gampa Dee

Yours is an equally valid way to calculate the time required for the pulse to reach the mirror. Mine is only slightly simpler since we don't first need to calculate the total distance travelled but only the time required for the pulse to overtake the mirror (which is initially at the known distance L/gamma) with the knowledge of their relative velocities in the stationary inertial frame. Since the light pulse travels at velocity c and the mirror at velocity v, their relative velocity, and thus the rate at which the gap between them closes, is c - v (and c + v in the return trajectory). I'll nevertheless calculate it your way below.

2L*gamma /c was what I had in my first response to you :)

Thanks for pointing it out. I hadn't yet done the calculation back then ;-)

however you correctly pointed to me that gamma was a factor which increased the original value, where I needed one which would reduce the outcome ( length contraction).
Now, what I have is in stead 2L/gamma c.
I will try to clarify a bit my point. Since the velocity remains c, I think that all we need is the distance for the light to travel in order to calculate the time.
In the first case, (the vertical light clock) the distances the outside observer calculates are the two hypothenuses SQRT L^2 + (vt)^2, the total being 2 * SQRT L^2 + (vt)^2
In the second case,for the horizontal clock, I have L/gamma. + vt one way, and the return path being L/gamma – vt.
If L/gamma +vt = L* [SQRT 1 –v^2/c^2] +vt ..and.the second path is even shorter.
Here’s my problem...as v tends to c, in the vertical clock the path tends towards L^2 +ct^2 ...a very long path,if not infinite, whereas for the horizontal path , it seems the path tends towards 0.
I seem to have two extreme opposite situations.

In the case of the horizontal clock you indeed have d1 = L/gamma + vt for the first path and d2 = L/gamma - vt_2 for the return path. I use "t_2" since the time for traveling the return path is different (shorter). Since in both cases the distance is travelled at c, we have the two equations:

d1 = L/gamma + vt = ct
d2 = L/gamma + vt_2 = ct_2

Isolating t and t_2 in both equations and summing them up, we get the total time:

T = L/((gamma(c - v)) + L/(gamma(c + v)) with is the same result I had obtained more directly by considering the relative velocities of the light pulse and clock.

I had misspoken in the previous post while mentioning the relative velocity between the source and mirror. Good catch! I meant to refer to the relative velocity between the light pulse and mirror (as measured in the stationary frame).

Also, as previously mentioned, although the forward path travelled indeed approaches zero as v tends towards c, the time for travelling it still approaches infinity as our final equation T = 2L*gamma/c shows.

In the case of the horizontal clock you indeed have d1 = L/gamma + vt for the first path and d2 = L/gamma - vt_2 for the return path. I use "t_2" since the time for traveling the return path is different (shorter). Since in both cases the distance is travelled at c, we have the two equations:

d1 = L/gamma + vt = ct
d2 = L/gamma + vt_2 = ct_2 — Pierre-Normand

ok: Would vt_2 be equal to -vt?

T = L/((gamma(c - v)) + L/(gamma(c + v)) with is the same result I had obtained more directly by considering the relative velocities of the light pulse and clock. — Pierre-Normand

This is where it gets foggy for me; you seem to divide by a relative velocity (c+v) instead of adding another distance vt....I’m not saying that you’re wrong, only that I can’t visualize it . If v causes a foreshortening of L, then why not say T = L / (c – v) + L / ( c+v) ? but here, we would be in Newtonian mechanics wouldn’t we? :)

Would it be possible to give the calculation without having (c+v) or (c –v) in the equation?
I understand a bit why you’re doing this but I’m not comfortable with it. For example: if we take c = 1
and v = .5 , then L /(c+v) = L / 1.5 and L/(c-v) = L/.5...Now let L = 1
We would then have L / 1.5 + L/.5 = .66666 + 2 = 2.66666
But, for ( L +vt) / c and (L – vt) / c, we would have [(1+.5t) + (1 -.5t) / 1] = 2
If we start with what you once wrote:

In the case of the horizontal clock you indeed have d1 = L/gamma + vt for the first path and d2 = L/gamma - vt_2 for the return path. I use "t_2" since the time for traveling the return path is different (shorter). Since in both cases the distance is travelled at c, we have the two equations:

d1 = L/gamma + vt = ct
d2 = L/gamma + vt_2 = ct_2 — Pierre-Normand

Without using (c+v)(c-v), could you derive T = 2L*gamma/c in another way ?

Thank you again for your time and patience.

Grampa Dee.

ps: Your name tells me that you might be a french speaking person? I am as well...my name is Andre



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