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Comment by irthomasthomas | Hacker News Reader

"The more you move in space, the less you move in time"

The consequences of this simple rule are rather shocking, as the recent nobel winner Roger Penrose pointed out.

Take the case of two people on Earth, one stationary and one travelling past in a car. They each have different events which they consider the present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. To the person on Earth who is moving, the debate still going on, but in the reference frame of the stationary person, it's a day or so later in Andromeda and the invasion fleet is already on it's way. If there is no absolute reference frame, and both observers reference frames are equally valid, then the outcome of the invasion debate is a foregone conclusion. This is the crux of the Andromeda Paradox and the Reitdijk-Putnam-Penrose argument. https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argume...

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I don't think I understand what's shocking about this. It's like saying that for somebody who watches a taping of a soccer match the result is not yet known, yet for somebody who watched it live it's a foregone conclusion. I don't really get what's the paradox here.

Or maybe more to the point: if you were watching a soccer game Earth from Proxima Centauri, you could only get the result about 4 years after the game took place on earth, so for you the issue is uncertain while for somebody on Earth "at the same moment" the result has been known for years. But of course then the whole concept of "at the same moment" is pretty ambiguous and fuzzy.

I don't really get what's paradoxical here.

The notion of “at the same moment” is not ambiguous and fuzzy. You use clocks and synchronize them. What relativity adds to the picture is the requirement for a common reference frame, which is surprising. It creates paradoxes because our intuitive notion of “at the same moment” does not include the reference frame, so there is a conflict between our intuitive understanding of past/future (which does not change whether you are moving) and the relativistic description of past/future (where two people can disagree about whether a particular event is int the past or the future).

Because of this disagreement, if you had FTL communication and wired it up so you could make a phone call to Andromeda, your phone call would arrive before or after the debate depending on your reference frame on Earth, and you could use it to send information backwards in time.

Synchronize the clocks how? Last I knew, this was still impossible, unless you employ hand-waving.

If I synchronize two clocks next to each other, and then move one away, they are no longer synchronized as one was moving. And we still don't have the speed of c one way, so you can't use that either.

Move clocks at the exact same speed and acceleration in opposite directions, so they stay synchronized.

I don’t think this works either because you can’t meaningfully agree on when light was emitted from one of the clocks. The only solution should involve a single clock but then you are always measuring 2 way and not 1 way speed.

> I don’t think this works either because you can’t meaningfully agree on when light was emitted from one of the clocks.

You can in fact meaningfully agree. You put the clocks in similar reference frames (like “standing on the surface of the Earth”), and accept some small but non-zero margin for error. The fact that a spaceship traveling around the earth does not measure light pulses emitted by these clocks as simultaneous is irrelevant—because we know that the notion of simultaneity relies on reference frame. What we do get is that anyone standing on the Earth’s surface can measure the pulses as simultaneous, within the specified margin of error. This error must necessarily account for the the fact that time progresses differently at different altitudes and latitudes, if your clocks are accurate enough. Because General Relativity is an extremely accurate theory and we have accurate measurements of the relevant physical constants & the mass of the Earth, we can account for the different reference frames and run the clocks at the correct rates so they continue to be synchronized even when they are free running (again, with the appropriate margin of error).

If you are using ordinary quartz clocks, then the clocks probably have enough error that you can ignore relativistic effects. I’m assuming we want atomic clocks if we’re series about chronometry, especially considering how cheap they are these days.

The idea that synchronizing clocks is somehow impossible stems from an unrealistic idea of how people measure time in the first place.

Veritasium just had a good video which discusses this: https://www.youtube.com/watch?v=pTn6Ewhb27k

It turns out there's some circularity in your definitions of "Move clocks at the exact same speed and acceleration in opposite directions" and "synchronized"; that's basically the definition of "synchronized", which is fine from a certain point of view, but from the point of view of examining the nature of space and time themselves, not adequate.

That was a very neat video, and I learned some stuff too! Thanks for posting that.

He clickbaited me but good on that one, but it delivered the goods.

Long time Veritasium subscriber here. He actually made a great video a while ago explaining why professional Youtubers don't have much of a choice when it comes to clickbaiting with titles and thumbnails, because it's the only way to reliably get lots of impressions and views and grow their channel: https://www.youtube.com/watch?v=fHsa9DqmId8

It made me gain a bit of empathy for creators using these tactics on Youtube and tolerate it as long as it's not being used to promote content that's devoid of any substance, which is pretty much never the case for Veritasium videos or any of the other educational channels I subscribe to.

Yes, I understand and agree. It makes me sad as well but I've made my peace with it.

Nevertheless, I commented about this one in particular because when I saw the title card, I legitimately thought, even having seen many of his videos, that he couldn't possibly deliver on that. He got me; he did. I was impressed.

> Last I knew, this was still impossible, unless you employ hand-waving.

I think you may be thinking of synchronization as perfect synchronization for ideal clocks. If you go down this route everything becomes impossible. Instead, think of synchronization as assurance that the maximum error is below some known bound. In general, the bounds can be made quite low.

This is not intended as sarcastic, but you solve the theoretical problem by making it a practical problem?

If 2 clocks are out synch, but only to a small amount that doesn't affect my ability to meet someone for dinner, that doesn't mean they are in sync.

I agree that if you go down this route everything becomes impossible, because at some point you're talking about Planck time, which thankfully we don't need to meetup for dinner.

Two physical objects or measurements are never equal in theory. :-/

> This is not intended as sarcastic, but you solve the theoretical problem by making it a practical problem?

I think this is based on some false idea that error is somehow “not theoretical” which makes no sense. There is a rich set of about error and even an entire field dedicated to its study (statistics). The only reason we are interested in theories in the first place is because the theories correspond to the real world. If you have some theory about time which cannot be measured, or cannot explain errors, then that theory belongs in the garbage. (Think about this: if your theory cannot explain errors, but any actual experiment produces errors, then any actual experiment will demonstrate that your theory is “wrong”.)

Or consider other concepts like “flat”. What does it mean for a surface to be “flat”? No matter how flat a real surface is, it will never be mathematically flat. So either we have to throw away the word “flat” and stop using it outside mathematics (which is a stupid idea), or we define “flat” to mean that a surface is within some deviation from mathematical flatness.

You can’t escape error, even in theory, unless you leave the world of physics and do pure mathematics.

Oh sure, bring statistics into theory. If we were to listen to statistics, it would have us believe spherical cows don't really exist.

Its not impossible. Civil time is just this, in fact.

Its true that if two observers use their own local atomic standard to precisely measure elapsed time then they would have difficulty agreeing on when something happened. However, that's not how civil timekeeping works. One clock declares itself to be a master clock and broadcasts a time+position standard to everyone else. Other observers then construct their own PLL to compute a running estimate of the total phase shift between their local time standard and the one that is broadcast.

In effect, received civil time has a velocity relative to your local atomic time. If every observer can label their observations with civil time then the paradox disappears and you are left with information flow that is bounded to the speed of light. A fast-moving observer has a local atomic standard of time that moves at one second per second, and a received civil time that appears to be running much faster.

A peer-to-peer version of this is how we define international atomic time. Subtle variations in local gravity conspire to actually give the different clocks in the network a different local speed of time. They steer a global PLL to minimize the total squared phase error in the network. Each node in the network can make observations on the TAI timebase by adding its own clock offset to their local clock.

But you can calculate the difference, which happens with GPS satellites all the time.

GPS is based on synced clocks. Problem is that the satellites suffer the rules of relativity. But the good news is that we know the rules of relativity, and therefore can compensate for them.

I always thought relativity was purely theoretical, but it is actually practically applied in GPS sattelites.

I think it's still surprising, if not "paradoxical" (obviously it's not paradoxical if it's reality).

The difference is: in your two examples we know there's a delay, and all you did was say that some people will know the result before others who are receiving the delayed result.

What the original question is saying is that you can't ask "well, what is happening right now on Proxima Centauri?" since the very question of "now" is not specific. I think that's quite different.

On Earth, with Newtonian physics, we intuitively think that "now" is shared, so we really can say "I wonder whether someone has scored a goal now," and the answer shouldn't depend on whether you're in a car or not.

>On Earth, with Newtonian physics, we intuitively think that "now" is shared, so we really can say "I wonder whether someone has scored a goal now," and the answer shouldn't depend on whether you're in a car or not.

That's insightful, and actually it made me realize that it's probably true that nowadays we expect information to be available worldwide effectively instantly, but that obviously wasn't always the case. "Right now" we're having this discussion on Hacker News with people from around the world, but merely a few decades ago this type of simultaneity wouldn't have been possible. Nothing of what would could've done locally could've immediately influenced dozens of people around the globe.

This shared "now" is effectively a modern invention.

I think the unusual part is that it is not a limit of communication, it is time itself. With a tape, you know that it happened in the past, for this, both are experiencing their real present time, but they don't agree with each other.

It's only surprising if you don't understand that this is a block universe.

> I don't really get what's paradoxical here.

IIRC, the implication is that change predetermined and fixed, so is essentially static.

Not paradoxical, but it does suggest that the future is as taped as that football match.

> the consequences of this simple rule

The consequence you refer to is not a logical necessity based on relativity. It's just a particular interpretation, the "block universe" interpretation, which is not accepted by all physicists.

See here for a refutation of the argument referred to:

https://www.physicsforums.com/insights/block-universe-refuti...

I don't know why it would follow from relativity, but the block universe just makes sense. To me, it follows from determinism and Occam's razor.

Because relativity does away with the alternative, that of a universally accessible “now”.

> relativity does away with the alternative, that of a universally accessible “now”

Relativity does away with "now" period--"now" is a frame-dependent concept in relativity, and frame-dependent concepts, in relativity, have no physical meaning.

As I noted in the article I linked to upthread, the physically meaningful division of spacetime, at some particular event "here and now" (like you sitting in your chair reading this), is into three parts, not two: the past light cone, the future light cone, and the spacelike separated region (what Roger Penrose, in the very same book where he presents the Andromeda scenario, calls "elsewhere"). The past light cone behaves like our intuitive concept of "past", and the future light cone behaves like our intuitive concept of "future", but the spacelike separated region does not behave like anything our intuition is familiar with. The whole "Andromeda paradox" argument is based on failing to recognize that the spacelike separated region exists in relativity and doesn't match up with our intuitions about either "past" or "future".

> To me, it follows from determinism

I think it follows from just determinism; you don't even need Occam's Razor.

The reason it isn't logically required by relativity is that relativity does not logically require determinism.

Is this actually a problem? By the time the person travelling in the car and the stationary person synchronise their information enough to communicate won’t their frames of reference also sync up? Like if I’m moving and I see something before you, won’t you see it as well before or at the same time I can tell you I saw it?

From the wiki... "Notice that neither observer can actually "see" what is happening in Andromeda, because light from Andromeda (and the hypothetical alien fleet) will take 2.5 million years to reach Earth. The argument is not about what can be "seen"; it is purely about what events different observers consider to occur in the present moment."

But the entire point of relativity is that there’s no such thing as a joint “present moment” between more than observer. The only meaningful construct is your own present moment, about which information radiates outward at the maximum speed of information transfer in space-time (speed of light/gravity). Information reaches other observers based on their trajectory and position in space time. No such thing as the universal now.

Which circles right back to the paradox. The moving persons reference frame has aliens still debating an invasion, and the stationary persons reference frame has the aliens already on their way. How can there be any room for free will in the deliberations of the alien government, if the timelines of both observers are equally valid? The article on relativity of simultaneity has much more detail on the subject https://en.wikipedia.org/wiki/Relativity_of_simultaneity

For there to be a paradox, the observers would have to find out about it sooner than it would take light to communicate the result.

Otherwise, the earliest time that the aliens can find out if they're going to invade or not is when they make the decision. Sure, the observers can find out, and try to tell each other and the aliens, but since it takes at least a round trip of light from the aliens to the observers, the observers always find out after the aliens have made up their minds.

If the aliens find out that they make the decision when they make the decision, it seems to me at least that they actually made the decision rather than having it be predestined

Why would it be a day or so later? The Wikipedia makes that claim, but the linked source does not: https://archive.org/details/emperorsnewmindc00penr/page/302/...

The two people would perceive the changing of a traffic light on the same street at almost the same time - why would it be different for the Andromedans?

Welcome to the ancient times. The speed of information travel has always been capped but now we know that there is absolute upper limit - c. It still works on earth, now is not shared, but for most practical purposes the synchronization delay does not matter, except when it does like stock and sport betting.

I think about this like this. The universe is always in exactly one state but for each inside observer the knowledge about this state depends on its location.

Is the person in the car moving away from or towards Andromeda?

The example you gave can be interpreted two ways and my intuition tells me that the example is only true in the case that the car is moving _away_ from Andromeda.

Is it also, weirdly, the case that if the car is travelling towards Andromeda that time slows down sufficiently that they perceive the outcome of the debate _after_ the person standing still?

It is also weird that there is now a sports car that at various points in its orbit is moving towards Andromeda.

I gave up the idea of time being a dimension long ago.

It allows me to think in ways others do not.

I made a video on a different way about thinking time slows near the speed of light:

https://youtu.be/A-2XQQDD6QQ

This is a nice video explaining simultaneity.

https://www.youtube.com/watch?v=wteiuxyqtoM

I'm fairly convinced this is intellectual masturbation. I think two situations are being confused for one another:

a) If you travel close to the speed of light, causality goes more slowly (e.g. a clock ticks more slowly) than it does for someone who is stationary. So, two clocks will diverge. This is true, AFAIK.

b) If you travel close to the speed of light, and somebody else is stationary, they are traveling "into the future" relative to you, whereas you are "in the past" relative to them. I believe this is nonsense. But, I believe this is required for the "Andromeda Paradox" to hold. Thus, I don't think it holds. (BTW, we know that paradoxes never hold, so there must be something wrong with it.)

The solution to the Andromeda Paradox that I am proposing is to say that there is one universal ordering of events (among both observers and the Andromedans), but the two Earthling observers have different times on their clocks at the particular point in the sequence of events where the Andromedans decide to invade.

>The solution to the Andromeda Paradox that I am proposing is to say that there is one universal ordering of events

Proposing this is fine, but proving it is quite a matter altogether - you have to replace special relativity. Special relativity pretty much explicitly states this isn't the case, making an exception for events that are causally connected, but there's been a slew of experiments over the past several decades that call into question even that exception at long distances, and more recently, even ones for local observers, e.g. https://advances.sciencemag.org/content/5/9/eaaw9832

Personally, I'm in the Rovelli and loop quantum gravity camp - time probably isn't actually a real thing on its own, and what we perceive as time is just an emergent property of thermodynamics.

I agree! Time is emergent. It is only comparing one thing moving relative to another thing. Without anything moving relative to each other, time can't exist:

https://youtu.be/A-2XQQDD6QQ

Yea, i think time is kind of used to define two different things and that seems to make these discussions confusing. I think if you are close to the speed of light, your atoms are moving slower than those of the stationary person and so your local clock time seems to stay constant while the stationary persons clock time seems to speed up in relation. But it's all a matter of perception of clock time passing and now is the same everywhere.

To be clear, my conception of a "universal ordering" doesn't mean we can always measure when things happen relative to one another. If two things are causally related, we know one happened first. If a tree falls on Andromeda "right now," I don't know if that happened before or after a particular timestamp here on Earth, but it either did or it didn't. (Same goes for all possible timestamps for all clocks going at whatever speed they are going; their timestamps will diverge, but they could still be ordered if we knew the speed they travel relative to light and the starting value and how often they tick, e.g. once per second nanosecond or whatever. So if we had an observer on Andromeda with such a clock, we could eventually order events there relative to events on Earth based on the timestamp they report, though it would take a very long time for their report to reach Earth).

Are you sure that's not compatible with special relativity? Genuinely asking. If not, is it possible to explain why it isn't? I'd like to know (but if I'm asking you to write a book, never mind).

When you say you're in the Rovelli and loop quantum gravity camp - is that compatible with special relativity? I'm guessing yes, but let me know.

I think time is an emergent property of causality. That sounds close to what you are saying (possibly a different way to say the same thing).

I believe what you’re talking about with an universal ordering of events is called the Relativity of Simultaneity. https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity

I believe you are correct in that the closest you can get to change the order of two events is to make them simultaneous (in the case of photons, which do not experience time) but you cannot change one event ordering beyond that since that would violate causality.

You could change the event ordering by forcing some events to take a longer path through space?

For a real world example, we can predict supernovas because we've already seen them from another trajectory of light: https://youtu.be/ljoeOLuX6Z4 so we can both see the remote event before and after local events

Relative to a clock on earth, moving at a given speed relative to the speed of light, the supernova happened when it happened.

All that is changing with lensing is that you're seeing the light coming from it earlier looking in one direction than another. Either way, it happened in the past. The order of events is not changing.

It's like saying that a stock trader using a fiber connection figures out about a price movement more quickly than a stock trader using a dial-up connection.

At least, I think that's right; not a physicist.

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