# B But in reality, time isn't relative at all, right?

#### GuillemVS

I don't know how to make that question better, to not seem as if I'm asking why is time relative (that's not what I'm looking, I think).

When we say that time is relative, we look at how many time takes light to go from one point to another, in order to be seen from another perspective. So, when something is seen after it happened, that's where relative comes. Right?

Here's is my question: if light defines when something will be seen in time, it means that time isn't relative at all, it just keeps moving, but things are seen maybe after it happened because of the speed of light. Or is it that light's speed is the maximum "rate" of the univers in which time goes forward? So that if something happened here it means that by the time it reaches there, for them, it will be when it happened relative to them, because time moves at that speed too?

Little confused, thanks in advance.

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#### PeroK

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Special Relativity, which is Einstein's theory of space and time, has nothing to do with the delay in light signals reaching different observers. That is a common misconception.

#### Orodruin

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”Time is relative” is a very vague phrase without any real substance. The actual physical concept is the relativity of simultaneity and its consequences. Given an inertial observer, that observer can construct an inertial coordinate frame where ”simultaneity” is defined as events that occur at the same time coordinate. This includes taking the travel time of light into account and is ultimately not defined as when the light from the event reaches the observer (but rather that time minus the light travel time).

The relativity of simultaneity is the fact that different inertial observers with a non-zero relative velocity constructing their inertial coordinates using the same procedures will lead to different definitions of simultaneity, ie, events that are simultaneous for one observer might not be simultaneous for the other.

#### Ibix

You are misunderstanding. The point of the Einstein's train thought experiment is that if I (on the platform) see two flashes of light arrive at the same time from things that I know are the same distance away from me then I know the flashes were emitted at the same time. But my friend (on the train) also knows that the flashes came from the same distance away from her, but she did not see them at the same time, so they were emitted at different times.

This has nothing to do with light travel time, except that you need to subtract that time out to get the emission time from the reception time. Once you do that, you find that observers at different velocities do not agree on whether events were simultaneous or not.

You can repeat the thought experiment with both observers at the front of the train when the lightning strikes, if you like.

#### PeroK

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You can repeat the thought experiment with both observers at the front of the train when the lightning strikes, if you like.
The weakness in this experiment is the reliance on events being equidistant in order to assess their simultaneity or otherwise.

Also, the emphasis on light signals can be misleading. Both in terms of lightning flashes - why lightning? And in terms of each observer receiving light signals from lightning strikes.

#### vanhees71

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"Light" is the most simple case here, because for all observers the speed of light is, irrespective of the movements of the light sources, the same. If you'd use sound waves, it's even more complicated. Here the Doppler effect (to which this finally reduces to) depends not only on the relative motion of observer and source, as is the case for light in vacuo, but it depends on the motion of the observer and the source of sound relative to the rest frame of the medium (e.g., air).

It's an interesting exercise to think through this carefully. It sheds a lot of light on the specialty of light (or a massless field to put it in modern lingo) and what relativity is all about, namely about being able to handle massless fields, and indeed the em. field is a massless field. That's why relativity has been discovered in connection with electromagnetism to begin with. Today we know, it's simply the incompatibility of the concept of a massless field with the Galilei-Newtonian space-time structure! That then explains, why Einstein's ingenious insight that the quibble about the non-Galilei-invariance of Maxwell's equations must not be solved by changing Maxwell's equations, which were well known to be empirically correct in 1905, but the very description of space and time itself, is an unavoidable consequence.

#### Ibix

The weakness in this experiment is the reliance on events being equidistant in order to assess their simultaneity or otherwise.
That's why I was suggesting this asymmetric version, but on reflection the maths is complicated. A better way might be the usual configuration, with a third flash happening in the middle of the train at the instant the two observers pass one another. You use this one in the simultaneous flash frame to illustrate the point that we don't necessarily regard things seen at different times as having occurred at different times, then look at the other frame to get relativity of simultaneity.
Also, the emphasis on light signals can be misleading. Both in terms of lightning flashes - why lightning? And in terms of each observer receiving light signals from lightning strikes.
My impression has always been that Einstein was attempting to avoid (irrelevant) questions about who set up the timing and how it was done by having an Act of God deliver two conveniently placed and timed flashes of light. Since they are basically random chance that we take advantage of (impossible to set up, but easy to analyse if it did happen to occur), there's no opening to propose that simultaneity is somehow naturally absolute but relative when people set it up.

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#### Grinkle

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it means that time isn't relative at all, it just keeps moving, but things are seen maybe after it happened because of the speed of light.
All observers measure the speed of light to be the same number hence they cannot measure the time between events to be the same number. I say that like it should be obvious, and after enough pondering it does become more and more intuitve, but for me at least it took a great deal of pondering.

What one means by time is imo also worth thinking on. Time has to be measured as some ratio of events, one to the other. We pick a set of events and we call that our clock, we pick another set of events that we want to express in terms of how separated in time they are and we take a ratio. For example, if I want to talk about how long I can hold my breath, I count how many times my watch second hand ticks between the beginning and ending of the process of me holding my breath. The answer is the ratio of ticks it took to fill that interval to the number of intervals I measured (in this case one interval, I only held my breath once). There is no way to ever talk about measuring time that does not involve comparing one set of events that is the clock to another set of events that is being measured. I guess this is why most discussions about time dilation start with the definition of the clock being used. To me, discussing clocks per se is distracting and makes one look for the "trick" - thinking that the discussion is all about picking a particular clock that makes it look as though time itself is, as you put it, relative. There is no trick, though - any clock one chooses to describe will behave the same tricky way.

If I understand your question, time is indeed relative in a very fundamental way - clocks running slowly is not just an optical illusion or a idiosyncrasy of book keeping between two frames that are in motion wrt each other. Observers in different reference frames will experience different amounts of time between events - there will be no way of looking at it (there is no "preferred frame") that removes this difference.

#### Grinkle

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One thing to add to an already wordy response, but to me it was long a point of personal confusion.

I might re-state your question as "is there such a thing in the universe as a second"? There is not. There are events in the universe, and one picks some event that is sufficiently brief and regular that some count of them makes a convenient "second". Someone else counting those same events occurring in their own frame will not see a 1:1 ratio between frames - they will see one second being different counts of that basic tick happening in their frame vs that basic tick happening in another frame if they use that other frames 'tick' to attempt to measure one second in their own frame. This is what I mean if I say that "time flows at different rates", which I try not say because its not a straightforward statement to define or discuss.

#### Pencilvester

I might re-state your question as "is there such a thing in the universe as a second"? There is not. There are events in the universe, and one picks some event that is sufficiently brief and regular that some count of them makes a convenient "second"
This is kind of like saying “there is no such thing as beaches—only tiny little rocks”. If we can all agree on the definition of something, it doesn’t really make sense to say that that thing doesn’t really exist.

#### Grinkle

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If we can all agree on the definition of something
Photons exist, electrons exist, etc. As far as I know, any sufficiently advanced alien species would precisely agree with us what a photon is.

No specific measure of time or quanta of time or particle of time exists outside the context of a human imposed convention to define it, and humans in different reference frames will only agree that each frame has its own "second" and that the two "seconds" have a ratio to each other that is different than unity when both are compared to a third event in either frame.

Certainly the concept of one second can be well enough defined that different humans will agree and be consistent with each other.

The reason I think this is important is because if one starts reasoning from the perspective that one second is a universally unchanging quanta, then one is already off on the wrong track and looking for the "trick" that makes my second seem longer or shorter than your second. Anyone's "second" is just some count of events that we decide / agree will constitute one second. Starting from there, and understanding that when looking at a different frame events in that frame take longer or shorter than identical events in my own frame I can easily see that seconds themselves are different between the frames.

That reasoning works well for me, at least - of course its hueristic and there are surely different lines of reasoning that will seem simpler and more intuitive to other people than starting with "there is no spoon (second)".

#### Pencilvester

Photons exist, electrons exist, etc. As far as I know, any sufficiently advanced alien species would precisely agree with us what a photon is...
I’m not saying a “second” exists in any material or universally inherent way—I’m saying it’s simply an agreed upon thing, therefore it doesn’t make sense to say it does or doesn’t exist. Maybe a better analogy: it’s like saying “matrix multiplication exists” (or “doesn’t exist”). It doesn’t really make sense. What we can say is that it’s useful or not useful.

#### pervect

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Grinkle: Do you think that the "ground-state hyperfine transition frequency of the caesium 133 atom " exists?

Any question about existence is philosophical, but I would say that it does.

The reason that this is relevant is that 9 192 631 770 of these transistions define the second, which is a unit of proper time.

I'm not sure where you're at on the whole proper time vs coordinate time issue - if you're aware of the difference, a bit more precision in your wording could be helpful, as you talk about "time", not distinguishing between proper time and coordinate time. If you're not aware of the difference, I'm not sure what more can be done, because I know I've seen long threads on it in the past in which you've been involved.

#### Grinkle

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a bit more precision in your wording could be helpful
I think I am aware of the difference, but I have not tested my understanding by using this vocabulary in my posts. Critique accepted - I will make the attempt. Now I am trying to help myself as opposed to the OP, I hope this post isn't a highjack.

Grinkle: Do you think that the "ground-state hyperfine transition frequency of the caesium 133 atom " exists?
Yes, I think the frequency exists. I accept the use of that frequency to define a second in my own reference frame (@Pencilvester this is a useful definition / concept of a second), and I think this second is what a caesium 133 atom based clock that is co-moving in my reference frame ticks at. As you noted in your post, this is a unit of proper time because it is defined in the context of a specific reference frame.

If I stop counting my own clock's CS atom transitions and I abstract myself to only counting my own clock's seconds, and then I observe some other frame's CS atom clock and I count the transitions on that clock, I will see that my clock's seconds are ticking off at a number that is not equal to

9 192 631 770
transitions of the CS atoms in the other reference frame. 1 second of proper time in my own frame is not the same as one second of proper time in the other reference frame.

For me personally, when asking if time is relative it is helpful to start by recognizing that physically what I am doing to decide what constitutes a second of proper time is to count CS atom transitions on a clock that is co-moving with me, and if I recognize that these transitions themselves look faster or slower in a different reference frame then it is immediately obvious that summation of them will take more or less of my own proper time seconds to accumulate vs some other frame's proper time seconds.

When I glibly and un-precisely say that a second does not exist, I say that because for me at least, if I think of a second as just a collection of

9 192 631 770
CS atom transitions it is much easier for me to comprehend that different observers experience different proper times at every level - there is no level at which it becomes illusory.

I won't defend that choice of words further ('a second does not exist'); I will agree its not the best way to say that proper times don't equal each other.

One can translate proper time (s) to co-ordinate time (s) by selecting a particular set of co-ordinates that one finds useful, and if two different observers agree on those co-ordinates, they will both agree on the co-ordinate time elapsed between events in their own frame (s), and this co-ordinate time can be measured in seconds and both observers will agree on the nature of that co-ordinate time second in terms of how many CS atom transitions it spans in either of their own frames.

I agree that proper time / co-ordinate time is better language to be using in this (and similar) threads than "there is no spoon" language. I do truly appreciate the nudge to clean up my phrasing - as you say, I have been exposed to enough of these discussions to be doing better by now.

#### Pencilvester

1 second of proper time in my own frame is not the same as one second of proper time in the other reference frame.
If both frames define one second the same way, then yes, they are the same. One second on your clock may not be the same as the elapsed coordinate time that you assign to the beginning and end of one second on the clock in the other frame.

#### A.T.

I will see that my clock's seconds are ticking off at a number that is not equal to [9 192 631 770 ] transitions of the CS atoms in the other reference frame. 1 second of proper time in my own frame is not the same as one second of proper time in the other reference frame.
What you observe is in your frame, not in the other frame.

#### pervect

Staff Emeritus
If I stop counting my own clock's CS atom transitions and I abstract myself to only counting my own clock's seconds, and then I observe some other frame's CS atom clock and I count the transitions on that clock, I will see that my clock's seconds are ticking off at a number that is not equal to
Generally, one needs a simultaneity convention (which is observer dependent) to measure the proper time of a remote clock. This is something that's easy to overlook, but because simultaneity is relative, it's important.

However, it is possible to define a mathematical formula that gives the proper time for a remote clock as a function of the coordinate times and positions.

The mathematical formula for computing proper time from coordinate time and coordinate position is:

$$d\tau^2 = dt^2 - \frac{1}{c} \left( dx^2 + dy^2 + dz^2 \right)$$

Here $\tau$ is the proper time, t is coordinate time, and x,y,z, are position coordinates.

The "usual" philosophy is that this proper time "exists" and is observer independent, thus it's the same for everyone.

There are perhaps other ways to demonstrate the remote observation of proper time without using this formula. Suppose you had a remote cesuim clock, and two flashes emitted from a flashtube. The cesium cycles from the remote clock are being transmitted as a signal, so that you can observe them. If you start counting the cesium clock cycles when you receive the first flash from the flashtube, and stop counting the cesium clock cycles when you receive the second flash, you will remotely count and observe the proper time interval between the flashes without using the above formula.

If the remote source is not conveniently emitting some standardized time signal like this, though, you'll need to use your own clocks and the formula to compute proper time from the observations. THe observations themsleves involve some computations - for instance, you might have a radar set, and a clock. The actual observations will be the radar signal emission time (as read by the local clock), and the radar signal reception time (as read by the local clock). From these radar observations, and the knowledge of the speed of light, you can compute the position coordinates of the remote object as a function of the time coordinate, which is a level of abstraction from what you actually measure. A further level of abstraction on top of this gives the proper time as a function of the time and position coordinates, which are also computed rather than directly observed.

However, you don't have to go through two levels of abstraction like this if you really don't want to. You do need to realize that the signals from the remote object are doppler shifted, and you need to know how much doppler shift a given amount of velocity generates. Then you can compute what signal the remote clock would have been sending if it were sending a signal from what your own clock reads. You can think of this as generating a "synthetic" remote signal from the reference clock you carry. Then you can use the mtehod describe of counting the number of cycles of this synthetic signal to get the proper time between the two flashes.

Exactly which stages of this process one regards as "real" are up to personal philospohy, but generally some framework is construrcted and regarded as "real" that is more complex than "radar signal sent @ time @ direction" and "radar signal received @ time @ direction".

#### Orodruin

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As you noted in your post, this is a unit of proper time because it is defined in the context of a specific reference frame.
Proper times have nothing to do with frames. Frames by definition deal with coordinate times.

You can, of course, set up a coordinate system where the coordinate time coincides with the proper time of some particular observer, but they are definitely not the same concept.

#### Grinkle

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Suppose you had a remote cesuim clock, and two flashes emitted from a flashtube.
Does the remote clock need to be co-moving with the flashtube in order for the proper time I see on the clock be the same an any other observer would see? If not, I am confused.

Edit: Does the remote clock need to be co-moving with the flashtube in order for the delta-proper-time I see elapsed on the clock between the flashes be the same delta-time any other observer would also see elapsed on the clock between the flashes?

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#### Grinkle

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Proper times have nothing to do with frames. Frames by definition deal with coordinate times.
This is a unit of proper time because it is the output of a clock (full stop?)?

I thought proper time is the time a clock records as it travels, and one can attach a reference frame to the clock and call the time the clock is recording the proper time for the reference frame that is co-moving with the clock.

#### Orodruin

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I thought proper time is the time a clock records as it travels, and one can attach a reference frame to the clock and call the time the clock is recording the proper time for the reference frame that is co-moving with the clock.
This is a definition of a particular coordinate time. It is just the assignment of an arbitrary number to events along a world line. It is far from sufficient to define even a local coordinate frame on its own. In order to do that you need some other (also arbitrary) way of assigning coordinate times to events that are not on the world line as well as three additional coordinates to all events. The procedure, however, remains arbitrary whereas proper time is not - it is a coordinate independent quantity.

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