An Anti-Verificationist Critique of Einstein’s Argument Against Absolute Simultaneity

I. Introduction

In his classic book Relativity: The Special and the General Theory, Albert Einstein gave a famous argument for the relativity of simultaneity, i.e., for the thesis that the simultaneity/non-simultaneity of two events in time at different locations in space is relative to the reference frame that the events are observed in and that not all reference frames will be in agreement with respect to which events are simultaneous/non-simultaneous. Further, Einstein argues that all reference frames are equally valid and that the notion of frame-transcendent simultaneity is meaningless. Einstein concludes from all of this that there is no relation of absolute simultaneity. In this post, I shall give a detailed summary and logical reconstruction of Einstein’s argumentation and then offer a critique of it. I will argue that Einstein’s conclusion that there is no relation of absolute simultaneity relies on the logical positivist principle of verification. Insofar as this principle is false (as is widely acknowledged), Einstein’s argument fails to show that there is no relation of absolute simultaneity and is thus unsound. As will be seen, this failure has some important upshots.

 

II. Summary and Reconstruction of Einstein’s Argument

Einstein’s argument initially proceeds from two key assumptions: (1) the principle of relativity (in the restricted sense) and (2) the constancy of the speed of light in a vacuum as a general law of nature.[1] Einstein defines (1) as follows:

Principle of Relativity (in the restricted sense): “If, relative to K, K’ is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect K’ according to exactly the same general laws as with respect to K.”[2]

Here, K and K’ are Galileian/inertial reference frames. A Galileian/inertial reference frame is a system of coordinates defined with reference to a fixed rigid body such that the state of motion of objects measured relative to it obeys the law of inertia according to which “[a] body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line.”[3] A simpler way to put the principle of relativity (in the restricted sense) is that general laws of nature are the same in all inertial reference frames.

From (1) and (2), it follows that (3) the speed of light in a vacuum is the same in all inertial reference frames. After getting to this stage, Einstein proceeds to consider the notion of simultaneity. He settles on the following operational definition of simultaneity of spatially separated events:

Simultaneity: E₁ and E₂ (located at distinct spatial positions A and B) are simultaneous ≡ An observer O appropriately situated at the midpoint M of the line segment AB perceives E₁ and E₂ occurring at the same time.[4]

The basic idea is that in order for O to perceive E₁ and E₂, light must travel from each of them to O. Since the speed of light is constant, the amount of time it takes light to travel from A to M is the same as the amount of time it takes for light to travel from B to M since the distance from A to M is the same as the distance from B to M. So, given (3), this definition seems quite reasonable. Moreover, and importantly for Einstein, such a definition allows for simultaneity to be empirically verifiable.

From here, Einstein constructs a famous thought experiment involving two different inertial reference frames: a train and an embankment. The thought experiment is as follows. Suppose that there is a train traveling across a railway embankment in a vacuum at a constant velocity v as represented in Figure 1 below.

Figure 1.[5]

Further suppose (as depicted in Figure 1) that there are two positions A and B marked on the railway and a midpoint M marked between them. Now, suppose that two flashes of lightning strike the train as it passes by at the positions A and B, respectively, and further suppose that an observer O is appropriately situated at M and perceives the two flashes at the same time. Then, by definition, the two lightning flashes are simultaneous. Thus, with respect to the reference frame of the embankment, the two lightning flashes are simultaneous.

But consider another observer O’ who is appropriately situated at position M’ on the train so that right as O perceives the lightning flashes occur at the same time at positions A and B, M’ coincides exactly with M so that M’ will be exactly midway between the positions A and B. The key question is whether O’ will perceive the two flashes at the same time from his reference frame. Einstein argues that he will not. For he is moving at a constant velocity v relative to the embankment so that he is speeding toward the beam of light coming from the lightning strike at B and speeding away from the beam of light coming from the lightning strike at A. Consequently, the beam of light coming from B will meet him before the beam of light coming from A does and so he will perceive the lighting strike at A before he perceives the lightning strike at B. But by (3), the speed of light is the same for the beam of light traveling from B to M’ as it is for the beam of light traveling from A to M’. Consequently, both beams of light must travel the same distance in the same amount of time. Since, then, the beam of light coming from B reaches M’ before the beam of light coming from A does, the lightning flash at A must have occurred earlier than the lighting flash at B. Thus, as Einstein says, “Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A.”[6]

The overall upshot of this is that simultaneity is relative to an inertial frame of reference. Two events that are simultaneous in one reference frame may not be simultaneous in another reference frame. Thus, the foregoing thought experiment establishes the following premise: (4) If the speed of light in a vacuum is the same in all inertial reference frames, then simultaneity (in Einstein’s sense) is relative to an inertial reference frame. One might think that it immediately follows from this that there is no relation of absolute simultaneity, but this is far too hasty. For Einstein’s definition of simultaneity is clearly a definition of frame-relative simultaneity. The observer is always making his observations/measurements relative to a particular reference frame.

The conclusion that follows validly from the argumentation so far is that such frame-relative simultaneity is not absolute in the sense that it is not the case that it either holds or does not hold between two spatially separated events in all reference frames. A proponent of absolute simultaneity, however, might hold that there is a frame-transcendent simultaneity relation that is absolute in the sense that it holds or does not hold between two spatially separated events objectively, universally, and frame-independently. What we need, then, is an argument for why such a frame-transcendent simultaneity relation does not exist. Einstein in fact supplies us with such an argument, though it is not entirely explicit. In his discussion leading up to his definition of simultaneity, Einstein makes the following statement:

We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, [an observer] can decide by experiment whether or not the lightning strokes occurred simultaneously. As long as this requirement is not satisfied, I allow myself to be deceived… when I imagine that I am able to attach a meaning to the statement of simultaneity.[7]

So, for Einstein, a statement of simultaneity is meaningless unless it is empirically verifiable. It is quite likely that Einstein is here presupposing the logical positivist principle of verification[8], which can be expressed as follows:

Principle of Verification: A statement S is meaningful if and only if it is either analytic or empirically verifiable.[9]

According to the prominent twentieth-century logical positivist philosopher A.J. Ayer, a statement is analytic if and only if it is a mere tautology, true by definition (e.g., “all bachelors are unmarried”). A statement is empirically verifiable if and only if it can be confirmed or disconfirmed by observation/experience.[10] It is clear that a statement of simultaneity is not analytic. Consequently, given the principle of verification, if such a statement is also not empirically verifiable, then it is meaningless. This is right in line with Einstein’s thinking.

Now, (plausibly) all empirical observations/experiences occur relative to a reference frame. If this is so, then a statement of simultaneity is empirically verifiable only if the simultaneity in question is frame-relative. It follows that frame-transcendent simultaneity is meaningless. As such, there is no relation of frame-transcendent simultaneity and, a fortiori, no relation of absolute frame-transcendent simultaneity. Since, then, there is no frame-relative absolute simultaneity either, it follows that there simply is no relation of absolute simultaneity. Given all of the foregoing, we can formulate Einstein’s complete argument against absolute simultaneity as follows:

1. General laws of nature are the same in all inertial reference frames.
2. It is a general law of nature that the speed of light in a vacuum is constant.
3. So, the speed of light in a vacuum is constant in all inertial reference frames (1, 2).
4. If the speed of light in a vacuum is constant in all inertial reference frames, then there is no frame-relative absolute simultaneity (Einstein’s thought experiment).
5. So, there is no frame-relative absolute simultaneity (3, 4).
6. Frame-transcendent simultaneity is neither analytic nor empirically verifiable.
7. Whatever is neither analytic nor empirically verifiable is meaningless (principle of verification).
8. So, frame-transcendent simultaneity is meaningless (6, 7).
9. If frame-transcendent simultaneity is meaningless, then there is no relation of frame-transcendent simultaneity.
10. If there is no relation of frame-transcendent simultaneity, then there is no relation of frame-transcendent absolute simultaneity.
11. If there is neither a relation of frame-relative absolute simultaneity nor a relation of frame-transcendent absolute simultaneity, then there is no relation of absolute simultaneity.
12. So, there is no relation of frame-transcendent simultaneity (8, 9).
13. So, there is no relation of frame-transcendent absolute simultaneity (10, 12).
14. Therefore, there is no relation of absolute simultaneity (5, 11, 13).

 

III. Critique of Einstein’s Argument and Some Resulting Upshots

It is clear from the foregoing that Einstein’s argument crucially depends on the principle of verification (premise 7). Thus, if the principle of verification is false, then Einstein’s argument fails. It is widely acknowledged today by philosophers of all stripes that the principle of verification is false. Perhaps the most fundamental argument against it is that it is self-defeating in that it entails its own meaninglessness. For the principle of verification is itself evidently neither analytic nor empirically verifiable. Thus, according to its own standard, the principle of verification is literally meaningless and is thus not true. (For additional discussion and critique of the principle of verification, see my previous post HERE). Consequently, (7) is false, and Einstein’s argument that there is no relation of absolute simultaneity fails. Although the argument is logically valid, it rests on a false premise and is thus unsound.

A significant upshot of this is that Einstein has not provided a successful argument against, for instance, the A-theory of time according to which there is an objective and absolute present, an objective and absolute now.[11] If the A-theory of time is true, then all present events are absolutely simultaneous. Consequently, if there is no relation of absolute simultaneity, then the A-theory is false. Since Einstein’s argument fails, the A-theory is not threatened by Einstein’s reasoning. An additional upshot is that the notion of absolute time, i.e., time that is independent of the state of motion of a body of reference, has not been refuted. Einstein draws as a corollary of his argument the falsity of the thesis of absolute time, referring to statements about the time of an event without regard for a body of reference as meaningless.[12] As this inference, too, clearly relies on the principle of verification, it is unsound. As such, Einstein’s argument does not conclusively settle much of anything about the fundamental nature of time. Happily, this means that metaphysicians may still find plenty of work in the philosophy of time (at least as far as Einstein’s argument is concerned).

 

Reference

Ayer, A. J. (1952). Language, Truth and Logic (2nd ed.). Dover Publications.

Einstein, A. (1992). Autobiographical Notes. A Centennial Edition (P. A. Schilpp, Ed.). Open Court.

Einstein, A. (2015). Relativity: The Special and the General Theory - 100th Anniversary Edition (H. Gutfreund & J. Renn, Eds.). Princeton University Press.

Emery, N., Markosian, N., & Sullivan, M. (2020, November 24). Time. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/time/

 

---

[1] Einstein’s arguments for the truth of (1) and (2) are beyond the scope of this post.

[2] Einstein (2015), pg. 24.

[3] Ibid., pg. 18.

[4] Cf. ibid., pg. 33. ‘Appropriately situated’ should be understood to mean that the observer is equipped with the ability to perceive at the same time both spatial positions at which the events in question will occur. Einstein suggests a setup involving two mirrors inclined at 90^o.

[5] Taken from Einstein (2015), pg. 36.

[6] Ibid., pg. 37.

[7] Ibid., pg. 33.

[8] It is noteworthy in this regard that later in his life, Einstein reflected on the philosophical influences on his thinking about the relativity of simultaneity as follows: “The type of critical reasoning required for the discovery of this central point [viz., the relativity of simultaneity] was decisively furthered, in my case especially, by the reading of David Hume’s and Ernst Mach’s philosophical writings” (Einstein (1992), pg. 51). The thought of Hume and Mach was greatly influential with respect to the project of logical positivism and its principle of verification (cf. Ayer (1952), pg. 31, 136-137).

[9] Cf. Ayer (1952), pg. 9.

[10] Ibid.

[11] For an overview of the A-theory of time, see, e.g., Emery, Markosian, & Sullivan (2020).

[12] Einstein (2015), pg. 38: “[U]nless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.”