# Time dialation when viewing across the universe

• DarkMatterHol
In summary, Brian Greene's Nova special discussed time dilation when frames are moving towards or away from each other. This can happen when two frames are separated by great distances and can cause time to be shifted in either direction. If we observe a distant solar system while traveling towards it, the 'now' time for that galaxy will be shifted towards the future in our frame, while if we travel away from it the 'now' time for that galaxy will be shifted towards the past in our frame. For very distant frames, the shift is hundreds or thousands of years. My question is, does this mean that if we were to travel in a circle, as we ride the Earth around the sun, moving towards and then away from the solar system in

#### DarkMatterHol

Hi. Just watched a Nova special with Brian Greene, "The Fabric of the Universe/The Illusion of time", describing significant time dilation when two frames are moving towards or away from each other at low velocities, when the two frames are separated by great distance.

This left me with a couple of questions. The first would be, doesn't this mean, in an expanding universe, that we see the rest of the universe as it was, very much earlier than we otherwise would by taking only the speed of light into account?
Since time began with the big bang, and distant parts of the universe are dilated to earlier times, does this not mean that from any frame, most of the observable universe gets scrunched into the moments after the big bang? I mean there will be a huge dilation shift for events soon after the big bang, because these events are both so far away and moving away so fast at the same time, that those events would be shifted in time to before the big bang itself, unless those events were squished against the big bang boundary, or... this is what i would like to understand.

The other question that came up is the following - Let's say we have two distant galaxies, and we, in our galaxy have a telescope with which to observe a solar system within the distant galaxy. If we observe the distant solar system while traveling at say arbitrarily at 20MPH towards that galaxy, the 'now' time for that galaxy will be shifted toward the future in out frame. Conversely, if we travel away from that galaxy at 20MPH the 'now' time for that galaxy will be shifted toward the past in out frame. for very distant frames the shift is hundreds or thousands of years. My question is, does this mean that if we were to travel in a circle, as we ride the Earth around the sun, moving towards and then away from the solar system in the distant galaxy, would we not see the planets in that solar system running forward and then backwards, once every year? Would we not see time in that distant solar system oscillate forward and then backward, as a sine wave? The planets processing forward, then backward each Earth year?

To my understanding, the only requirements for this to be true, the orbits of the planets would need to be on the order of years, while the distance between galaxies would have to be sufficient to dilate relative time by a factor of several years. The procession of local times would distort the sine wave function of relative time slightly as local times move along.

Looking forward to your thoughts, explanations.

Regards,

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Assuming I understood you correctly, one thing I can say is time cannot run backwards. While simultaneity can be disrupted, causality cannot be. Time can be slowed (and sped up in GR), but never put in reverse.

Also, yes when we look out into the distant universe we see it as it once was.

That sounds like it would be right, but, if i understand what was said to happen,
then relative to when you are not traveling with respect to the distant frame, when you are traveling towards the hypothetical solar system, relative 'now' time is many years shifted to the future, while when you are traveling away from that galaxy, the relative 'now' time is shifted years to the past. So what do you see when you observe the distant solar system with a telescope the entire time you are traveling in a circle, as the Earth does in its orbit? If the relative 'now' time shifts from future to past over and over?

Another example might be when you [and your telescope] accelerate away from the distant solar system in a straight line. The relative time line for the distant solar system will smoothly shift further and further back in time while you accelerate - hence the distant planets will run backwards, and 'people' on those planets will grow younger.

So, what am i missing? - or what isn't Brian Greene telling us? And what do we see through the telescope?

Could it be that once we are seeing earlier and earlier times, we cease seeing the solar system at all? does it simply disappear from our access? Does this form our cosmic horizon?
An interesting aspect of this is that for great distances, the shift can be a great many years for small changes in relative velocity.

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I'm not really in a position to answer, it's too complicated to be worked through logically and it surpasses the realm of equations I can work with as we are dealing with accelerating reference frames: the property of GR.

One idea I have that is completely out of the blue, but would validate both what you are saying and my (hopefully correct) view would be to say that yes the relative time changes, but the math would always work out to prevent the time from going backwards, instead to end up just slowing at an oscillating rate, I have no way to prove this however,

The surface of last scattering is the most distant part of the observable universe [at least in EM wavelengths] with a redshift of about z = 1100. The big bang occurred at z = infinity. Looking to great distances is like watching an ever slowing clock tick. The clock ticks at a rate of approximately 1/[1+z]. Obviously, the clock cannot run backwards.

Thanks Chronos. I do understand that part. That given, as per my question #2, I would like to know what we see through the hypothetical telescope as we watch relative 'now' time go from future time to past time as we change relative velocity with an observable distant location, such as a solar system in a distant but observable galaxy.

I know that, as you point out, the universe we observe 'now' time goes backward in time the further out we look, all the way to the time that matter first condensed and space became transparent. This can be explained by the limited speed of light alone, but is compounded by the shift in relative 'now' times for moving frames. Let's assume that the galaxy and solar system in question are within the observable universe.

What i am specifically interested in are observations of shifts forward or back in relative 'now' as we change relative motion between distant frames, and what it would look like through a hypothetical [or not so hypothetical] telescope.

To help visualize this, the Nova program shows the universe as unfolding as orthogonal time-slices across a time line through space. For observers in the same inertial frame the slices of 'now' are orthogonal and directly 'across', as in a loaf of sliced bread, but when we move towards or away from the distant location, as in riding on a bicycle, the time-slices of 'now' time cross the universe at an angle, angled backwards in time if you are moving away, and angled forward in time as you move towards the distant point [planet in this case]. Here's a link:
www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.html#fabric-time
If the video is not working you can also read the transcript - the part i am asking about starts at "To see what I mean, think of spacetime as a loaf of bread" or just before.

When the time-slice goes from orthogonal to angled back in time, when we start moving away from the distant planet, something observable happens. what is it? The Nova program seemed to indicate that a velocity shift of a few miles per hour can result in a shift back in time of hundreds of years if the observed and the observer are far enough apart.
What was never discussed in the program, is what do we observe as 'now' time goes back those many years, as we accelerate up to speed on our bicycle? Since changes in velocity do not take place instantly, what is observed as we change velocity, that is, as the angle of time-slices are changing? I visualize that time for the distant object would speed up and slow down, and seemingly to even go backwards when the change of velocity for the observer is large enough, and the observer and the observed are far enough apart.

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Time can never go backwards for any observer at any time. The equations already given should have made this clear. From a GR perspective, time and space are different manifestions of the same thing - gravity.

Thanks for the equations Chronos - 1/[1+z] . I'm still a little confused regarding my second question.
BTW- i am not a student. I am very interested in cosmology though, and the so called "now" slice phenomenon as laid out in the nova program is intriguing. I am not sure at this point how the red shift equation explains what the Nova program claims, and how it provides a definitive an answer to what we would see when we change the angle of the 'now slice' so that it intersects with an earlier 'now time' for distant objects.

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I think you are reading unintended [and incorrect] meaning into the Nova program.

Thanks Chronos. You have clearly answered what does not happen.

Admittedly, I probably did a poor job of explaining myself, but essentially I'm simply looking for an answer to the question:

"What would we see while observing the distant planet with a telescope", while accelerating back and forth with respect to it? To make it interesting, let's assume we can see the people moving around on the surface of the planet.

Here is a link to the full scenario, for anyone that's interested.
The scenario I'm asking about starts at 19:00 and runs through 26:00
The same scenario has also been described in countless books on Relativity.

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DarkMatterHol said:
"What would we see while observing the distant planet with a telescope", while accelerating back and forth with respect to it?

Maybe, if all the angles are right, and your telescope is powerful enough, you could see a small "wobble" in the planets orbit. At some point it would appear to orbit faster and at other times slower. I don’t think you would see time going forwards and backwards.

What I found interesting in the video is that time is not universal. That alien in another galaxy could be on a planet with higher gravity, and when an alien cosmologist tries to figure out when the Big Bang happened, he/she/it would think that we humans are off by a few billion years.

Acceleration [and accompanying time dilation] does not vary to any appreciable extent. We would see time moving slowly [by our clocks] on a planet in the distant reaches of the universe. It might occasionally speed up or slow down very slightly, but, never run in reverse.

Chronos said:
Acceleration [and accompanying time dilation] does not vary to any appreciable extent. We would see time moving slowly [by our clocks] on a planet in the distant reaches of the universe. It might occasionally speed up or slow down very slightly, but, never run in reverse.

I agree with you Chronos. That's why what Brian Greene said here is so intriguing.

In his own words:
BRIAN GREENE: To get a feel for the bizarre effect this can have, imagine an alien, here, in a galaxy 10-billion light years from Earth, and way over there, on Earth, the guy at the gas station. Now, if the two are sitting still, not moving in relation to one other, their clocks tick off time at the same rate, and so they share the same now slices, which cut straight across the loaf. But watch what happens if the alien hops on his bike and rides directly away from Earth.

Since motion slows the passage time, their clocks will no longer tick off time at the same rate. And if their clocks no longer agree, their now slices will no longer agree either.

The alien's now slice cuts across the loaf differently. It's angled towards the past. Since the alien is biking at a leisurely pace, his slice is angled to the past by only a minuscule amount. But across such a vast distance, that tiny angle results in a huge difference in time. So what the alien would find on his angled now slice—he considers as happening right now, on Earth—no longer includes our friend at the gas station, or even 40 years earlier when our friend was a baby.

Amazingly, the alien's now slice has swept back through more than 200 years of Earth history and now includes events we consider part of the distant past, like Beethoven finishing his 5th Symphony: 1804 to 1808.

DAVID KAISER: Even at a relatively slow speed we can have, actually, tremendous disagreements on our labeling of "now," what happens at the same time, if we're spread out far enough in space.

BRIAN GREENE: And if that's not strange enough, the direction you move makes a difference, too. Watch what happens when the alien turns around and bikes toward Earth. The alien's new "now slice" is angled to…toward the future, and so it includes events that won't happen on Earth for 200 years: perhaps our friend's great-great-great granddaughter teleporting from Paris to New York.

So this is what has me wondering 'what gives', and what does an observer see during the transition from bicycling 'towards', to bicycling 'away from'.

From what Dr. Greene says here, it clearly seems that an observer should be able to look backwards through time as he changes direction and the time slice angle changes from future to past. What am i missing? could Dr. Greene just be wrong about this?

*Note there is no acceleration involved in the two conditions Dr. Greene describes, just biking at a leisurely pace directly away from, and towards the distant location. I am interested in what an observer would see during the transition between moving 'towards' to moving 'away', a period of time that does include modest acceleration...

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DarkMatterHol said:
I agree with you Chronos. That's why what Brian Greene said here is so intriguing.

In his own words:
BRIAN GREENE: To get a feel for the bizarre effect this can have, imagine an alien, here, in a galaxy 10-billion light years from Earth, and way over there, on Earth, the guy at the gas station. Now, if the two are sitting still, not moving in relation to one other, their clocks tick off time at the same rate, and so they share the same now slices, which cut straight across the loaf. But watch what happens if the alien hops on his bike and rides directly away from Earth.

Since motion slows the passage time, their clocks will no longer tick off time at the same rate. And if their clocks no longer agree, their now slices will no longer agree either.

The alien's now slice cuts across the loaf differently. It's angled towards the past. Since the alien is biking at a leisurely pace, his slice is angled to the past by only a minuscule amount. But across such a vast distance, that tiny angle results in a huge difference in time. So what the alien would find on his angled now slice—he considers as happening right now, on Earth—no longer includes our friend at the gas station, or even 40 years earlier when our friend was a baby.

Amazingly, the alien's now slice has swept back through more than 200 years of Earth history and now includes events we consider part of the distant past, like Beethoven finishing his 5th Symphony: 1804 to 1808.

DAVID KAISER: Even at a relatively slow speed we can have, actually, tremendous disagreements on our labeling of "now," what happens at the same time, if we're spread out far enough in space.

BRIAN GREENE: And if that's not strange enough, the direction you move makes a difference, too. Watch what happens when the alien turns around and bikes toward Earth. The alien's new "now slice" is angled to…toward the future, and so it includes events that won't happen on Earth for 200 years: perhaps our friend's great-great-great granddaughter teleporting from Paris to New York.

So this is what has me wondering 'what gives', and what does an observer see during the transition from bicycling 'towards', to bicycling 'away from'.

From what Dr. Greene says here, it clearly seems that an observer should be able to look backwards through time as he changes direction and the time slice angle changes from future to past. What am i missing? could Dr. Greene just be wrong about this?

*Note there is no acceleration involved in the two conditions Dr. Greene describes, just biking at a leisurely pace directly away from, and towards the distant location. I am interested in what an observer would see during the transition between moving 'towards' to moving 'away', a period of time that does include modest acceleration...

Now slices are a completely imaginary calculated quantity. It is like saying, "So you are 18 years now. Through the power of mathematics, I predict that in exactly one year you will be 19 years old! The future is determined! No escape!"

I don't mean to be sarcastic. That really is pretty much what he is saying. Mr. Greene should be embarrassed and ashamed of himself. If you look at a distant planet, your velocity does not change the time you see there. This is a simple experimental fact.

Ok. Thanks all. It looks like this is taken up in more detail in two threads in the Relativity section.

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Well, we know if I throw a ball across the room toward the east, in the direction of the Earth's rotation, that the ball is moving faster than me and the earth, and therefore time slows down on the ball a little bit. Two tremendously accurate watches, one on my wrist and one on the ball, would show that a tiny fraction of a second less will have elapsed on the ball when it bounces against the wall, compared with my time. This was proven with the Hafele–Keating experiment where atomic clocks aboard airplanes were compared with atomic clocks on the ground. So I am looking into my past when I look at the ball. Agreed?

If I could throw the ball really fast, an appreciable fraction of the speed of light, I would be looking further into my past when I looked at the ball. I am aging faster than the ball. So I have no trouble with the concept. Where I go nuts is when I try to wrap my mind around the idea that because of the huge space between observers in the Nova story, a short bike ride through spacetime by one observer can produce such a huge time effect on the other end.

I know that spacetime is sometimes mapped by relativists on an analytic geometry graph, where the vertical dimension X is space and the horizontal direction Y is time. And such a mapping would give the slice effect shown on the program, where a slight angle at one end becomes a huge gap at the other end. But in terms of this guy riding a llttle bicycle a few steps away from me and then becoming simultaneous in time with Beethoven...well...whoa... ... ... ...<choke>...

False

The observer on Earth sees the space ship. It flies away on its course. but will be back to teach you time dilation.

The ship expends massive DeltaV to get to 99.9 % light speed.
It does a big loop and heads back to earth.
Already 1 year has passed on earth. and 6 months on ship.

Now the 'chronos' [the ship]
blasts though our solar system. To us it is an object moving VERY fast and at 99% c takes a 'few days' to enter and exit the solar system.
For those on the chronos.. it is a few hours.

STrange and wonderfull.. motion and thus time slow. all laws associated with motion and time slow as well. Light 'fits' to the the current paradigm.
Space itself in the ship has become separate from space outside

You are asking the wrong questions.
its not what it look like from outside..
But what it is inside. The two are are not linked but for perspective

howdy op,

i think the folks here are answering without being familiar with the original material so here it is folks:

http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.html#fabric-time

start at the 21 min mark.

what i don't get is why the time slice gets ANGLED. i understand that as you move faster, the clock ticks slower for you than your surroundings but why does that impart an ANGLE to the time slice as opposed to simply OFFSETTING your time slice?

in which case, the offset slice would be just as miniscule a million light years away as it is right where the alien is peddling his tricycle at 3 mph.

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but i WANT to believe! haha, because if it's true, it really would answer a lingering question of mine - does the past actually persist or does it actually continue to exist... or is it simply an incorrect analogy that human beings have created because of our familiarity with space (where space previously traversed does not "disappear" and can be returned to) or perhaps mediums like books where page 10 continues to exist when i have read to page 11 and i can return to page 10.

but if the angled time slice thing works out, that means that all of time from past to future exists now... it's just our current access to time/space is limited but everything exists such that the past and the future are just as "REAL" as NOW.

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as for your question OP, i think the trick to the thought experiment from the episode is that you'd be so far away, that you'd never see anything that gave any indication of time moving backwards... and/or, there's something we're not considering in terms of what transpires as light travels from Earth to the alien.

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hopefully, some real physicists will take a look at the episode and give a better answer to you and to me!

jin

The problem with understanding the alien on a bicycle example stems from our human perception, where we refer to events happening here or there, or in the past or future. There is no such thing as space and time, there is “spacetime”. The more you have of one, the less you have of the other. In the extreme case,

You can either be located at one infinitesimal point in space for all eternity (like a photon traveling at light speed as a particle, for which all events occur simultaneously)

Or

You can be located at every point in space for an infinitesimal instant (like the photon’s electromagnetic field, which permeates the entire Universe at once)

It helps to visualize a sound wave. If you perform a Fourier transform of the amplitude with respect to time, you get an oscilloscope trace. If you perform it relative to space (wavelength), you get a spectrum analyzer trace.

For a pure audio tone, the time-based transform looks like an endless sine wave, and the space-based transform looks like a sharp single peak.

From a more philosophical standpoint:

“At the highest level of satori from which people return, the point of consciousness becomes a surface or a solid which extends throughout the whole known universe.” - John Lilly

“Time-like physical beings dwell inside the light cone. Space-like abstract beings dwell outside the light cone. Beings of light dwell on the light cone.” - Tony Smith

thanks cakewalk.

but the issue is that brian greene makes very specific claims. are those claims wrong?

and as human beings, we don't have access to the entire volume of time (for some reason) and the notions of past, future and present are inescapably real for us.

but the remarkable thing for me is that greene's thought experiment about the angled time slice tells me that the future and the past are just as real as the now... which i was not convinced of before...

so again, my question would be - why is the bicycling alien inducing an angle in the time slice across space instead of simply an offset?

jin

jinchoung said:
thanks cakewalk.

but the issue is that brian greene makes very specific claims. are those claims wrong?

and as human beings, we don't have access to the entire volume of time (for some reason) and the notions of past, future and present are inescapably real for us.

but the remarkable thing for me is that greene's thought experiment about the angled time slice tells me that the future and the past are just as real as the now... which i was not convinced of before...

so again, my question would be - why is the bicycling alien inducing an angle in the time slice across space instead of simply an offset?

jin

All of our information comes from light and its relatives. The speed of such information is limited by the speed of light. So we can know only the past. We can say that the present exists only in our imagination. In particular with these aliens, they know nothing of what is going on on Earth, and no matter what they do it will be at least ten billion years before they do know.

If the alien on the bicycle continues on that path for ten billion years, somehow evading the gravity of his planet and other obstacles, then by his clock it will have been ten billion minus two hundred years. I do not think that this proves that the future is predetermined. Hardly anyone except Greene thinks that this shows that the future is predetermined, it just shows that his clock acts differently from what one might expect. Maybe the future is predetermined, maybe it isn't -- this argument seems completely irrelevant to me. I prefer to think that it shows that the idea of the present is completely imaginary. If one alien's imaginary present is different from that of another alien's, so what?

Suppose I ask you how old your sister is. You respond eighteen years. I respond, "Through the power of mathematics I predict that in exactly one year your sister will be nineteen years old. The future is predetermined!" I think that this is better than Greene's argument. At least in one year the prediction can be tested.

"In particular with these aliens, they know nothing of what is going on on Earth, and no matter what they do it will be at least ten billion years before they do know."

absolutely. the thought experiment is talking about the reality of the "now slice" - even though that alien would have absolutely NO ACCESS to that now moment on Earth by any means because of the speed limit of light.

but that inability to access the conditions of Earth from the alien biker does not disqualify the thought experiment itself.

so again, the question is:

WHY is the now slice ANGLED instead of simply OFFSET? why does a miniscule clock tick difference expand with distance like the mis-aim of a gun?

Time does not move linearly from the perspective of a photon.

Chronos said:
Time does not move linearly from the perspective of a photon.

but we're not talking about a photon. we're talking about an alien on a bicycle. did you see the brian greene video?

jin

jinchoung said:
the thought experiment is talking about the reality of the "now slice" - even though that alien would have absolutely NO ACCESS to that now moment on Earth by any means because of the speed limit of light.

but that inability to access the conditions of Earth from the alien biker does not disqualify the thought experiment itself.

On the contrary, the fact that the experiment is physically impossible DOES disqualify it. "If X event that could never possibly happen were to occur, what would be the result?" This is the realm of speculation and fantasy, and no result of such a thought experiment would give any information about the nature of reality.

jinchoung said:
so again, the question is:

WHY is the now slice ANGLED instead of simply OFFSET? why does a miniscule clock tick difference expand with distance like the mis-aim of a gun?

At around 23:30 in that video, Brian Greene says "Since motion slows the passage of time, their clocks will no longer tick off time at the same rate." He then goes on to say that this phenomenon allows one to look into the past. He's made a huge logical jump here that does not make sense. Even VERY slow time is still 'moving forward'. Slow does not mean reverse. Looking at a stationary clock as you move away from it, it will appear that the clock is moving slowly, but it will never appear that the clock is moving backwards. If you're moving fast enough away (.99999999999999999c), it may seem that the clock has entirely stopped, but you'll never be able to see 'into the past' in the way Brian Greene is saying.

edit for elaboration: Brian Greene's slice-of-bread analogy can be useful if he used it in a more appropriate way. Imagine it this way instead. (This is going to be hard for me to explain the picture in my mind.) Rather than thinking that the alien's motion away from Earth has caused a sliced time-angle, imagine this: because the alien is now moving away from Earth, HIS side of the loaf of bread will be moving forward at a faster rate than the Earthling's. Over time, this lopsided forward motion of the "now slice" will cause the alien's end to be much further forward than the Earthling's end.

The angle of the "now slice" increases with time depending on the velocities of the two observers. It doesn't instantly happen like Brian Greene describes it. The alien will never see 'into the past', he'll just see the Earthling moving slower through time. The angle of the "now slice" will grow larger and larger if the alien continues his travel away from Earth.

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"On the contrary, the fact that the experiment is physically impossible DOES disqualify it. "If X event that could never possibly happen were to occur, what would be the result?""

that's a mistake of equating something that is not generally observable to the party in question with that which is "physically impossible".

one could not ever report back what happens after you cross the event horizon of a black hole and yet we have a theoretical idea of what happens.

there is nothing physically impossible with an alien riding a bike.

also, as a lay man, it does seem rather odd to me to hear people dismiss (so quickly) a renowned physicist's assertion rather than doing the more reasonable thing (imo) of trying to understand it assuming the fault lies with oneself.

jin

jinchoung said:
that's a mistake of equating something that is not generally observable to the party in question with that which is "physically impossible".

one could not ever report back what happens after you cross the event horizon of a black hole and yet we have a theoretical idea of what happens.

there is nothing physically impossible with an alien riding a bike.

also, as a lay man, it does seem rather odd to me to hear people dismiss (so quickly) a renowned physicist's assertion rather than doing the more reasonable thing (imo) of trying to understand it assuming the fault lies with oneself.

jin

It's not the alien riding a bike that is physically impossible, it's the being able to 'see' something as it's happening that's occurring light years away.

And for the record, many people have a problem with what Brian Greene says. I know he's a very intelligent man and I'm sure he knows a lot more about physics than I do, but the idea of being able to go/look BACKWARDS in time is fringe at best.

His video does give the impression that he believes it's possible to look back in time, but that may only have been a problem of presentation, because there's an article in which he emphasizes that going back in time is not possible: here

"it's the being able to 'see' something as it's happening that's occurring light years away."

again, he NEVER makes the claim that you can see it! it is indeed physically impossible to see into the past (in this way, that is - of course you see into the past everytime you see the stars).

but that's not what the thought experiment is about at all.

it's saying that (even though you can't see it), when you ride your bike toward a galaxy millions of light years away, your NOW is "simultaneous" with an alien's past.

again - he is not saying that you can SEE anything.

"he emphasizes that going back in time is not possible"

right. and he's not saying any different with the video.

Chronos said:
I think you are reading unintended [and incorrect] meaning into the Nova program.

I watched that program and used the segment about NOW with the alien on a bike in my intro physics class last week. Chronos is right, you've misunderstood Greene. He's only talking about special relativity, not general relativity. SR holds locally in GR, but not globally so you can't use the exact version of that example in a GR cosmology. The concept of NOW in SR is something you probably use often, e.g., "I wonder what my brother is doing right now in Indiana." Greene tries to make this clear with his use of a clock, cat, bird in Venice, asteroid collision with the Moon, ... . He's defining a spatial surface of constant time via a collection of events that you deem simultaneous.

In SR, moving clocks run slow and moving objects shrink, but motion is relative, so the person whose clocks you say are slow and whose meter sticks you say are short is saying the same thing about your clocks and meter sticks. Who's right?

If you believe there is no absolute frame of reference (most do, since there's no way to distinguish one inertial frame from another via physics experiments), then you'd have to say that whether or not the meter stick is short is frame dependent. You can construct a single spacetime in which both facts obtain (your sticks are ok, his are short, and vice-versa) by allowing the notion of simultaneity to be relative. That is, each person has his own NOW.

That is what leads to Greene's slicing of spacetime. I'll attach a document I use to teach this to intro physics students.

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• SR Example Phy200.pdf
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RUTA said:
That is what leads to Greene's slicing of spacetime. I'll attach a document I use to teach this to intro physics students.

Here's another version with better graphics: