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Also, what does the statement "The combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light" mean?

Can someone care to explain these questions? Thanks.

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- Thread starter goodabouthood
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- #1

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Also, what does the statement "The combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light" mean?

Can someone care to explain these questions? Thanks.

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Just thinking this through in my head....I guess time can only be thought of in terms of intervals. So for someone at rest experiencing an interval of time delta t, we say their clock 'runs faster' because in someone moving fast's reference frame the interval of time is less than delta t.

In other words, time at any one point can't (to my mind) be defined - only movement through it can be. Someone moving fast moves through time slower than someone moving slowly and this is how we can compare various passages through time.

In terms of understanding why velocity through spacetime is equal to c, the easiest explanation is simply by looking at the velocity four vector. The magnitude of this vector is c. E.g. in a stationary frame we have (c,0,0,0).

If you don't know what a four vector is I'll leave the unenviable task of explaining why this is true to someone else!

In other words, time at any one point can't (to my mind) be defined - only movement through it can be. Someone moving fast moves through time slower than someone moving slowly and this is how we can compare various passages through time.

In terms of understanding why velocity through spacetime is equal to c, the easiest explanation is simply by looking at the velocity four vector. The magnitude of this vector is c. E.g. in a stationary frame we have (c,0,0,0).

If you don't know what a four vector is I'll leave the unenviable task of explaining why this is true to someone else!

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The words "move through time" really don't mean anything, alas. One attempt at interpreting them is the metaphorical sense where "time is a river", but the exact physical meaning of said metaphor isn't clear.

The words are sometimes used as an attempt to popularize relativity originated by Brian Greene, in which chase the "velocity through time" is actually a component of the four-velocity.

It turns out that the four-velocity of any object (which can be expressed in coordinate terms as dt/dtau, dx/dtau, dy/dtau, dz/dtau, where t,x,y, and z are the coordinates and tau is proper time) is a four vector and has a norm of 1 - which is a norm of 'c' if you use standard units.

It's clear that dt/dtau, the relevant component of the four velocity, is related to a velocity, but it's not any normal sort of velocity. In particular, proper time tau is not used to measure velocity, though it's used to measure concepts that are very closely related to velocity, such as "celerity" which is also known sometimes called "proper velocity", but only for the spatial coordinates.

The words are sometimes used as an attempt to popularize relativity originated by Brian Greene, in which chase the "velocity through time" is actually a component of the four-velocity.

It turns out that the four-velocity of any object (which can be expressed in coordinate terms as dt/dtau, dx/dtau, dy/dtau, dz/dtau, where t,x,y, and z are the coordinates and tau is proper time) is a four vector and has a norm of 1 - which is a norm of 'c' if you use standard units.

It's clear that dt/dtau, the relevant component of the four velocity, is related to a velocity, but it's not any normal sort of velocity. In particular, proper time tau is not used to measure velocity, though it's used to measure concepts that are very closely related to velocity, such as "celerity" which is also known sometimes called "proper velocity", but only for the spatial coordinates.

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Also, what does the statement "The combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light" mean?

Can someone care to explain these questions? Thanks.

Move through time? In my opinion it is an English idiom with no literal meaning. One can look at a clock and see the time change, that is all.

"The combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light" This is a very confusing statement that seems to me impossible to ever unravel and can lead only to befuddlement.

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ghwellsjr

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I am looking at this right now and there is an equation c = velocity of space + velocity of time

Can someone give me an example of this with actual numbers?

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It is quite common in discussions and writings on special relativity to see the concept of observers moving along their world lines (their own rest system time axis) at the speed of light. Here is a space-time diagram showing a black rest system with a blue inertial frame in motion with respect to the black coordinates.

In this sketch we use proper time to show the points corresponding to arrival of black and blue guys after 30 years of travel at the speed of light (events A and B). Event C is the point of arrival for the black guy after about 26 years of travel.

If the black guy is at event A after 30 years along with the blue guy, how is it that the blue guy can "see" him back at the black 26 year event C? I know you will say it's just time dilation, but physically how does it happen?

In this sketch we use proper time to show the points corresponding to arrival of black and blue guys after 30 years of travel at the speed of light (events A and B). Event C is the point of arrival for the black guy after about 26 years of travel.

If the black guy is at event A after 30 years along with the blue guy, how is it that the blue guy can "see" him back at the black 26 year event C? I know you will say it's just time dilation, but physically how does it happen?

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I also would say something about the light traveling from C to B taking time but I don't think that is right either.

So how does it go?

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For instance I say light travels at 186,000 miles per second but what do I even mean by saying one second?

I'm confused more now.

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For instance I say light travels at 186,000 miles per second but what do I even mean by saying one second?

I'm confused more now.

goodabouthood, I really hesitate to jump in here, because you have hit on a controversal subject in special relativity. The forum tries to stay clear of speculative hypotheses for which there is not widely held respect as a serious candidate for physical theory. I'll try to be reasonable here.

First of all, the sketches in my posts above are not out of the mainstream at all. However, the implications of my questioning hint of the controversial aspect of special relativity. In any case, here are at least two concepts that go to an attempt to bring some kind of physical understanding to the question I posed--and shed light on your questions about time.

1) The space-time diagrams along with the mathematical equations (Lorentz transformations) are to be taken only as symbolic mathematical representations of the relationships among observers in a mathematical 4-dimensional space-time. In other words, the 4-dimensional space is not to be taken as a real external objective world "out there." The 3-D world is real and "out there", but the special relativistic effects can only be explained mathematically and taken as "that's just how nature works." (Many philosophers will not accept that there is really an external objective 3-D world "out there.").

The effects predicted by special relativity are correct. That is, for example, time dilation really happens, length contraction is a real observable effect, and the twin paradox result would really occur as predicted by special relativity. It's just that there is no underlying physical explanation--there's just the mathematics that predicts results, and there is the actual observation of the predicted phenomena.

Special relativity is a proven theory (so far as can be validated after over one hundred years of experimentation).

2) A quite natural underlying physical explanation for the question I posed with the above space-time diagram (how can the black guy be in two places at once?) is the following: The black guy can be in two places at once (and many more) because he physically IS in two different places in 4-dimensional space at once.

It works quite easily if you regard the universe as having four spatial dimensions and is populated by 4-dimensional objects (including the bodies of the black and blue observers in the diagrams). But if the objects populating the 4-D universe are themselves 4-dimensional, that means they are frozen in 4-D space and do not move at all. Thus, in the space-time diagram, one 3-D section of the 4-D black guy is at event "A" while another 3-D section of the 4-D black guy is at event "C".

Then, you say, "Wait a minute, I thought all observers move along their 4th dimension at the speed of light?" The answer to that is that the bodies do not move at all--just some aspect of consciousness is doing the moving. It's a little like watching a movie. The movie film is a physical structure--a sequence of frames which give the psychological impression of time flowing with the action viewed by the observer.

A clock is not intrinsically connected to time; it is after all just a 4-dimensional object with periodic markers along the spatial 4th dimension, indicating elapsed time via psychological effects (since the consciousness is moving along watching the clock frames fly by at the speed of light).

We could put one minute time markers along an interstate and require all drivers to drive 60 mph, then, going from point A to point B along the highway we could keep track of our progress by reading how many minutes have elapsed since leaving point A. The time markers on the highway become a clock. That doesn't make the path along the highway "time." The 4th dimension is just another spatial dimension with the special aspect that it is the direction our conscousness moves at light speed. Presumeably, it has something to do with the fact the objects are typically thousands of billions of miles long along the 4th dimension (X4) and only a few feet in the other dimensions (X1, X2, X3).

Many other questions flow from this, but then we get dangerously close to violating the ground rules of the physics forum. We begin to stray far away from established physics principles and end up discussing philosophy.

There is more we could say and more space-time sketches that could be presented to clarify these ideas, but we have covered this topic in other threads and many here are pretty weary of the subject. I just thought it not fair to you to cut it too short, since it's not your fault that contentious discussions have already taken place.

You should check out the other posts linked to with ghwellsjr's post above. And yoron's post gives you a pretty good link, although it seems you would like a little clarification on some of what you've read there.

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I don't want this thread to turn into philosophy.

I still have a hard time understanding this 4-D universe. Can you give me some math examples with numbers?

If clocks aren't intrinsically connected to time do they really physically slow down in special relativity?

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Hi, clocks are instruments that are meant to measure "time". One even defines "time" with reference clocks. And as described in the first time dilation example, a clock that is moved away and then brought back will really lag behind the clock that was not moved (see section 4 of http://www.fourmilab.ch/etexts/einstein/specrel/www/ ).[..]

If clocks aren't intrinsically connected to time do they really physically slow down in special relativity?

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Assuming that the best clock must be radiation, 'c'. That as it is a 'constant' in the theory of relativity. Using it as the 'clock of choice' you will find, although never varying for you measuring it inside your 'frame of reference' (aka 'locally') against a known 'periodicity' like your heartbeats. :) It still will relative all other 'frames of reference', present them as having different 'time rates', relative your own 'local invariant clock'.

But moving there you will find them to be exactly the same as your local definition of time. You can see this as your 'clock' adapting to the 'relative motion/acceleration/mass' of that other system, but as I defined the 'clock' as radiation, and as radiation is a 'constant' that becomes very difficult to propose. Or you can see it as a consequence of the properties of radiation (coupled relative 'relative motion'/acceleration/'gravity'/mass).

If we assume that there is a 'beat' to processes/interactions/transformations, then radiation should be it. And 'c' never varies, no matter how fast you, or what you measure it against, are 'moving'. Neither do it vary depending on where you are (mass locally). The only way to define it otherwise is to use a 'conceptual frame', in where you compare the propagation A-B to B-A in a accelerated frame, as I know. And then you must ignore gravity to make it into a 'variable', according to Einstein's definitions of GR.

But if you think of SpaceTime as being of a consistent 'size' you could argue that they have different 'distances' to cover as measured by your clock, and that this should mean that 'c' can 'vary'. But to do that you also must ignore the Lorentz contraction/time dilation, relative the path measured.

Well, as I see it.

=

For this purpose you better view a mass (planet) as per the equivalence principle in GR. Meaning that Earth is constantly uniformly 'accelerating' at one gravity. And that the difference we measure in 'clock rates' then becomes a question on where that 'clock' is placed relative the gravity defined at that point, as observed by you. It's not that hard to imagine, as gravity must change with distance (position in a four dimensional SpaceTime).

But moving there you will find them to be exactly the same as your local definition of time. You can see this as your 'clock' adapting to the 'relative motion/acceleration/mass' of that other system, but as I defined the 'clock' as radiation, and as radiation is a 'constant' that becomes very difficult to propose. Or you can see it as a consequence of the properties of radiation (coupled relative 'relative motion'/acceleration/'gravity'/mass).

If we assume that there is a 'beat' to processes/interactions/transformations, then radiation should be it. And 'c' never varies, no matter how fast you, or what you measure it against, are 'moving'. Neither do it vary depending on where you are (mass locally). The only way to define it otherwise is to use a 'conceptual frame', in where you compare the propagation A-B to B-A in a accelerated frame, as I know. And then you must ignore gravity to make it into a 'variable', according to Einstein's definitions of GR.

But if you think of SpaceTime as being of a consistent 'size' you could argue that they have different 'distances' to cover as measured by your clock, and that this should mean that 'c' can 'vary'. But to do that you also must ignore the Lorentz contraction/time dilation, relative the path measured.

Well, as I see it.

=

For this purpose you better view a mass (planet) as per the equivalence principle in GR. Meaning that Earth is constantly uniformly 'accelerating' at one gravity. And that the difference we measure in 'clock rates' then becomes a question on where that 'clock' is placed relative the gravity defined at that point, as observed by you. It's not that hard to imagine, as gravity must change with distance (position in a four dimensional SpaceTime).

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Now he will see the light have to travel a longer distance on the spaceship therefore in his view he sees time slowing down for the spaceship.

Does the guy on the spaceship also see this in the light clock for the guy on the ground?

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ghwellsjr

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Yes.

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Now another question here. A lot of people say the velocity of time + velocity of space = speed of light. So let's say you were traveling at .6c, what makes up the remainder to give you the total speed of light?

Also, is there no such thing as a true stationary object in our Universe? For example everything seems to be moving around something else. Now if all the motions of the Universe were frozen, would time be frozen?

What I am seeing for time in my mind is movement. I still am confused.

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atyy

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[..] Also, is there no such thing as a true stationary object in our Universe? For example everything seems to be moving around something else. Now if all the motions of the Universe were frozen, would time be frozen?

What I am seeing for time in my mind is movement. I still am confused.

Yes, "time" depends on movements: from the start, the concept of time has been based on natural clocks such as the solar day. If everything is frozen then all clocks are frozen as well.

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It is quite common in discussions and writings on special relativity to see the concept of observers moving along their world lines (their own rest system time axis) at the speed of light. Here is a space-time diagram showing a black rest system with a blue inertial frame in motion with respect to the black coordinates.

In this sketch we use proper time to show the points corresponding to arrival of black and blue guys after 30 years of travel at the speed of light (events A and B). Event C is the point of arrival for the black guy after about 26 years of travel.

If the black guy is at event A after 30 years along with the blue guy, how is it that the blue guy can "see" him back at the black 26 year event C? I know you will say it's just time dilation, but physically how does it happen?

It's a very nice question Bob, and one that have me question both 'distances', as well as 'time'. Defined from my view, which then will be a idea of 'locality' the local 'time/clock' always will be an invariant, a 'constant' coupled to 'c'. But if I then look at some other frame of reference like something moving relative me they will seem out of 'sync' with my definition of my clocks durations. And as the Lorenz contraction must be a 'symmetry' in my book, to make sense of what 'A' sees, relative what I see, then the question to me becomes one of what a 'distance' really is, as well as that time dilation.

If I define it from locality then what you see will be your reality, as what I see will be mine. The reason we find them different is conceptual, meaning that to do this we have to compare our frames of reference relative each other. What that states to me is that you at no 'time' or 'place' ever will find a contradiction, other than conceptually, when comparing.

But it doesn't answer the question of why it can happen, it just give me a reason, which then, to me, must be 'c'.

If distances and time is 'plastic' relative motion, mass (& energy, whatever that is), then SpaceTime is plastic. And the 'plasticity' is defined locally. But we also have this 'radiation propagating' (and gravity). Radiation is what you observe, all measurements are done through, and in, it. Radiation is the constant 'c' joining my definition of a 'distance' and a 'time' to yours through Lorentz transformations.

Gravity is something else, it's coupled to mass and to me representing a 'constant inertia' relative accelerated (uniform, but to me as I define it as inertia, all) motion. We define it in 'displacements' relative some positional 'point' (inside times arrow 'locally' defined). To see what I'm aiming on here we need to consider the equivalence principle, making all 'mass' constantly uniformly accelerating..

In fact, looking at this way there is no motion without a 'inertia' involved, at some stage, even though 'uniformly moving' at some later stage. That we can't define where that uniform motion came from doesn't state that there wasn't a 'inertia/acceleration/gravity' involved at a initial SpaceTime point. Although the idea of a 'inflation' makes it somewhat tricky.

And then we have mass.

And 'energy' as some weird idea of a 'ground state', as I see it.

But compare that to indeterminacy.

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