# Philosophic comments on time in Relativity.

Hello all.

I was bored and so did a little browsing on the subject of time in relativity and came across this article entitled “The Problem of Time in Science and Philosophy” by Oliver L. Reiser. Which appeared in The Philosophical Review. Vol 35 issue 3 (May 1926) It comes from the JSTOR archive. The following is an extract from the article. I believe the author has written many “well received” philosophical books.

My question is whether this is an example of a philosopher knowing little physics and mathematics or are there subtleties which I am failing to appreciate.

----In the theory of relativity the ideal simplification of nature is carried to its highest state of perfection. In this physical doctrine space coordinates are tied up with time in one equation. Here any one coordinate could be said to depend on the other three. Analytically, such equations are dealt with in the same way as those of three dimensions. Under such conditions it is hard to state which is the independent variable and which the dependent. Time seems to be turned into space merely by giving it a minus sign. This clearly shows that it is not easy to state just what time really does mean in physics, and hence to say that it must necessarily function as an independent variable is inaccurate. Whether, in the last analysis, the Newtonian concept of an absolute and evenly flowing time must be reintroduced into relativity theory, in the form perhaps of the velocity of light, and whether “simultaneity” can be given an absolute meaning, are matters which the physicists have been unable to decide.-----

Matheinste.

Dale
Mentor
2020 Award
Under such conditions it is hard to state which is the independent variable and which the dependent.
I think that is consistent with the geometric interpretation. You can parameterize a 1D curve, such as the worldline of a point particle, with one parameter and that parameter need not be "time". All 4 components of the four-vector position of such a particle can then be considered dependent variables and the parameter can be considered the independent variable. You can also consider the worldline to be a simple geometric object where the ideas of dependent and independent variables don't even really apply.

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Hello Dalespam.

I appreciate your point. I was more concerned about the staement "Time seems to be turned into space merely by giving it a minus sign.". I know that the minus sign in the signature gives the four dimensional structure its essential characteristics, but chageing time into space?

Matheinste

Hello Dalespam.

I appreciate your point. I was more concerned about the staement "Time seems to be turned into space merely by giving it a minus sign.". I know that the minus sign in the signature gives the four dimensional structure its essential characteristics, but chageing time into space?

Matheinste
evening M;

The expression starts as an equality, x^2 + y^2 + z^2 - (ct)^2 = 0. The time element is transformed to a complex quantity via i^2, resulting in all positive components of a 4D vector. It facilitates mathematical manipulation, but does not change the character of the variables, i.e. time is not a dimension. I'll find some quotes later.

evening M;

The expression starts as an equality, x^2 + y^2 + z^2 - (ct)^2 = 0. The time element is transformed to a complex quantity via i^2, resulting in all positive components of a 4D vector. It facilitates mathematical manipulation, but does not change the character of the variables, i.e. time is not a dimension. I'll find some quotes later.

Hello phyti

Thanks for your reply. I understand the interval and its derivation and its invariance but I am not altogether happy with your explanation of how the time coordinate transforms.

Time here is modelled as a dimension mathematically but as for time being a "real" or "physical" dimension, that's an argument I don't want to get into.

Matheinste

Dale
Mentor
2020 Award
I was more concerned about the staement "Time seems to be turned into space merely by giving it a minus sign."
Although that statement is essentially correct, I don't believe that it is particularly important. An equivalent geometric statement would be "a hyperboloid seems to be turned into an ellipsoid merely by giving it a minus sign". Despite that fact, a hyperboloid is not an ellipsoid. The presence of the minus sign is not an optional whim but an essential reflection of the geometry.

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Although the statement is essentially correct, I don't believe that it is particularly important. An equivalent geometric statement would be "a hyperboloid seems to be turned into an ellipsoid merely by giving it a minus sign". Despite that fact, a hyperboloid is not an ellipsoid. The presence of the minus sign is not an optional whim but an essential reflection of the geometry.
I see the geometry of the situation. It is the physical reference that I do not see. I.e turning space into time. I have no problem with spactime viewed as a whole but not with time and space viewed seperately and one being turned into the other. The following is a quote from Tolman, Relativity,Thermodynamics and Cosmology which, I think, puts forward a similar objection

---That there must be a difference between the spatial and temporal axes in our hyper-space is made evident, by contrasting the physical possibility of rotating a meter stick from a direction in which it measures distances in the x direction to one where it measures distances in the y direction, with the impossibility of rotating it into a direction where it would measure time intervals. In other words the impossibility of rotating a meter stick into a clock.-----

Matheinste

Dale
Mentor
2020 Award
Sorry about accidentally editing my above after you had replied. I hope I restored it. Anyway, I think this is still relevant, but I will read and reply in depth tomorrow:

The really important feature of the spacetime interval is not meremy that time has a minus sign, but that it is there at all. In other words, that space and time are part of a unified spacetime on which a single combined measure of "distance" can be used to describe both physical clocks and rods.

Sorry about accidentally editing my above after you had replied. I hope I restored it. Anyway, I think this is still relevant, but I will read and reply in depth tomorrow:

The really important feature of the spacetime interval is not meremy that time has a minus sign, but that it is there at all. In other words, that space and time are part of a unified spacetime on which a single combined measure of "distance" can be used to describe both physical clocks and rods.
Thanks Dalespam.

I am completely at home with the interval and the idea of treating spacetime as a four dimensional manifold. As you say the minus sign in the metric gives it its, at first encounter, surprising properties. (I know some authors use +--- instead of -+++) However I am always aware that my belief that I know something is not always reflected in fact and so I am always interested in any comments or assistance that you, and others may offer.

Matheinste.

Dale
Mentor
2020 Award
I see the geometry of the situation. It is the physical reference that I do not see. I.e turning space into time. ...

---That there must be a difference between the spatial and temporal axes in our hyper-space is made evident, by contrasting the physical possibility of rotating a meter stick from a direction in which it measures distances in the x direction to one where it measures distances in the y direction, with the impossibility of rotating it into a direction where it would measure time intervals. In other words the impossibility of rotating a meter stick into a clock.-----
I agree. You cannot turn time into space any more than you can turn a hyperboloid into a sphere. You cannot rotate a rod into a clock any more than you can rotate a hyperboloid of one sheet into a hyperboloid of two sheets, even permitting hyperbolic angles and hyperbolic rotations.

There is a difference between time and space, and it is described by that minus sign.

Hello all.

I was bored and so did a little browsing on the subject of time in relativity and came across this article entitled “The Problem of Time in Science and Philosophy” by Oliver L. Reiser. Which appeared in The Philosophical Review. Vol 35 issue 3 (May 1926) It comes from the JSTOR archive. The following is an extract from the article. I believe the author has written many “well received” philosophical books.

My question is whether this is an example of a philosopher knowing little physics and mathematics or are there subtleties which I am failing to appreciate.

----In the theory of relativity the ideal simplification of nature is carried to its highest state of perfection. In this physical doctrine space coordinates are tied up with time in one equation. Here any one coordinate could be said to depend on the other three. Analytically, such equations are dealt with in the same way as those of three dimensions. Under such conditions it is hard to state which is the independent variable and which the dependent. Time seems to be turned into space merely by giving it a minus sign. This clearly shows that it is not easy to state just what time really does mean in physics, and hence to say that it must necessarily function as an independent variable is inaccurate. Whether, in the last analysis, the Newtonian concept of an absolute and evenly flowing time must be reintroduced into relativity theory, in the form perhaps of the velocity of light, and whether “simultaneity” can be given an absolute meaning, are matters which the physicists have been unable to decide.-----

Matheinste.
So in answer to my original question, in the extract above, the author is OK with his mathematics and physics.

Thanks.

Matheinste

DrGreg
Gold Member
I was bored and so did a little browsing on the subject of time in relativity and came across this article entitled “The Problem of Time in Science and Philosophy” by Oliver L. Reiser. Which appeared in The Philosophical Review. Vol 35 issue 3 (May 1926) It comes from the JSTOR archive.

...Whether, in the last analysis, the Newtonian concept of an absolute and evenly flowing time must be reintroduced into relativity theory, in the form perhaps of the velocity of light, and whether “simultaneity” can be given an absolute meaning, are matters which the physicists have been unable to decide.​
I wouldn't agree with that. Physicists have been able to decide, and the answer is "no". Mind you, he was writing in 1926, so maybe things weren't so clear back then.

Dale
Mentor
2020 Award
So in answer to my original question, in the extract above, the author is OK with his mathematics and physics.
No, as I mentioned above I do not think that it is physically correct to talk about turning time into space by "giving it a minus sign" any more than it is mathematically correct to talk about turning an ellipsoid into a hyperbolid by "giving it a minus sign". If you did that it wouldn't be a hyperboloid any more.

It is correct that time and space are part of the same spacetime interval formula. It is correct that time is distinguished from space by the minus sign in the formula. It is incorrect that it is particularly physically or mathematically meaningful to talk about changing the minus sign and thereby changing time into space.

No, as I mentioned above I do not think that it is physically correct to talk about turning time into space by "giving it a minus sign" any more than it is mathematically correct to talk about turning an ellipsoid into a hyperbolid by "giving it a minus sign". If you did that it wouldn't be a hyperboloid any more.

It is correct that time and space are part of the same spacetime interval formula. It is correct that time is distinguished from space by the minus sign in the formula. It is incorrect that it is particularly physically or mathematically meaningful to talk about changing the minus sign and thereby changing time into space.

Thanks Dalespam.

Matheinste.

So in answer to my original question, in the extract above, the author is OK with his mathematics and physics.

Thanks.

Matheinste
Because time is treated as a dimension in the mathematical model, does not imply a literal
interpretation.
If you checked your Funk & Wagnalls, dimension can also mean attribute or feature.
Here is one opinion that has more credibility than mine.

Einstein's Theory of Relativity, Max Born, pg 307
"Thus Minkowski's transformation u=ict is to be valued only as a mathematical artifice which illuminates certain formal analogies between space coordinates and time
coordinates without however, allowing them to be interchanged."

Because time is treated as a dimension in the mathematical model, does not imply a literal
interpretation.
If you checked your Funk & Wagnalls, dimension can also mean attribute or feature.
Here is one opinion that has more credibility than mine.

Einstein's Theory of Relativity, Max Born, pg 307
"Thus Minkowski's transformation u=ict is to be valued only as a mathematical artifice which illuminates certain formal analogies between space coordinates and time
coordinates without however, allowing them to be interchanged."
You quote an opinion with "more credibility" than yours. What is your "less credible" opinion?

Matheinste.

You quote an opinion with "more credibility" than yours. What is your "less credible" opinion?

Matheinste.
It's the same, but he wrote a book and I didn't.

Lets say I have lump of lead that has a mass (m) of 1000 gms and a lump of steel that has a volume (v) of 400 cm3 and a density(p) of 8 gms/cm3. How much more does the lead weigh than the steel? The answer is:

diff = m - v*p = 1000 - (100*8) = 200gms

Have I turned volume into mass by using a minus sign? No I have not. I have used a density (p) figure to mathematically convert the volume to mass but that in no way implies that volume and mass are the same thing.

Lets also say 1 took a journey of distance (d) = 300 miles and another journey that took time (t) of 3 hrs at a speed (v) of 60 mph. How much longer was the first journey than the second? Again the answer is:

diff = d - t*v = 300 - (3*60) = 120 miles.

Again, I have not turned time into distance by using a minus sign. I have done it by using velocity to mathematically convert time units into distance units.

The same is true for the invariant interval in relativity:

S^2 = x^2 - (c*t)^2

(I have used the 2D version for simplicity here.)

The time has not been converted into distance by the minus sign. The time has simply been converted into units of distance by multiply by a velocity (c) and there is no physical implication of time turning into distance, anymore than there is any physical implication of volume turning into mass in my first example.

Sorry to labour the point, but some people really believe that time turns into distance and vice versa in the context of below the event horizon of a black hole and it the source of much confusion.

Basically the invariant interval finds the difference between how far a particle travels, compared to how far a photon would travel at the speed of light (c) in the same time. If the difference by subtraction is zero, then the particle is a photon. If the particle travels less distance then it must be a particle with mass travelling at less than the speed of light. If the particle travels further then it must be a purely hypothetical particle that is travelling at greater than the speed of light. Nothing mystical at all.

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JesseM
Because time is treated as a dimension in the mathematical model, does not imply a literal
interpretation.
What is a "literal interpretation"? What would be the difference between being "treated as a dimension" and being "literally" a dimension? The definition of a "dimension" is itself purely mathematical.

JesseM
Sorry to labour the point, but some people really believe that time turns into distance and vice versa in the context of below the event horizon of a black hole and it the source of much confusion.
Coordinate time in Schwarzschild coordinates does turn into a spacelike dimension and the radial coordinate turns into a timelike dimension below the event horizon. Of course this is just a quirk of Schwarzschild coordinates rather than something of physical significance.

DrGreg
Gold Member
Coordinate time in Schwarzschild coordinates does turn into a spacelike dimension and the radial coordinate turns into a timelike dimension below the event horizon.
I think it's potentially confusing to talk about "coordinate time in Schwarzschild coordinates" when it would be better to refer to it as "the Schwarzschild t coordinate". In fact the confusion is really that there isn't a single Schwarzschild frame, there are two of them, one outside the event horizon and another inside, with no connection between them apart from the "coincidence" that they share the same metric equation. So even to say "the Schwarzschild t coordinate does turn into a spacelike dimension below the event horizon" is a bit misleading because it suggests some continuous deformation from time to space.

It would be better really to talk of two different Schwarzschild charts.

The "outside" chart satisfying

$$ds^2 = \left(1 - \frac{2M}{r} \right) dt^2 - \frac{dr^2}{1-2M/r} - r^2 \left(d\theta^2 + \sin^2\theta \, d\phi^2\right)$$​

for $r > 2M$, and the "inside" chart satisfying

$$ds^2 = \frac{dT^2}{2M/T-1} -\left(\frac{2M}{T} - 1\right) dR^2 - T^2 \left(d\Theta^2 + \sin^2\Theta \, d\Phi^2\right)$$​

for $T < 2M$.

Einstein's Theory of Relativity, Max Born, pg 307
"Thus Minkowski's transformation u=ict is to be valued only as a mathematical artifice which illuminates certain formal analogies between space coordinates and time
coordinates without however, allowing them to be interchanged."
Minkowski introduced the convention of using

$$x_1 = x, x_2 = y, x_3 =z, x_4 = ict$$

so that the interval

$$\sqrt{ x^2+y^2+z^2 - (ct)^2}$$

could be replaced with

$$\sqrt{ x_1^2 + x_2^2 +x_3^2 +x_4^2 }$$

This is just a mathematical convenience so that the 4 dimensions could be easily summed, but unfortunately the dimensions expressed this way makes time look like just another dimension.

We should not get too excited about the imaginary number (i) associated with time dimension. It is just there so that when squared the time element has a minus sign. To see an example of someone getting over-excited by the ict expression, see the essay "Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics" by Elliot McGucken near the bottom of http://fqxi.org/community/forum/category/10". (There are many interesting essays (and opinions) in that essay contest and some are by well known authors such as Carlo Rovelli and Sean Carroll).

It might be worth mentioning that we can remove any spatial dimension from the invariant interval and still have a dynamic description of spacetime, but if the time dimension is removed the whole thing becomes useless.

It might also be worth mentioning that time is unique in that the spatial elements can be positive or negative (+/-dx), but the time element (dt) is always positive and advancing according to thermodynamics. No experimental evidence has been shown of an observer or particle going backwards in time that can not be interpreted as going forwards in time from another perspective. Time travel to the past remains as elusive as ever outside of scifi movies.

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Hey Matheinste;

We should not get too excited about the imaginary number (i) associated with time dimension.
I didn't get excited, how about you?

Hey Matheinste;
I didn't get excited, how about you?
I never said anyone here got excited, but I did show an example of someone that thought it had physical significance. ;)

Hey Matheinste;

I didn't get excited, how about you?
No. I had already been warned by Eddington who says in his Mathematical Theory of Relativity that:-

----When we encounter (i) in our investigations, we must remember that it has been introduced by our choice of measure code and must not think of it as occurring with some mystical significance in the external world.

Matheinste.